TSTP Solution File: SWW227+1 by Leo-III---1.7.7

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWW227+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n005.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 : Fri May 19 12:22:12 EDT 2023

% Result   : Theorem 30.18s 7.84s
% Output   : Refutation 31.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      : 1268
% Syntax   : Number of formulae    : 2441 ( 762 unt;  97 typ;   0 def)
%            Number of atoms       : 6351 (1704 equ;   0 cnn)
%            Maximal formula atoms :   18 (   2 avg)
%            Number of connectives : 33335 ( 399   ~; 123   |; 672   &;28929   @)
%                                         ( 283 <=>;2929  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  104 ( 104   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   99 (  97 usr;  15 con; 0-3 aty)
%            Number of variables   : 4967 (   0   ^;4902   !;  65   ?;4967   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_Orderings_Oord__class_Oless_type,type,
    c_Orderings_Oord__class_Oless: $i > $i > $i > $o ).

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

thf(c_Rings_Oinverse__class_Odivide_type,type,
    c_Rings_Oinverse__class_Odivide: $i > $i > $i > $i ).

thf(c_Groups_Oone__class_Oone_type,type,
    c_Groups_Oone__class_Oone: $i > $i ).

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

thf(tc_Nat_Onat_type,type,
    tc_Nat_Onat: $i ).

thf(c_Nat_OSuc_type,type,
    c_Nat_OSuc: $i > $i ).

thf(c_Groups_Oplus__class_Oplus_type,type,
    c_Groups_Oplus__class_Oplus: $i > $i > $i > $i ).

thf(v_N1_____type,type,
    v_N1____: $i ).

thf(v_N2_____type,type,
    v_N2____: $i ).

thf(c_Groups_Oabs__class_Oabs_type,type,
    c_Groups_Oabs__class_Oabs: $i > $i > $i ).

thf(c_Groups_Ominus__class_Ominus_type,type,
    c_Groups_Ominus__class_Ominus: $i > $i > $i > $i ).

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

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

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

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

thf(v_z_____type,type,
    v_z____: $i ).

thf(c_Groups_Ouminus__class_Ouminus_type,type,
    c_Groups_Ouminus__class_Ouminus: $i > $i > $i ).

thf(v_s_____type,type,
    v_s____: $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(class_Rings_Oordered__semiring_type,type,
    class_Rings_Oordered__semiring: $i > $o ).

thf(c_Orderings_Oord__class_Oless__eq_type,type,
    c_Orderings_Oord__class_Oless__eq: $i > $i > $i > $o ).

thf(c_Groups_Ozero__class_Ozero_type,type,
    c_Groups_Ozero__class_Ozero: $i > $i ).

thf(c_Groups_Otimes__class_Otimes_type,type,
    c_Groups_Otimes__class_Otimes: $i > $i > $i > $i ).

thf(class_Rings_Odivision__ring_type,type,
    class_Rings_Odivision__ring: $i > $o ).

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

thf(class_Rings_Olinordered__idom_type,type,
    class_Rings_Olinordered__idom: $i > $o ).

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

thf(class_Rings_Oordered__cancel__semiring_type,type,
    class_Rings_Oordered__cancel__semiring: $i > $o ).

thf(class_Fields_Olinordered__field_type,type,
    class_Fields_Olinordered__field: $i > $o ).

thf(c_Rings_Oinverse__class_Oinverse_type,type,
    c_Rings_Oinverse__class_Oinverse: $i > $i > $i ).

thf(class_Groups_Oordered__ab__group__add_type,type,
    class_Groups_Oordered__ab__group__add: $i > $o ).

thf(class_Rings_Omult__zero_type,type,
    class_Rings_Omult__zero: $i > $o ).

thf(class_Rings_Olinordered__semidom_type,type,
    class_Rings_Olinordered__semidom: $i > $o ).

thf(class_Rings_Ocomm__semiring__1_type,type,
    class_Rings_Ocomm__semiring__1: $i > $o ).

thf(class_Groups_Oordered__ab__semigroup__add_type,type,
    class_Groups_Oordered__ab__semigroup__add: $i > $o ).

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

thf(class_Groups_Ogroup__add_type,type,
    class_Groups_Ogroup__add: $i > $o ).

thf(class_Rings_Olinordered__semiring__strict_type,type,
    class_Rings_Olinordered__semiring__strict: $i > $o ).

thf(class_Rings_Ocomm__semiring_type,type,
    class_Rings_Ocomm__semiring: $i > $o ).

thf(class_Rings_Olinordered__ring__strict_type,type,
    class_Rings_Olinordered__ring__strict: $i > $o ).

thf(class_Groups_Oab__semigroup__add_type,type,
    class_Groups_Oab__semigroup__add: $i > $o ).

thf(class_Rings_Odivision__ring__inverse__zero_type,type,
    class_Rings_Odivision__ring__inverse__zero: $i > $o ).

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

thf(class_Rings_Oordered__ring__abs_type,type,
    class_Rings_Oordered__ring__abs: $i > $o ).

thf(class_Fields_Olinordered__field__inverse__zero_type,type,
    class_Fields_Olinordered__field__inverse__zero: $i > $o ).

thf(class_Rings_Olinordered__semiring__1__strict_type,type,
    class_Rings_Olinordered__semiring__1__strict: $i > $o ).

thf(class_Rings_Olinordered__semiring__1_type,type,
    class_Rings_Olinordered__semiring__1: $i > $o ).

thf(class_Groups_Oordered__ab__group__add__abs_type,type,
    class_Groups_Oordered__ab__group__add__abs: $i > $o ).

thf(class_Rings_Oring_type,type,
    class_Rings_Oring: $i > $o ).

thf(class_Rings_Olinordered__ring_type,type,
    class_Rings_Olinordered__ring: $i > $o ).

thf(class_Fields_Ofield__inverse__zero_type,type,
    class_Fields_Ofield__inverse__zero: $i > $o ).

thf(class_Fields_Ofield_type,type,
    class_Fields_Ofield: $i > $o ).

thf(class_Groups_Ocomm__monoid__add_type,type,
    class_Groups_Ocomm__monoid__add: $i > $o ).

thf(class_Rings_Oordered__ring_type,type,
    class_Rings_Oordered__ring: $i > $o ).

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

thf(class_Groups_Olinordered__ab__group__add_type,type,
    class_Groups_Olinordered__ab__group__add: $i > $o ).

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

thf(class_Rings_Oordered__comm__semiring_type,type,
    class_Rings_Oordered__comm__semiring: $i > $o ).

thf(class_Rings_Olinordered__semiring_type,type,
    class_Rings_Olinordered__semiring: $i > $o ).

thf(class_Groups_Omonoid__mult_type,type,
    class_Groups_Omonoid__mult: $i > $o ).

thf(class_Groups_Oab__group__add_type,type,
    class_Groups_Oab__group__add: $i > $o ).

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

thf(class_Groups_Oordered__comm__monoid__add_type,type,
    class_Groups_Oordered__comm__monoid__add: $i > $o ).

thf(class_Rings_Osemiring_type,type,
    class_Rings_Osemiring: $i > $o ).

thf(class_Groups_Oordered__ab__semigroup__add__imp__le_type,type,
    class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).

thf(class_Groups_Ocomm__monoid__mult_type,type,
    class_Groups_Ocomm__monoid__mult: $i > $o ).

thf(class_Groups_Ozero_type,type,
    class_Groups_Ozero: $i > $o ).

thf(class_Rings_Olinordered__comm__semiring__strict_type,type,
    class_Rings_Olinordered__comm__semiring__strict: $i > $o ).

thf(c_SEQ_Osubseq_type,type,
    c_SEQ_Osubseq: $i > $o ).

thf(v_f_____type,type,
    v_f____: $i ).

thf(class_Rings_Ono__zero__divisors_type,type,
    class_Rings_Ono__zero__divisors: $i > $o ).

thf(class_Rings_Ozero__neq__one_type,type,
    class_Rings_Ozero__neq__one: $i > $o ).

thf(class_Groups_Omonoid__add_type,type,
    class_Groups_Omonoid__add: $i > $o ).

thf(class_Groups_Oab__semigroup__mult_type,type,
    class_Groups_Oab__semigroup__mult: $i > $o ).

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

thf(class_Rings_Oring__1_type,type,
    class_Rings_Oring__1: $i > $o ).

thf(class_Groups_Oone_type,type,
    class_Groups_Oone: $i > $o ).

thf(class_Rings_Oring__1__no__zero__divisors_type,type,
    class_Rings_Oring__1__no__zero__divisors: $i > $o ).

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

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

thf(class_Rings_Oring__no__zero__divisors_type,type,
    class_Rings_Oring__no__zero__divisors: $i > $o ).

thf(class_Rings_Oidom_type,type,
    class_Rings_Oidom: $i > $o ).

thf(class_Groups_Ocancel__semigroup__add_type,type,
    class_Groups_Ocancel__semigroup__add: $i > $o ).

thf(class_Groups_Ocancel__ab__semigroup__add_type,type,
    class_Groups_Ocancel__ab__semigroup__add: $i > $o ).

thf(class_Groups_Oordered__cancel__ab__semigroup__add_type,type,
    class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).

thf(class_Groups_Oabs__if_type,type,
    class_Groups_Oabs__if: $i > $o ).

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

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

thf(hBOOL_type,type,
    hBOOL: $i > $o ).

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

thf(v_g_____type,type,
    v_g____: $i > $i ).

thf(v_d_____type,type,
    v_d____: $i ).

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

thf(55,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonnegative__iff__nonnegative) ).

thf(1322,plain,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ B )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(505,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) )
      = ( c_Int_OBit0 @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I10_J) ).

thf(2822,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) )
      = ( c_Int_OBit0 @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(124,axiom,
    class_Groups_Oab__group__add @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).

thf(1586,plain,
    class_Groups_Oab__group__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(58,axiom,
    ! [A: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ c_Int_OPls @ A )
      = c_Int_OPls ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Pls) ).

thf(1337,plain,
    ! [A: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ c_Int_OPls @ A )
      = c_Int_OPls ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(826,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
     => ~ ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
         => ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leE) ).

thf(3883,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
     => ~ ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
         => ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).

thf(445,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
    <=> ? [B: $i] :
          ( A
          = ( c_Nat_OSuc @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).

thf(2612,plain,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
       => ? [B: $i] :
            ( A
            = ( c_Nat_OSuc @ B ) ) )
      & ( ? [B: $i] :
            ( A
            = ( c_Nat_OSuc @ B ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(1119,axiom,
    ! [A: $i,B: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).

thf(4835,plain,
    ! [A: $i,B: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).

thf(138,axiom,
    class_Groups_Ogroup__add @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).

thf(1633,plain,
    class_Groups_Ogroup__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(688,axiom,
    class_Groups_Ocancel__ab__semigroup__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).

thf(3434,plain,
    class_Groups_Ocancel__ab__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(374,axiom,
    ! [A: $i] :
      ( A
     != ( c_Nat_OSuc @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).

thf(2412,plain,
    ! [A: $i] :
      ( A
     != ( c_Nat_OSuc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(955,axiom,
    class_Fields_Olinordered__field @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).

thf(4290,plain,
    class_Fields_Olinordered__field @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).

thf(822,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv2) ).

thf(3863,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) @ B ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).

thf(247,axiom,
    ( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
   != ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__neq__1) ).

thf(1982,plain,
    ( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
   != ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(418,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
     => ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
       => ( B
          = ( c_Nat_OSuc @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucE) ).

thf(2544,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
     => ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
       => ( B
          = ( c_Nat_OSuc @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( ( class_Int_Onumber__ring @ B )
        & ( class_Rings_Olinordered__idom @ B ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OPls ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I3_J) ).

thf(1179,plain,
    ! [A: $i,B: $i] :
      ( ( ( class_Int_Onumber__ring @ B )
        & ( class_Rings_Olinordered__idom @ B ) )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OPls ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OPls )
         => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(727,axiom,
    ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) @ v_r )
    & ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) )
      = ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096cmod_A0_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A0_J_A_061_A_N_A_I_N_Acmod_A_Ipoly_Ap_A0_J_J_096) ).

thf(3566,plain,
    ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) @ v_r )
    & ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) )
      = ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).

thf(47,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oordered__ring__abs @ C )
     => ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
            | ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
          & ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
            | ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
       => ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
          = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__eq__mult) ).

thf(1295,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oordered__ring__abs @ C )
     => ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
            | ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
          & ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
            | ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
       => ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
          = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(1171,axiom,
    class_Int_Onumber @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber) ).

thf(4992,plain,
    class_Int_Onumber @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).

thf(116,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Ofield @ B )
     => ( ( A
         != ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ A )
          = ( c_Groups_Oone__class_Oone @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__inverse) ).

thf(1554,plain,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Ofield @ B )
     => ( ( A
         != ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ A )
          = ( c_Groups_Oone__class_Oone @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(913,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Groups_Oabs__class_Oabs @ B @ A )
          = ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonpos) ).

thf(4166,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Groups_Oabs__class_Oabs @ B @ A )
          = ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).

thf(565,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Oring @ F )
     => ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C )
          = ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
      <=> ( C
          = ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff2) ).

thf(3053,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Oring @ F )
     => ( ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C )
            = ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
         => ( C
            = ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) ) )
        & ( ( C
            = ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) )
         => ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C )
            = ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(349,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).

thf(2341,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(555,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
      | ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).

thf(3008,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
      | ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(84,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
     => ( ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A )
          = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
      <=> ( ( B
            = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
          & ( A
            = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).

thf(1454,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
     => ( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A )
            = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
         => ( ( B
              = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
            & ( A
              = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) )
        & ( ( ( B
              = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
            & ( A
              = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
         => ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A )
            = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(1142,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__eq) ).

thf(4909,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).

thf(286,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__le__imp__le__neg) ).

thf(2109,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(1116,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).

thf(4824,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).

thf(946,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ogroup__add @ B )
     => ( ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__minus) ).

thf(4262,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ogroup__add @ B )
     => ( ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).

thf(760,axiom,
    class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).

thf(3661,plain,
    class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).

thf(674,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Int_Onumber__ring @ C )
     => ( ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__diff) ).

thf(3399,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Int_Onumber__ring @ C )
     => ( ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(914,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leD) ).

thf(4169,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).

thf(1139,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
       => ( ( A
            = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
          | ( A
            = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__pos__lt__two__imp__zero__or__one) ).

thf(4899,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
       => ( ( A
            = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
          | ( A
            = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).

thf(801,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).

thf(3798,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).

thf(393,axiom,
    class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).

thf(2463,plain,
    class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(673,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D @ C )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).

thf(3397,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D @ C )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(734,axiom,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096cmod_A_Ipoly_Ap_A_Ig_A_If_A_IN1_A_L_AN2_J_J_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_A_If_A_IN1_A_L_AN2_J_J_J_096) ).

thf(3581,plain,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).

thf(1125,axiom,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_e2) ).

thf(4852,plain,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).

thf(425,axiom,
    class_Groups_Ozero @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).

thf(2559,plain,
    class_Groups_Ozero @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(694,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( B != A )
       => ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).

thf(3449,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( B != A )
       => ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).

thf(356,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A )
        = ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).

thf(2363,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A )
        = ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(856,axiom,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ v_N2____ ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_N2) ).

thf(3990,plain,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ v_N2____ ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).

thf(410,axiom,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ A )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).

thf(2512,plain,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ A )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(569,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
      <=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).

thf(3072,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ C )
     => ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
        & ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(284,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
        <=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__divide__le__eq) ).

thf(2104,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) )
          & ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(974,axiom,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th000_I3_J) ).

thf(4339,plain,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).

thf(45,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oabs__class_Oabs @ C @ A ) @ B )
          = ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__pos) ).

thf(1290,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oabs__class_Oabs @ C @ A ) @ B )
          = ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(453,axiom,
    ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ c_Int_OPls )
    = c_Int_OPls ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Pls) ).

thf(2644,plain,
    ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ c_Int_OPls )
    = c_Int_OPls ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(805,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib) ).

thf(3813,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).

thf(723,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
          = A ) )
      & ( ( B
         != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
          = ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__if) ).

thf(3549,plain,
    ! [A: $i,B: $i] :
      ( ( ( B
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
          = A ) )
      & ( ( B
         != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
          = ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).

thf(74,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
        & ( class_Int_Onumber @ D ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
      <=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ B ) ) )
          & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
           => ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ B ) @ C ) )
              & ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__eq__number__of) ).

thf(1401,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
        & ( class_Int_Onumber @ D ) )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
         => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
             => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ B ) ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ B ) @ C ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) ) )
        & ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
             => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ B ) ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ B ) @ C ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(233,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A )
      = ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).

thf(1939,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A )
      = ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(328,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( A
           != ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
            = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_division__ring__inverse__add) ).

thf(2282,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( A
           != ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
            = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(288,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Oordered__ring @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).

thf(2114,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Oordered__ring @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(675,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
     => ( ( C
          = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ A ) ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ C )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).

thf(3402,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
     => ( ( C
          = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ A ) ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ C )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).

thf(163,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
        <=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__divide__le__eq) ).

thf(1692,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ B ) )
          & ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ B )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(49,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
      <=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
            & ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
          | ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
            & ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__0__iff) ).

thf(1305,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ C )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
              & ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
            | ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
              & ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) )
        & ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
              & ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
            | ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
              & ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(1,conjecture,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(1173,plain,
    ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(935,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).

thf(4226,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).

thf(1021,axiom,
    ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) )
   => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) ) )
     => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_091_124_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_059_A0_A_060_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_124_093_061_061_062_Ainverse_A_Ireal_A_ISuc_A_IN1_A_L_AN2_J_J_J_A_060_Ainverse_A_I2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_J_096) ).

thf(4500,plain,
    ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) )
   => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) ) )
     => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).

thf(315,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
      <=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
            & ( c_Orderings_Oord__class_Oless @ D @ B @ A ) )
          | ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
            & ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).

thf(2231,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ D )
     => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
         => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
              & ( c_Orderings_Oord__class_Oless @ D @ B @ A ) )
            | ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
              & ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) )
        & ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
              & ( c_Orderings_Oord__class_Oless @ D @ B @ A ) )
            | ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
              & ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(447,axiom,
    ! [A: $i,B: $i] :
      ( ( ( class_Fields_Olinordered__field__inverse__zero @ B )
        & ( class_Int_Onumber__ring @ B ) )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
       => ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_half__gt__zero) ).

thf(2622,plain,
    ! [A: $i,B: $i] :
      ( ( ( class_Fields_Olinordered__field__inverse__zero @ B )
        & ( class_Int_Onumber__ring @ B ) )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
       => ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(78,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).

thf(1443,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(493,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ c_Int_OPls )
       => ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ A ) )
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
      & ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ c_Int_OPls )
       => ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ A ) )
          = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__mult__left) ).

thf(2776,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ c_Int_OPls )
       => ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ A ) )
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
      & ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ c_Int_OPls )
       => ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ A ) )
          = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(711,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
     => ( ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__1) ).

thf(3509,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
     => ( ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).

thf(133,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
       => ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
         => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__inverse) ).

thf(1618,plain,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
       => ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
         => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(633,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq) ).

thf(3285,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(462,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add1__zle__eq) ).

thf(2671,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(463,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Int_Onumber__ring @ D )
     => ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ominus__class_Ominus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__diff1) ).

thf(2676,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Int_Onumber__ring @ D )
     => ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ominus__class_Ominus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(260,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
      <=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
          | ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__less__1__iff) ).

thf(2014,plain,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ B )
     => ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
         => ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
            | ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) )
        & ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
            | ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) )
         => ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(1083,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
        & ( class_Int_Onumber @ D ) )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
      <=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
           => ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ B ) ) )
          & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
           => ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ B ) @ C ) )
              & ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq__number__of) ).

thf(4711,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
        & ( class_Int_Onumber @ D ) )
     => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
         => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
             => ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ B ) ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ B ) @ C ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) ) )
        & ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
             => ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ B ) ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ B ) @ C ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).

thf(1056,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ B )
     => ( ? [C: $i] :
            ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
            & ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ C ) )
      <=> ? [C: $i] :
          ! [D: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__NBseq__def2) ).

thf(4603,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ B )
     => ( ( ? [C: $i] :
              ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
              & ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ C ) )
         => ? [C: $i] :
            ! [D: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) )
        & ( ? [C: $i] :
            ! [D: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) )
         => ? [C: $i] :
              ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
              & ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).

thf(929,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Ocancel__semigroup__add @ D )
     => ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
          = ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
       => ( C = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).

thf(4215,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Ocancel__semigroup__add @ D )
     => ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
          = ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
       => ( C = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).

thf(364,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ E )
     => ( ( c_Groups_Otimes__class_Otimes @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ A ) )
        = ( c_Rings_Oinverse__class_Odivide @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__times__eq) ).

thf(2380,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ E )
     => ( ( c_Groups_Otimes__class_Otimes @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ A ) )
        = ( c_Rings_Oinverse__class_Odivide @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(168,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Olinordered__ab__group__add @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).

thf(1705,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Olinordered__ab__group__add @ B )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(614,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ A ) )
      <=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff2) ).

thf(3217,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ A ) )
         => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ A ) ) )
        & ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ A ) )
         => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(131,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
      <=> ( ( B
            = ( c_Groups_Ozero__class_Ozero @ C ) )
          & ( A
            = ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).

thf(1608,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ C )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( ( B
              = ( c_Groups_Ozero__class_Ozero @ C ) )
            & ( A
              = ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
        & ( ( ( B
              = ( c_Groups_Ozero__class_Ozero @ C ) )
            & ( A
              = ( c_Groups_Ozero__class_Ozero @ C ) ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(686,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__right__mono__neg) ).

thf(3429,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(1046,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
     => ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).

thf(4575,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).

thf(866,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).

thf(4011,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).

thf(175,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ C )
     => ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
        = ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__left) ).

thf(1735,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ C )
     => ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
        = ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(216,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
       != ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
     => ( ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ C )
          = ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ C ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__right__cancel) ).

thf(1867,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
       != ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
     => ( ( ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ C )
            = ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ C ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ C )
            = ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(1063,axiom,
    c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096) ).

thf(4638,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).

thf(1042,axiom,
    ! [A: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).

thf(4564,plain,
    ! [A: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).

thf(300,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ D )
     => ( ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ B )
          = A )
      <=> ( ( ( B
             != ( c_Groups_Ozero__class_Ozero @ D ) )
           => ( C
              = ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) )
          & ( ( B
              = ( c_Groups_Ozero__class_Ozero @ D ) )
           => ( A
              = ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq) ).

thf(2168,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ D )
     => ( ( ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ B )
            = A )
         => ( ( ( B
               != ( c_Groups_Ozero__class_Ozero @ D ) )
             => ( C
                = ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) )
            & ( ( B
                = ( c_Groups_Ozero__class_Ozero @ D ) )
             => ( A
                = ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) )
        & ( ( ( ( B
               != ( c_Groups_Ozero__class_Ozero @ D ) )
             => ( C
                = ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) )
            & ( ( B
                = ( c_Groups_Ozero__class_Ozero @ D ) )
             => ( A
                = ( c_Groups_Ozero__class_Ozero @ D ) ) ) )
         => ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ B )
            = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(643,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).

thf(3313,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(511,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc) ).

thf(2844,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(732,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
      <=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).

thf(3577,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
         => ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).

thf(1096,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__real__le) ).

thf(4762,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).

thf(631,axiom,
    ! [A: $i] :
      ( ( class_Int_Onumber__ring @ A )
     => ( ( c_Groups_Oplus__class_Oplus @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Oone__class_Oone @ A ) )
        = ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__add__one__is__two) ).

thf(3276,plain,
    ! [A: $i] :
      ( ( class_Int_Onumber__ring @ A )
     => ( ( c_Groups_Oplus__class_Oplus @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Oone__class_Oone @ A ) )
        = ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(938,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq2) ).

thf(4234,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).

thf(156,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ D )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ D @ A ) )
         => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ D ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__inverse__cancel) ).

thf(1671,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ D )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ D @ A ) )
         => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ D ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(889,axiom,
    class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).

thf(4090,plain,
    class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).

thf(148,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__div__pos__le) ).

thf(1655,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(786,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
     => ( ( C
          = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ A ) ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).

thf(3745,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
     => ( ( C
          = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ A ) ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).

thf(1000,axiom,
    ! [A: $i] :
      ( ( c_SEQ_Osubseq @ A )
    <=> ! [B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ B ) @ ( hAPP @ A @ ( c_Nat_OSuc @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subseq__Suc__iff) ).

thf(4418,plain,
    ! [A: $i] :
      ( ( ( c_SEQ_Osubseq @ A )
       => ! [B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ B ) @ ( hAPP @ A @ ( c_Nat_OSuc @ B ) ) ) )
      & ( ! [B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ B ) @ ( hAPP @ A @ ( c_Nat_OSuc @ B ) ) )
       => ( c_SEQ_Osubseq @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).

thf(1091,axiom,
    class_Groups_Ozero @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).

thf(4739,plain,
    class_Groups_Ozero @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).

thf(553,axiom,
    class_Rings_Olinordered__semiring__strict @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).

thf(3004,plain,
    class_Rings_Olinordered__semiring__strict @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(1121,axiom,
    ! [A: $i] :
      ( ( c_Int_OBit1 @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__def) ).

thf(4839,plain,
    ! [A: $i] :
      ( ( c_Int_OBit1 @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).

thf(1068,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( B
          = ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
      <=> ( A
          = ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equation__minus__iff) ).

thf(4647,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( ( B
            = ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
         => ( A
            = ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) )
        & ( ( A
            = ( c_Groups_Ouminus__class_Ouminus @ C @ B ) )
         => ( B
            = ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).

thf(660,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) @ c_Int_OPls )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I10_J) ).

thf(3367,plain,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) @ c_Int_OPls )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) @ c_Int_OPls ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(1135,axiom,
    ! [A: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).

thf(4884,plain,
    ! [A: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).

thf(1130,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono2) ).

thf(4870,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).

thf(530,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__leI) ).

thf(2918,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(386,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).

thf(2448,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(649,axiom,
    class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).

thf(3338,plain,
    class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(748,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B )
        = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
    <=> ( C = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).

thf(3616,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B )
          = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
       => ( C = A ) )
      & ( ( C = A )
       => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B )
          = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).

thf(23,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__mono) ).

thf(1233,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(951,axiom,
    class_Groups_Oab__semigroup__mult @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).

thf(4279,plain,
    class_Groups_Oab__semigroup__mult @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).

thf(625,axiom,
    ! [A: $i,B: $i] :
      ( ( ( class_Int_Onumber__ring @ B )
        & ( class_Rings_Olinordered__idom @ B ) )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
      <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I3_J) ).

thf(3253,plain,
    ! [A: $i,B: $i] :
      ( ( ( class_Int_Onumber__ring @ B )
        & ( class_Rings_Olinordered__idom @ B ) )
     => ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls ) )
        & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls )
         => ( c_Orderings_Oord__class_Oless @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(809,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      <=> ( A
          = ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__le__zero__iff) ).

thf(3826,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ B )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
         => ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).

thf(390,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) @ v_r )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_s1m) ).

thf(2459,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) @ v_r )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(185,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
      <=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ B ) )
          & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
           => ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) )
              & ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__divide__eq) ).

thf(1761,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ D )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
         => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
             => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ B ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) )
        & ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
             => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ B ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(958,axiom,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).

thf(4294,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).

thf(702,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__numeral__1) ).

thf(3481,plain,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).

thf(99,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ D )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ D @ A ) )
         => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ D ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__inverse__cancel2) ).

thf(1507,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ D )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ D @ A ) )
         => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ D ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(777,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Complex_Ocomplex @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__diff__def) ).

thf(3717,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Complex_Ocomplex @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).

thf(1153,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__0__number__of) ).

thf(4941,plain,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).

thf(1106,axiom,
    ! [A: $i] :
      ( ( c_SEQ_Osubseq @ A )
    <=> ! [B: $i,C: $i] :
          ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ C )
         => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subseq__def) ).

thf(4792,plain,
    ! [A: $i] :
      ( ( ( c_SEQ_Osubseq @ A )
       => ! [B: $i,C: $i] :
            ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ C )
           => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) ) ) )
      & ( ! [B: $i,C: $i] :
            ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ C )
           => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) ) )
       => ( c_SEQ_Osubseq @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).

thf(721,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__semidom @ A )
     => ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Oplus__class_Oplus @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).

thf(3545,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__semidom @ A )
     => ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Oplus__class_Oplus @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).

thf(752,axiom,
    ! [A: $i] :
      ( ( class_Int_Onumber__ring @ A )
     => ( ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit1 @ c_Int_OPls ) )
        = ( c_Groups_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__1__eq__1) ).

thf(3634,plain,
    ! [A: $i] :
      ( ( class_Int_Onumber__ring @ A )
     => ( ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit1 @ c_Int_OPls ) )
        = ( c_Groups_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).

thf(623,axiom,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ v_d____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_d_I1_J) ).

thf(3249,plain,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ v_d____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(796,axiom,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th31) ).

thf(3777,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).

thf(1109,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( ( c_Groups_Oabs__class_Oabs @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
        = ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__cancel) ).

thf(4803,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( ( c_Groups_Oabs__class_Oabs @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
        = ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).

thf(923,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).

thf(4198,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ B ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ B )
       => ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).

thf(411,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono1) ).

thf(2516,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(1156,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Oordered__ab__semigroup__add @ E )
     => ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mono) ).

thf(4948,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Oordered__ab__semigroup__add @ E )
     => ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).

thf(135,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Odivision__ring @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( B
            = ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) )
         => ( ( c_Rings_Oinverse__class_Odivide @ D @ B @ C )
            = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__imp) ).

thf(1623,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Odivision__ring @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( B
            = ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) )
         => ( ( c_Rings_Oinverse__class_Odivide @ D @ B @ C )
            = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(11,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonneg__pos) ).

thf(1196,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(877,axiom,
    ! [A: $i] :
      ( ( class_Rings_Ozero__neq__one @ A )
     => ( ( c_Groups_Oone__class_Oone @ A )
       != ( c_Groups_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).

thf(4047,plain,
    ! [A: $i] :
      ( ( class_Rings_Ozero__neq__one @ A )
     => ( ( c_Groups_Oone__class_Oone @ A )
       != ( c_Groups_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).

thf(179,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).

thf(1746,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(580,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) )
          = ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oabs__class_Oabs @ C @ A ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__abs__divide) ).

thf(3103,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) )
          = ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oabs__class_Oabs @ C @ A ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(976,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).

thf(4343,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).

thf(616,axiom,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__minus__le__complex__mod) ).

thf(3236,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(490,axiom,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).

thf(2763,plain,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(836,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq3) ).

thf(3915,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).

thf(313,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__left__mono) ).

thf(2227,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(122,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ E )
     => ( ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E @ C @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).

thf(1576,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ E )
     => ( ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ E @ D @ ( c_Groups_Otimes__class_Otimes @ E @ C @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(146,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oordered__cancel__semiring @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).

thf(1650,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oordered__cancel__semiring @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(144,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).

thf(1645,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(171,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ C )
     => ( ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
        = ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ominus) ).

thf(1724,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ C )
     => ( ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
        = ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(90,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ A ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff2) ).

thf(1475,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(506,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
       => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
          = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).

thf(2825,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
       => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
          = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(242,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).

thf(1967,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(969,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Int_Onumber__ring @ C )
     => ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
        = ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__eq) ).

thf(4322,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Int_Onumber__ring @ C )
     => ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
        = ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).

thf(503,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucI) ).

thf(2819,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(193,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).

thf(1803,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(825,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
          = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__num__frac) ).

thf(3880,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
          = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).

thf(225,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__D1) ).

thf(1904,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(103,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
        <=> ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__divide__eq) ).

thf(1518,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
           => ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) ) )
          & ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) )
           => ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(37,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) )
      <=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
            & ( c_Orderings_Oord__class_Oless @ D @ C @ A ) )
          | ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
            & ( c_Orderings_Oord__class_Oless @ D @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).

thf(1265,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ D )
     => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) )
         => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
              & ( c_Orderings_Oord__class_Oless @ D @ C @ A ) )
            | ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
              & ( c_Orderings_Oord__class_Oless @ D @ A @ C ) ) ) )
        & ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
              & ( c_Orderings_Oord__class_Oless @ D @ C @ A ) )
            | ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
              & ( c_Orderings_Oord__class_Oless @ D @ A @ C ) ) )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(1101,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__right__mono) ).

thf(4775,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).

thf(519,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Oring__1__no__zero__divisors @ B )
     => ( ( ( c_Groups_Otimes__class_Otimes @ B @ A @ A )
          = ( c_Groups_Oone__class_Oone @ B ) )
      <=> ( ( A
            = ( c_Groups_Oone__class_Oone @ B ) )
          | ( A
            = ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).

thf(2869,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Oring__1__no__zero__divisors @ B )
     => ( ( ( ( c_Groups_Otimes__class_Otimes @ B @ A @ A )
            = ( c_Groups_Oone__class_Oone @ B ) )
         => ( ( A
              = ( c_Groups_Oone__class_Oone @ B ) )
            | ( A
              = ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) )
        & ( ( ( A
              = ( c_Groups_Oone__class_Oone @ B ) )
            | ( A
              = ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) )
         => ( ( c_Groups_Otimes__class_Otimes @ B @ A @ A )
            = ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(1025,axiom,
    ( ( c_Int_OBit0 @ c_Int_OPls )
    = c_Int_OPls ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__Pls) ).

thf(4511,plain,
    ( ( c_Int_OBit0 @ c_Int_OPls )
    = c_Int_OPls ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).

thf(219,axiom,
    ! [A: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ A )
     => ( ( c_Rings_Oinverse__class_Oinverse @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
        = ( c_Groups_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__inverse__zero) ).

thf(1887,plain,
    ! [A: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ A )
     => ( ( c_Rings_Oinverse__class_Oinverse @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
        = ( c_Groups_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(1062,axiom,
    class_Rings_Olinordered__semiring @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).

thf(4637,plain,
    class_Rings_Olinordered__semiring @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).

thf(622,axiom,
    class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).

thf(3248,plain,
    class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(562,axiom,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_e) ).

thf(3046,plain,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(487,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__idom @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oabs__class_Oabs @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) ) @ A )
      <=> ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) @ C )
          & ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__diff__less__iff) ).

thf(2755,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__idom @ D )
     => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oabs__class_Oabs @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) ) @ A )
         => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) @ C )
            & ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) )
        & ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) @ C )
            & ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oabs__class_Oabs @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(1095,axiom,
    class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).

thf(4761,plain,
    class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).

thf(808,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I15_J) ).

thf(3821,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).

thf(405,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
      <=> ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__iff) ).

thf(2501,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ C )
     => ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
         => ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) )
        & ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) )
         => ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(325,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Oordered__ring @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).

thf(2274,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Oordered__ring @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(483,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) )
          = ( c_Rings_Oinverse__class_Odivide @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__minus__divide__right) ).

thf(2745,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) )
          = ( c_Rings_Oinverse__class_Odivide @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(472,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).

thf(2703,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(1006,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_RealVector_Oreal__field @ F )
     => ( ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ ( c_Groups_Otimes__class_Otimes @ F @ C @ B ) ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ D @ B ) @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ C ) @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__mult__lemma) ).

thf(4439,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_RealVector_Oreal__field @ F )
     => ( ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ ( c_Groups_Otimes__class_Otimes @ F @ C @ B ) ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ D @ B ) @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ C ) @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).

thf(44,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( class_Int_Onumber__ring @ C )
        & ( class_Rings_Olinordered__idom @ C ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__number__of) ).

thf(1287,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( class_Int_Onumber__ring @ C )
        & ( class_Rings_Olinordered__idom @ C ) )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(442,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
    <=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__real__less) ).

thf(2603,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(1030,axiom,
    class_Rings_Osemiring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).

thf(4524,plain,
    class_Rings_Osemiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).

thf(844,axiom,
    ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I1_J) ).

thf(3938,plain,
    ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).

thf(977,axiom,
    class_Rings_Oring__1 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).

thf(4348,plain,
    class_Rings_Oring__1 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).

thf(501,axiom,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).

thf(2814,plain,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(248,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I13_J) ).

thf(1985,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(470,axiom,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).

thf(2698,plain,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(151,axiom,
    class_Groups_Ocomm__monoid__mult @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).

thf(1660,plain,
    class_Groups_Ocomm__monoid__mult @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(587,axiom,
    c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).

thf(3131,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(1161,axiom,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) @ A )
      = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).

thf(4956,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) @ A )
      = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).

thf(999,axiom,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).

thf(4415,plain,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).

thf(651,axiom,
    class_Groups_Oab__semigroup__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).

thf(3342,plain,
    class_Groups_Oab__semigroup__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(933,axiom,
    class_Rings_Oordered__ring__abs @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring__abs) ).

thf(4224,plain,
    class_Rings_Oordered__ring__abs @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).

thf(730,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__pos) ).

thf(3574,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).

thf(1069,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
        = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc) ).

thf(4654,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
        = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).

thf(384,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Olinordered__ab__group__add @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
      <=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).

thf(2444,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Olinordered__ab__group__add @ B )
     => ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
         => ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
        & ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
         => ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(308,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).

thf(2217,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(746,axiom,
    class_Rings_Oordered__comm__semiring @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).

thf(3612,plain,
    class_Rings_Oordered__comm__semiring @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).

thf(591,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ B )
      = ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__average__minus__first) ).

thf(3148,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ B )
      = ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(465,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring @ B )
     => ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__1) ).

thf(2682,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring @ B )
     => ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(202,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring @ C )
     => ( ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
          = ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
       => ( ( B
           != ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( ( A
             != ( c_Groups_Ozero__class_Ozero @ C ) )
           => ( B = A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__eq__imp__eq) ).

thf(1826,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring @ C )
     => ( ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
          = ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
       => ( ( B
           != ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( ( A
             != ( c_Groups_Ozero__class_Ozero @ C ) )
           => ( B = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(51,axiom,
    class_Rings_Olinordered__semiring__1 @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).

thf(1313,plain,
    class_Rings_Olinordered__semiring__1 @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(41,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ E @ B ) @ A ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ E )
         => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ E )
           => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).

thf(1279,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ E @ B ) @ A ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ E )
         => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ E )
           => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(978,axiom,
    ! [A: $i,B: $i] :
      ( ( ( class_Int_Onumber__ring @ B )
        & ( class_Rings_Olinordered__idom @ B ) )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
      <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I4_J) ).

thf(4349,plain,
    ! [A: $i,B: $i] :
      ( ( ( class_Int_Onumber__ring @ B )
        & ( class_Rings_Olinordered__idom @ B ) )
     => ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
         => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
        & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Int_OBit1 @ c_Int_OPls ) )
         => ( c_Orderings_Oord__class_Oless @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).

thf(788,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Oring @ F )
     => ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C )
          = ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
      <=> ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff1) ).

thf(3749,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Oring @ F )
     => ( ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C )
            = ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
         => ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C )
            = A ) )
        & ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C )
            = A )
         => ( ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C )
            = ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).

thf(428,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse) ).

thf(2562,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(204,axiom,
    class_Groups_Omonoid__add @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).

thf(1832,plain,
    class_Groups_Omonoid__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(525,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
      = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel) ).

thf(2897,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
      = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(250,axiom,
    class_Rings_Oring__1__no__zero__divisors @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).

thf(1992,plain,
    class_Rings_Oring__1__no__zero__divisors @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(656,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I17_J) ).

thf(3353,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(85,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ C )
     => ( ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
        = ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__right) ).

thf(1462,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ C )
     => ( ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
        = ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(561,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).

thf(3043,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(113,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonpositive__iff__nonpositive) ).

thf(1545,plain,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ B )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(467,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
        = ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__number__of__Bit0) ).

thf(2691,plain,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
        = ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(192,axiom,
    ! [A: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0__right) ).

thf(1800,plain,
    ! [A: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(897,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ c_Int_OPls ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__numeral__0__right) ).

thf(4119,plain,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ c_Int_OPls ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).

thf(92,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
        = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) )
    <=> ( ( C = A )
        | ( B
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel2) ).

thf(1479,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
          = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) )
       => ( ( C = A )
          | ( B
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
      & ( ( ( C = A )
          | ( B
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
       => ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
          = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(1158,axiom,
    class_RealVector_Oreal__normed__div__algebra @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).

thf(4952,plain,
    class_RealVector_Oreal__normed__div__algebra @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).

thf(142,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__pos) ).

thf(1641,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(947,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ocomm__monoid__mult @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).

thf(4265,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ocomm__monoid__mult @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).

thf(1073,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) )
      = ( c_Int_OBit1 @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit0__Bit1) ).

thf(4669,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) )
      = ( c_Int_OBit1 @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).

thf(814,axiom,
    class_Rings_Odivision__ring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).

thf(3840,plain,
    class_Rings_Odivision__ring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).

thf(662,axiom,
    ~ ! [A: $i] :
        ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
       => ~ ! [B: $i] :
              ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ v_z____ ) ) )
                & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ v_z____ ) ) @ A ) )
             => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ B ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bd_O_A_091_124_A0_A_060_Ad_059_AALL_Aw_O_A0_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_A_N_N_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

thf(3374,plain,
    ~ ! [A: $i] :
        ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
       => ~ ! [B: $i] :
              ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ v_z____ ) ) )
                & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ v_z____ ) ) @ A ) )
             => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ B ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(922,axiom,
    ~ ! [A: $i] :
        ~ ! [B: $i] :
            ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ B )
           => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( v_g____ @ ( hAPP @ v_f____ @ B ) ) @ v_z____ ) ) @ v_d____ ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_BN1_O_AALL_An_062_061N1_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

thf(4194,plain,
    ~ ! [A: $i] :
        ~ ! [B: $i] :
            ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ B )
           => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( v_g____ @ ( hAPP @ v_f____ @ B ) ) @ v_z____ ) ) @ v_d____ ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).

thf(421,axiom,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).

thf(2552,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(54,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).

thf(1319,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ B )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(220,axiom,
    ! [A: $i,B: $i] :
      ( ( ( class_Int_Onumber__ring @ B )
        & ( class_Rings_Olinordered__idom @ B ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I1_J) ).

thf(1890,plain,
    ! [A: $i,B: $i] :
      ( ( ( class_Int_Onumber__ring @ B )
        & ( class_Rings_Olinordered__idom @ B ) )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ A ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(361,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__left) ).

thf(2373,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(838,axiom,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).

thf(3919,plain,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).

thf(177,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oring @ C )
     => ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__left) ).

thf(1741,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oring @ C )
     => ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(967,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Omonoid__mult @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__right) ).

thf(4317,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Omonoid__mult @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).

thf(574,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Int_Onumber @ C )
     => ( ( ( c_Int_Onumber__class_Onumber__of @ C @ B )
          = A )
      <=> ( A
          = ( c_Int_Onumber__class_Onumber__of @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__reorient) ).

thf(3084,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Int_Onumber @ C )
     => ( ( ( ( c_Int_Onumber__class_Onumber__of @ C @ B )
            = A )
         => ( A
            = ( c_Int_Onumber__class_Onumber__of @ C @ B ) ) )
        & ( ( A
            = ( c_Int_Onumber__class_Onumber__of @ C @ B ) )
         => ( ( c_Int_Onumber__class_Onumber__of @ C @ B )
            = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(535,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( class_Int_Onumber @ C )
        & ( class_Orderings_Olinorder @ C ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
      <=> ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__number__of__eq__not__less) ).

thf(2929,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( class_Int_Onumber @ C )
        & ( class_Orderings_Olinorder @ C ) )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
         => ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) ) )
        & ( ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(699,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ B )
     => ( ? [C: $i] :
            ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
            & ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ C ) )
      <=> ? [C: $i] :
          ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__NBseq__def) ).

thf(3470,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ B )
     => ( ( ? [C: $i] :
              ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
              & ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ C ) )
         => ? [C: $i] :
            ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) ) )
        & ( ? [C: $i] :
            ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) ) )
         => ? [C: $i] :
              ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
              & ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ A @ D ) ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).

thf(1039,axiom,
    class_Rings_Ocomm__semiring @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).

thf(4551,plain,
    class_Rings_Ocomm__semiring @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).

thf(833,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff) ).

thf(3902,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).

thf(758,axiom,
    class_Int_Oring__char__0 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).

thf(3657,plain,
    class_Int_Oring__char__0 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).

thf(230,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
        <=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).

thf(1931,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) )
          & ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(335,axiom,
    class_Groups_Oordered__ab__group__add__abs @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).

thf(2301,plain,
    class_Groups_Oordered__ab__group__add__abs @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(95,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) )
           => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).

thf(1494,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) )
           => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(724,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
      <=> ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).

thf(3557,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
     => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
         => ( c_Orderings_Oord__class_Oless @ D @ C @ A ) )
        & ( ( c_Orderings_Oord__class_Oless @ D @ C @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).

thf(188,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ E )
     => ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
         => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ C )
           => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
             => ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono) ).

thf(1778,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ E )
     => ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
         => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ C )
           => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
             => ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(962,axiom,
    class_Rings_Oidom @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).

thf(4302,plain,
    class_Rings_Oidom @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).

thf(367,axiom,
    class_Groups_Oabs__if @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oabs__if) ).

thf(2388,plain,
    class_Groups_Oabs__if @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(823,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit1 @ A ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I22_J) ).

thf(3866,plain,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit1 @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ A ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).

thf(22,axiom,
    class_Groups_Oordered__ab__semigroup__add @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).

thf(1232,plain,
    class_Groups_Oordered__ab__semigroup__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(942,axiom,
    class_Rings_Ozero__neq__one @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).

thf(4253,plain,
    class_Rings_Ozero__neq__one @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).

thf(1165,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__eq) ).

thf(4967,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).

thf(865,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ C ) )
      <=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__iff1) ).

thf(4008,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
     => ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ C ) )
         => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) )
        & ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).

thf(1093,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
          = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__num) ).

thf(4756,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
          = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).

thf(508,axiom,
    ! [A: $i] :
      ( ? [B: $i] :
          ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
          & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ B ) ) @ A ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_s1) ).

thf(2829,plain,
    ! [A: $i] :
      ( ( ? [B: $i] :
            ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
            & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ B ) ) @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ A )
       => ? [B: $i] :
            ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
            & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ B ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(311,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__less__div__pos) ).

thf(2222,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(86,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__right__mono) ).

thf(1465,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(687,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit0 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Bit1) ).

thf(3431,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit0 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).

thf(608,axiom,
    ! [A: $i,B: $i] :
      ( ( ( class_Int_Onumber__ring @ B )
        & ( class_Rings_Olinordered__idom @ B ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I2_J) ).

thf(3199,plain,
    ! [A: $i,B: $i] :
      ( ( ( class_Int_Onumber__ring @ B )
        & ( class_Rings_Olinordered__idom @ B ) )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(570,axiom,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__self) ).

thf(3075,plain,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(277,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing2) ).

thf(2090,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(68,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).

thf(1373,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(960,axiom,
    ! [A: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).

thf(4297,plain,
    ! [A: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).

thf(763,axiom,
    ! [A: $i] :
      ( ( class_Rings_Ozero__neq__one @ A )
     => ( ( c_Groups_Ozero__class_Ozero @ A )
       != ( c_Groups_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__neq__one) ).

thf(3670,plain,
    ! [A: $i] :
      ( ( class_Rings_Ozero__neq__one @ A )
     => ( ( c_Groups_Ozero__class_Ozero @ A )
       != ( c_Groups_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).

thf(597,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).

thf(3163,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ B ) ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ B ) )
       => ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(1124,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).

thf(4847,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).

thf(416,axiom,
    c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos2) ).

thf(2540,plain,
    c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(348,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Olinordered__ab__group__add @ B )
     => ( ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
          = A )
      <=> ( A
          = ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__zero) ).

thf(2335,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Olinordered__ab__group__add @ B )
     => ( ( ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
            = A )
         => ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
            = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(593,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).

thf(3152,plain,
    ! [A: $i,B: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
     => ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(7,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__inverse__le) ).

thf(1183,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(794,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
      = ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).

thf(3771,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
      = ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).

thf(93,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).

thf(1489,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(1078,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Int_Onumber @ D )
        & ( class_Rings_Oring @ D ) )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__diff__distrib__number__of) ).

thf(4696,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Int_Onumber @ D )
        & ( class_Rings_Oring @ D ) )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).

thf(828,axiom,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__0961_A_P_Areal_A_ISuc_A_If_A_IN1_A_L_AN2_J_J_J_A_060_061_A1_A_P_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096) ).

thf(3887,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).

thf(343,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).

thf(2324,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(716,axiom,
    class_RealVector_Oreal__normed__vector @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).

thf(3527,plain,
    class_RealVector_Oreal__normed__vector @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(774,axiom,
    ! [A: $i] :
      ( ? [B: $i] :
          ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
          & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ B ) ) ) ) @ A ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_By_O_A_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_A_N_A_I_N_Acmod_A_Ipoly_Ap_Az_J_J_A_060_Ay_J_A_061_A_I_N_As_A_060_Ay_J_096) ).

thf(3702,plain,
    ! [A: $i] :
      ( ( ? [B: $i] :
            ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
            & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ B ) ) ) ) @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ A )
       => ? [B: $i] :
            ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
            & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ B ) ) ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).

thf(690,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).

thf(3438,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).

thf(907,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ~ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__not__less__zero) ).

thf(4147,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ~ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).

thf(878,axiom,
    class_Groups_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).

thf(4050,plain,
    class_Groups_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).

thf(290,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).

thf(2122,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(715,axiom,
    ! [A: $i] :
      ( ( ( class_Fields_Olinordered__field__inverse__zero @ A )
        & ( class_Int_Onumber__ring @ A ) )
     => ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Rings_Oinverse__class_Odivide @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_half) ).

thf(3525,plain,
    ! [A: $i] :
      ( ( ( class_Fields_Olinordered__field__inverse__zero @ A )
        & ( class_Int_Onumber__ring @ A ) )
     => ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Rings_Oinverse__class_Odivide @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).

thf(215,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).

thf(1864,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(533,axiom,
    class_Groups_Oone @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).

thf(2925,plain,
    class_Groups_Oone @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(853,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__less__0) ).

thf(3973,plain,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).

thf(331,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring @ B )
     => ( ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( A
          = ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__zero__imp__zero) ).

thf(2291,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring @ B )
     => ( ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( A
          = ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(73,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Fields_Ofield__inverse__zero @ D )
        & ( class_Int_Onumber @ D ) )
     => ( ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ B )
          = ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
      <=> ( ( ( B
             != ( c_Groups_Ozero__class_Ozero @ D ) )
           => ( C
              = ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ B ) ) )
          & ( ( B
              = ( c_Groups_Ozero__class_Ozero @ D ) )
           => ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
              = ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq__number__of) ).

thf(1383,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Fields_Ofield__inverse__zero @ D )
        & ( class_Int_Onumber @ D ) )
     => ( ( ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ B )
            = ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
         => ( ( ( B
               != ( c_Groups_Ozero__class_Ozero @ D ) )
             => ( C
                = ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ B ) ) )
            & ( ( B
                = ( c_Groups_Ozero__class_Ozero @ D ) )
             => ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
                = ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) )
        & ( ( ( ( B
               != ( c_Groups_Ozero__class_Ozero @ D ) )
             => ( C
                = ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ B ) ) )
            & ( ( B
                = ( c_Groups_Ozero__class_Ozero @ D ) )
             => ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
                = ( c_Groups_Ozero__class_Ozero @ D ) ) ) )
         => ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ B )
            = ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(319,axiom,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__refl) ).

thf(2254,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(638,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).

thf(3300,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(576,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__cancel) ).

thf(3093,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(1071,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Oordered__ring @ F )
     => ( ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
      <=> ( c_Orderings_Oord__class_Oless @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff2) ).

thf(4660,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Oordered__ring @ F )
     => ( ( ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
         => ( c_Orderings_Oord__class_Oless @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) ) )
        & ( ( c_Orderings_Oord__class_Oless @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) )
         => ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).

thf(358,axiom,
    class_Groups_Oordered__comm__monoid__add @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).

thf(2367,plain,
    class_Groups_Oordered__comm__monoid__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(70,axiom,
    class_Groups_Ocomm__monoid__add @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).

thf(1377,plain,
    class_Groups_Ocomm__monoid__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(872,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
       => ( ( c_Groups_Oabs__class_Oabs @ B @ A )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__pos) ).

thf(4033,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
       => ( ( c_Groups_Oabs__class_Oabs @ B @ A )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).

thf(1122,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).

thf(4842,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).

thf(222,axiom,
    class_Rings_Olinordered__comm__semiring__strict @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).

thf(1896,plain,
    class_Rings_Olinordered__comm__semiring__strict @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(804,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I15_J) ).

thf(3808,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).

thf(766,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).

thf(3676,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).

thf(1146,axiom,
    ? [A: $i] :
    ! [B: $i] :
      ( ? [C: $i] :
          ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ C ) @ v_r )
          & ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ C ) )
            = ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) )
     => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mth2) ).

thf(4924,plain,
    ? [A: $i] :
    ! [B: $i] :
      ( ? [C: $i] :
          ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ C ) @ v_r )
          & ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ C ) )
            = ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) )
     => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).

thf(129,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
      <=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
            & ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
          | ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
            & ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).

thf(1600,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ C )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
         => ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
              & ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
            | ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
              & ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) )
        & ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
              & ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
            | ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
              & ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(1059,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__field @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( B
           != ( c_Groups_Ozero__class_Ozero @ D ) )
         => ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ ( c_Rings_Oinverse__class_Oinverse @ D @ C ) @ ( c_Rings_Oinverse__class_Oinverse @ D @ B ) ) @ A )
            = ( c_Groups_Ouminus__class_Ouminus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Rings_Oinverse__class_Oinverse @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A ) ) @ ( c_Rings_Oinverse__class_Oinverse @ D @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__inverse__lemma) ).

thf(4628,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__field @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( B
           != ( c_Groups_Ozero__class_Ozero @ D ) )
         => ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ ( c_Rings_Oinverse__class_Oinverse @ D @ C ) @ ( c_Rings_Oinverse__class_Oinverse @ D @ B ) ) @ A )
            = ( c_Groups_Ouminus__class_Ouminus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Rings_Oinverse__class_Oinverse @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A ) ) @ ( c_Rings_Oinverse__class_Oinverse @ D @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).

thf(669,axiom,
    ! [A: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__1) ).

thf(3389,plain,
    ! [A: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(408,axiom,
    class_Groups_Oabs__if @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oabs__if) ).

thf(2508,plain,
    class_Groups_Oabs__if @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(545,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__real__def) ).

thf(2964,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(80,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).

thf(1447,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(401,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
      <=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).

thf(2483,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ B )
     => ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
         => ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(984,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oab__group__add @ C )
     => ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__distrib) ).

thf(4364,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oab__group__add @ C )
     => ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).

thf(360,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__zero) ).

thf(2371,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(620,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
     => ? [B: $i] :
        ! [C: $i] :
          ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ C )
         => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( v_g____ @ ( hAPP @ v_f____ @ C ) ) @ v_z____ ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fz_I2_J) ).

thf(3243,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
     => ? [B: $i] :
        ! [C: $i] :
          ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ C )
         => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( v_g____ @ ( hAPP @ v_f____ @ C ) ) @ v_z____ ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(500,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__conv) ).

thf(2809,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ B ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ B )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(874,axiom,
    class_Rings_Omult__zero @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).

thf(4038,plain,
    class_Rings_Omult__zero @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).

thf(452,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).

thf(2639,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(1066,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Oordered__ring @ F )
     => ( ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
      <=> ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff1) ).

thf(4643,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Oordered__ring @ F )
     => ( ( ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
         => ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C ) @ A ) )
        & ( ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).

thf(235,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__div__pos__less) ).

thf(1943,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(13,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).

thf(1201,plain,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(498,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
     => ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__less__mono) ).

thf(2804,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
     => ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(1029,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) @ c_Int_OPls )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OPls ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I27_J) ).

thf(4519,plain,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) @ c_Int_OPls )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OPls ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OPls )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) @ c_Int_OPls ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).

thf(743,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__shift) ).

thf(3606,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).

thf(297,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
    <=> ( A
        = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).

thf(2154,plain,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
      & ( ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(104,axiom,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).

thf(1521,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(1051,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__ge__zero) ).

thf(4588,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).

thf(603,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__unique) ).

thf(3184,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(1016,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__half__sum) ).

thf(4475,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).

thf(436,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).

thf(2586,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(245,axiom,
    class_Groups_Oone @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).

thf(1975,plain,
    class_Groups_Oone @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(886,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
        = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
     => ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B )
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).

thf(4082,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
        = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
     => ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B )
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).

thf(489,axiom,
    class_Rings_Olinordered__idom @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).

thf(2762,plain,
    class_Rings_Olinordered__idom @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(663,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__mult) ).

thf(3378,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).

thf(689,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Int_Onumber__ring @ C )
     => ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) ) @ A )
        = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__number__of__mult) ).

thf(3435,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Int_Onumber__ring @ C )
     => ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) ) @ A )
        = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).

thf(832,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
      & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th) ).

thf(3899,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
      & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ( class_Rings_Odivision__ring @ A )
     => ( ( c_Rings_Oinverse__class_Oinverse @ A @ ( c_Groups_Oone__class_Oone @ A ) )
        = ( c_Groups_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__1) ).

thf(1206,plain,
    ! [A: $i] :
      ( ( class_Rings_Odivision__ring @ A )
     => ( ( c_Rings_Oinverse__class_Oinverse @ A @ ( c_Groups_Oone__class_Oone @ A ) )
        = ( c_Groups_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(709,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__minus__cancel) ).

thf(3503,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).

thf(527,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) )
          = ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__minus__divide__divide) ).

thf(2910,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) )
          = ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(454,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
      <=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).

thf(2646,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
     => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
         => ( c_Orderings_Oord__class_Oless @ D @ B @ A ) )
        & ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(1033,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
        = ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__special_I1_J) ).

thf(4531,plain,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
        = ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).

thf(859,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).

thf(3995,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).

thf(965,axiom,
    ! [A: $i] :
      ( ( A
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).

thf(4312,plain,
    ! [A: $i] :
      ( ( A
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).

thf(254,axiom,
    class_Rings_Ocomm__semiring__1 @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).

thf(2000,plain,
    class_Rings_Ocomm__semiring__1 @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(592,axiom,
    class_Groups_Omonoid__mult @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).

thf(3151,plain,
    class_Groups_Omonoid__mult @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(258,axiom,
    class_Rings_Oring__no__zero__divisors @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).

thf(2011,plain,
    class_Rings_Oring__no__zero__divisors @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(578,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ B )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).

thf(3097,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ B )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(1126,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
    <=> ? [C: $i] :
          ( A
          = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).

thf(4853,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
       => ? [C: $i] :
            ( A
            = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) )
      & ( ? [C: $i] :
            ( A
            = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).

thf(735,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
     => ( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
        = ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__diff) ).

thf(3582,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
     => ( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
        = ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).

thf(433,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).

thf(2574,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(778,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
    <=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
        & ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).

thf(3720,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
          & ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) )
      & ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
          & ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).

thf(88,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Olinordered__semiring__1 @ F )
     => ( ( c_Orderings_Oord__class_Oless__eq @ F @ E @ D )
       => ( ( c_Orderings_Oord__class_Oless__eq @ F @ C @ D )
         => ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ B )
           => ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ A )
             => ( ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
                  = ( c_Groups_Oone__class_Oone @ F ) )
               => ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ E ) @ ( c_Groups_Otimes__class_Otimes @ F @ A @ C ) ) @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__le) ).

thf(1470,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Olinordered__semiring__1 @ F )
     => ( ( c_Orderings_Oord__class_Oless__eq @ F @ E @ D )
       => ( ( c_Orderings_Oord__class_Oless__eq @ F @ C @ D )
         => ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ B )
           => ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ A )
             => ( ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
                  = ( c_Groups_Oone__class_Oone @ F ) )
               => ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ E ) @ ( c_Groups_Otimes__class_Otimes @ F @ A @ C ) ) @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(169,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I31_J) ).

thf(1708,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(279,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__le__div__pos) ).

thf(2093,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(382,axiom,
    class_Rings_Ocomm__semiring__1 @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).

thf(2441,plain,
    class_Rings_Ocomm__semiring__1 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(224,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
      <=> ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
          | ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__le__1__iff) ).

thf(1900,plain,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ B )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
         => ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
            | ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) )
        & ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
            | ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(21,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
    <=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
        & ( B != A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__le) ).

thf(1223,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
          & ( B != A ) ) )
      & ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
          & ( B != A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(379,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I13_J) ).

thf(2428,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(417,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Bit1) ).

thf(2541,plain,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(1133,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ B )
        = ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__le) ).

thf(4878,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ B )
        = ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).

thf(18,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__inverse__less__neg) ).

thf(1217,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(890,axiom,
    ! [A: $i,B: $i] :
      ( ( ( class_Int_Onumber__ring @ B )
        & ( class_Rings_Olinordered__idom @ B ) )
     => ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_Groups_Oabs__class_Oabs @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
            = ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) )
        & ( ~ ( c_Orderings_Oord__class_Oless @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_Groups_Oabs__class_Oabs @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
            = ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__number__of) ).

thf(4091,plain,
    ! [A: $i,B: $i] :
      ( ( ( class_Int_Onumber__ring @ B )
        & ( class_Rings_Olinordered__idom @ B ) )
     => ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_Groups_Oabs__class_Oabs @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
            = ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) )
        & ( ~ ( c_Orderings_Oord__class_Oless @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_Groups_Oabs__class_Oabs @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
            = ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).

thf(610,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).

thf(3207,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(60,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ B )
     => ( ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
          = ( c_Groups_Oone__class_Oone @ B ) )
      <=> ( A
          = ( c_Groups_Oone__class_Oone @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__1__iff) ).

thf(1343,plain,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ B )
     => ( ( ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
            = ( c_Groups_Oone__class_Oone @ B ) )
         => ( A
            = ( c_Groups_Oone__class_Oone @ B ) ) )
        & ( ( A
            = ( c_Groups_Oone__class_Oone @ B ) )
         => ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
            = ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

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

thf(2560,plain,
    class_Rings_Oordered__ring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(439,axiom,
    class_Groups_Oordered__comm__monoid__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).

thf(2596,plain,
    class_Groups_Oordered__comm__monoid__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(995,axiom,
    class_Orderings_Olinorder @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).

thf(4397,plain,
    class_Orderings_Olinorder @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).

thf(33,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__neg__lemma) ).

thf(1255,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(1004,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__cancel__ab__semigroup__add @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).

thf(4434,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__cancel__ab__semigroup__add @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).

thf(1057,axiom,
    ! [A: $i] :
      ( ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__is__id) ).

thf(4609,plain,
    ! [A: $i] :
      ( ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).

thf(1170,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Ocancel__semigroup__add @ D )
     => ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
          = ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).

thf(4989,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Ocancel__semigroup__add @ D )
     => ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
          = ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).

thf(3,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Oordered__semiring @ E )
     => ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
           => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
             => ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono_H) ).

thf(1174,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Oordered__semiring @ E )
     => ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
           => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
             => ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(158,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__comm__semiring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).

thf(1676,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__comm__semiring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(295,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Fields_Ofield__inverse__zero @ D )
        & ( class_Int_Onumber @ D ) )
     => ( ( ( c_Int_Onumber__class_Onumber__of @ D @ C )
          = ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
      <=> ( ( ( A
             != ( c_Groups_Ozero__class_Ozero @ D ) )
           => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ A )
              = B ) )
          & ( ( A
              = ( c_Groups_Ozero__class_Ozero @ D ) )
           => ( ( c_Int_Onumber__class_Onumber__of @ D @ C )
              = ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of) ).

thf(2133,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Fields_Ofield__inverse__zero @ D )
        & ( class_Int_Onumber @ D ) )
     => ( ( ( ( c_Int_Onumber__class_Onumber__of @ D @ C )
            = ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
         => ( ( ( A
               != ( c_Groups_Ozero__class_Ozero @ D ) )
             => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ A )
                = B ) )
            & ( ( A
                = ( c_Groups_Ozero__class_Ozero @ D ) )
             => ( ( c_Int_Onumber__class_Onumber__of @ D @ C )
                = ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) )
        & ( ( ( ( A
               != ( c_Groups_Ozero__class_Ozero @ D ) )
             => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ A )
                = B ) )
            & ( ( A
                = ( c_Groups_Ozero__class_Ozero @ D ) )
             => ( ( c_Int_Onumber__class_Onumber__of @ D @ C )
                = ( c_Groups_Ozero__class_Ozero @ D ) ) ) )
         => ( ( c_Int_Onumber__class_Onumber__of @ D @ C )
            = ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(97,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A )
        = ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).

thf(1502,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A )
        = ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(181,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).

thf(1751,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ C )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(900,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ B ) )
      = ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__divide__square__eq) ).

thf(4128,plain,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ B ) )
      = ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).

thf(618,axiom,
    class_Fields_Ofield__inverse__zero @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).

thf(3239,plain,
    class_Fields_Ofield__inverse__zero @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(568,axiom,
    ! [A: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__2__right) ).

thf(3069,plain,
    ! [A: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(925,axiom,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).

thf(4204,plain,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).

thf(538,axiom,
    class_Groups_Olinordered__ab__group__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).

thf(2937,plain,
    class_Groups_Olinordered__ab__group__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(1010,axiom,
    ! [A: $i,B: $i] :
      ( ( ( class_Int_Onumber__ring @ B )
        & ( class_Rings_Olinordered__idom @ B ) )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
      <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I2_J) ).

thf(4449,plain,
    ! [A: $i,B: $i] :
      ( ( ( class_Int_Onumber__ring @ B )
        & ( class_Rings_Olinordered__idom @ B ) )
     => ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
         => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) )
        & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) @ A )
         => ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).

thf(1020,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
      <=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
            & ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
          | ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
            & ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__divide__iff) ).

thf(4493,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ C )
     => ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
         => ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
              & ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
            | ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
              & ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) )
        & ( ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
              & ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
            | ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
              & ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).

thf(806,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
     => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__less__half__sum) ).

thf(3816,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
     => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).

thf(67,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).

thf(1370,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(265,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ C ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus__eq) ).

thf(2032,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(550,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
        = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
    <=> ( ( B
          = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
        & ( A
          = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).

thf(2986,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
          = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
       => ( ( B
            = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
          & ( A
            = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
      & ( ( ( B
            = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
          & ( A
            = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
       => ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
          = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(624,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__field @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) )
          = ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__norm__divide) ).

thf(3250,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__field @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) )
          = ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(294,axiom,
    c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).

thf(2132,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(522,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__semidom @ A )
     => ~ ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).

thf(2890,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__semidom @ A )
     => ~ ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(650,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( ( c_Groups_Oabs__class_Oabs @ A @ ( c_Groups_Oone__class_Oone @ A ) )
        = ( c_Groups_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__one) ).

thf(3339,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( ( c_Groups_Oabs__class_Oabs @ A @ ( c_Groups_Oone__class_Oone @ A ) )
        = ( c_Groups_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(797,axiom,
    ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
    = ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I115_J) ).

thf(3778,plain,
    ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
    = ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).

thf(25,axiom,
    class_Rings_Oordered__semiring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).

thf(1238,plain,
    class_Rings_Oordered__semiring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(830,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
    <=> ? [C: $i] :
          ( A
          = ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).

thf(3889,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
       => ? [C: $i] :
            ( A
            = ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) ) )
      & ( ? [C: $i] :
            ( A
            = ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).

thf(846,axiom,
    class_Int_Onumber__ring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).

thf(3948,plain,
    class_Int_Onumber__ring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).

thf(207,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
         => ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__less__imp__less) ).

thf(1837,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
         => ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(303,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
              = ( c_Groups_Ozero__class_Ozero @ C ) )
          <=> ( ( B
                = ( c_Groups_Ozero__class_Ozero @ C ) )
              & ( A
                = ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).

thf(2200,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( ( ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
                = ( c_Groups_Ozero__class_Ozero @ C ) )
             => ( ( B
                  = ( c_Groups_Ozero__class_Ozero @ C ) )
                & ( A
                  = ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
            & ( ( ( B
                  = ( c_Groups_Ozero__class_Ozero @ C ) )
                & ( A
                  = ( c_Groups_Ozero__class_Ozero @ C ) ) )
             => ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
                = ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(920,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ C ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ath) ).

thf(4187,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ C ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).

thf(206,axiom,
    class_Rings_Oordered__ring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).

thf(1836,plain,
    class_Rings_Oordered__ring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(344,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
         => ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).

thf(2327,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
         => ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(1092,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
        = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
    <=> ( ( ( B
            = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
          & ( A
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
        | ( ( B
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
          & ( A
            = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__add) ).

thf(4740,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
          = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
       => ( ( ( B
              = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
            & ( A
              = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
          | ( ( B
              = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
            & ( A
              = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
      & ( ( ( ( B
              = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
            & ( A
              = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
          | ( ( B
              = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
            & ( A
              = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
       => ( ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
          = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).

thf(306,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ C ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff1) ).

thf(2211,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(139,axiom,
    class_Rings_Osemiring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).

thf(1634,plain,
    class_Rings_Osemiring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(677,axiom,
    class_Groups_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).

thf(3408,plain,
    class_Groups_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(121,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring @ B )
     => ( ( A
         != ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__inverse__eq) ).

thf(1573,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring @ B )
     => ( ( A
         != ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(492,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A )
        = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    <=> ( A
        = ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__eq__0__iff) ).

thf(2769,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ( A
          = ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) )
      & ( ( A
          = ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) )
       => ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(629,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ A ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).

thf(3271,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ A ) ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(850,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ c_Int_OPls ) @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ B )
        = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__eq__diff__pred) ).

thf(3958,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ c_Int_OPls ) @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ B )
        = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).

thf(394,axiom,
    class_Rings_Olinordered__comm__semiring__strict @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).

thf(2464,plain,
    class_Rings_Olinordered__comm__semiring__strict @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(952,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__pos__neg) ).

thf(4280,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).

thf(1050,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__diff__def) ).

thf(4585,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).

thf(380,axiom,
    ! [A: $i] :
      ( ( class_Int_Onumber__ring @ A )
     => ( ( c_Groups_Oone__class_Oone @ A )
        = ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I110_J) ).

thf(2433,plain,
    ! [A: $i] :
      ( ( class_Int_Onumber__ring @ A )
     => ( ( c_Groups_Oone__class_Oone @ A )
        = ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(398,axiom,
    class_Groups_Oone @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).

thf(2477,plain,
    class_Groups_Oone @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(1086,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ B )
          = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ A ) )
      <=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ B )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).

thf(4725,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ B )
            = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ A ) )
         => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ B )
            = A ) )
        & ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ B )
            = A )
         => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ B )
            = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).

thf(429,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).

thf(2565,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(347,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ C )
     => ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__mult__distrib) ).

thf(2332,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ C )
     => ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(910,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ E )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ B @ A ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__diff__triangle__ineq) ).

thf(4155,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ E )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ B @ A ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).

thf(1155,axiom,
    class_RealVector_Oreal__normed__field @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__field) ).

thf(4947,plain,
    class_RealVector_Oreal__normed__field @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).

thf(654,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
        = ( c_Groups_Oplus__class_Oplus @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

thf(3349,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
        = ( c_Groups_Oplus__class_Oplus @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(270,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
      <=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
            & ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
          | ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
            & ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__divide__iff) ).

thf(2068,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ C )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
         => ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
              & ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
            | ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
              & ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) )
        & ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
              & ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
            | ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
              & ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(201,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Odivision__ring @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( ( c_Rings_Oinverse__class_Odivide @ D @ B @ C )
            = A )
        <=> ( B
            = ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__divide__eq__eq) ).

thf(1819,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Odivision__ring @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( ( ( c_Rings_Oinverse__class_Odivide @ D @ B @ C )
              = A )
           => ( B
              = ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) )
          & ( ( B
              = ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) )
           => ( ( c_Rings_Oinverse__class_Odivide @ D @ B @ C )
              = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(419,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ D @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__sum__triangle__ineq) ).

thf(2547,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ D @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(404,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
        = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) )
    <=> ( ( B
          = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
        & ( A
          = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).

thf(2492,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
          = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) )
       => ( ( B
            = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
          & ( A
            = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
      & ( ( ( B
            = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
          & ( A
            = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
       => ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
          = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(780,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq2__sym) ).

thf(3727,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).

thf(42,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__field @ B )
     => ( ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Ozero) ).

thf(1281,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__field @ B )
     => ( ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(756,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
      <=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).

thf(3647,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
     => ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
         => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
        & ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).

thf(885,axiom,
    ? [A: $i] :
    ! [B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ B )
     => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( v_g____ @ ( hAPP @ v_f____ @ B ) ) @ v_z____ ) ) @ v_d____ ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_AN_O_AALL_An_062_061N_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_096) ).

thf(4080,plain,
    ? [A: $i] :
    ! [B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ B )
     => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( v_g____ @ ( hAPP @ v_f____ @ B ) ) @ v_z____ ) ) @ v_d____ ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).

thf(882,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( class_Int_Onumber__ring @ C )
        & ( class_Rings_Olinordered__idom @ C ) )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
      <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__number__of) ).

thf(4063,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( class_Int_Onumber__ring @ C )
        & ( class_Rings_Olinordered__idom @ C ) )
     => ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
         => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
        & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).

thf(457,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) )
        = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) @ ( c_Nat_OSuc @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq1) ).

thf(2653,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) )
        = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) @ ( c_Nat_OSuc @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(680,axiom,
    ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
    = ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ c_Int_OPls ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I113_J) ).

thf(3413,plain,
    ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
    = ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ c_Int_OPls ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(466,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring__inverse__zero @ B )
     => ( ( ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ A )
            = ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( A
           != ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ A )
            = ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__self__if) ).

thf(2685,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring__inverse__zero @ B )
     => ( ( ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ A )
            = ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( A
           != ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ A )
            = ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(194,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).

thf(1804,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ B )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(524,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq4) ).

thf(2895,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(510,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__div__algebra @ C )
     => ( ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult) ).

thf(2841,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__div__algebra @ C )
     => ( ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(69,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__ring @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Otimes__class_Otimes @ B @ A @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__square) ).

thf(1375,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__ring @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Otimes__class_Otimes @ B @ A @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(1003,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__gt__zero__cancel__iff) ).

thf(4429,plain,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).

thf(125,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
    <=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).

thf(1587,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) )
      & ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(409,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add) ).

thf(2509,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(667,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Olinordered__idom @ E )
     => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oabs__class_Oabs @ E @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oabs__class_Oabs @ E @ B ) @ A )
         => ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Oabs__class_Oabs @ E @ D ) @ ( c_Groups_Oabs__class_Oabs @ E @ B ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__less) ).

thf(3386,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Olinordered__idom @ E )
     => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oabs__class_Oabs @ E @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oabs__class_Oabs @ E @ B ) @ A )
         => ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Oabs__class_Oabs @ E @ D ) @ ( c_Groups_Oabs__class_Oabs @ E @ B ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(757,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
      <=> ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
            & ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
          | ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
            & ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__0__iff) ).

thf(3650,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ C )
     => ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
              & ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
            | ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
              & ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) )
        & ( ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
              & ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
            | ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
              & ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).

thf(895,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
        = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).

thf(4109,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
       => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).

thf(691,axiom,
    ( ? [A: $i] :
        ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) @ v_r )
        & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ A ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) )
  <=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_J_A_061_A_I_N_As_A_060_A_N_As_J_096) ).

thf(3440,plain,
    ( ( ? [A: $i] :
          ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) @ v_r )
          & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ A ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) )
     => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) )
    & ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) )
     => ? [A: $i] :
          ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) @ v_r )
          & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ A ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).

thf(852,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__less__iff) ).

thf(3968,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).

thf(64,axiom,
    class_Rings_Olinordered__semidom @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).

thf(1360,plain,
    class_Rings_Olinordered__semidom @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(697,axiom,
    ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
    = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__nat__def) ).

thf(3467,plain,
    ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
    = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).

thf(773,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) )
      = ( c_Int_OBit0 @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit0__Bit0) ).

thf(3699,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) )
      = ( c_Int_OBit0 @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).

thf(334,axiom,
    class_Rings_Oring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).

thf(2300,plain,
    class_Rings_Oring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(210,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).

thf(1851,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(186,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).

thf(1772,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(35,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
      = ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__numeral__code_I5_J) ).

thf(1259,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
      = ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(435,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
        = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
    <=> ( ( B
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
        & ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).

thf(2577,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( ( B
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
          & ( A
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
      & ( ( ( B
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
          & ( A
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
       => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(665,axiom,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).

thf(3381,plain,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(468,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ C )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono) ).

thf(2694,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ C )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(1031,axiom,
    ! [A: $i] :
      ( c_Int_OPls
     != ( c_Int_OBit1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I39_J) ).

thf(4525,plain,
    ! [A: $i] :
      ( c_Int_OPls
     != ( c_Int_OBit1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).

thf(1077,axiom,
    ! [A: $i] :
      ( ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ A )
      = ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__norm__def) ).

thf(4693,plain,
    ! [A: $i] :
      ( ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ A )
      = ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).

thf(1148,axiom,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).

thf(4930,plain,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).

thf(415,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring @ B )
     => ( ( A
         != ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ A )
          = ( c_Groups_Oone__class_Oone @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__self) ).

thf(2537,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring @ B )
     => ( ( A
         != ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ A )
          = ( c_Groups_Oone__class_Oone @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(600,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).

thf(3176,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(1114,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
     => ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
          = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).

thf(4817,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
     => ( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
            = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
            = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).

thf(956,axiom,
    class_RealVector_Oreal__field @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__field) ).

thf(4291,plain,
    class_RealVector_Oreal__field @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).

thf(973,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Ocancel__semigroup__add @ D )
     => ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
          = ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
      <=> ( C = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).

thf(4333,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Ocancel__semigroup__add @ D )
     => ( ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
            = ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
         => ( C = A ) )
        & ( ( C = A )
         => ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
            = ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).

thf(263,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oab__group__add @ C )
     => ( ( B = A )
      <=> ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).

thf(2023,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oab__group__add @ C )
     => ( ( ( B = A )
         => ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ C ) ) )
        & ( ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(817,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
      = ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__numeral__code_I6_J) ).

thf(3846,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
      = ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).

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

thf(1182,plain,
    class_Rings_Oordered__cancel__semiring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(776,axiom,
    ! [A: $i,B: $i] :
      ( ( ( class_Int_Onumber @ B )
        & ( class_Rings_Odivision__ring @ B ) )
     => ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
        = ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__divide__number__of) ).

thf(3714,plain,
    ! [A: $i,B: $i] :
      ( ( ( class_Int_Onumber @ B )
        & ( class_Rings_Odivision__ring @ B ) )
     => ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
        = ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).

thf(376,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) )
      = ( c_Int_OBit0 @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I7_J) ).

thf(2419,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) )
      = ( c_Int_OBit0 @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(1026,axiom,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__one__not__less__self) ).

thf(4513,plain,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).

thf(266,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Fields_Ofield__inverse__zero @ D )
        & ( class_Int_Onumber @ D ) )
     => ( ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
          = A )
      <=> ( ( ( ( c_Int_Onumber__class_Onumber__of @ D @ B )
             != ( c_Groups_Ozero__class_Ozero @ D ) )
           => ( C
              = ( c_Groups_Otimes__class_Otimes @ D @ A @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
          & ( ( ( c_Int_Onumber__class_Onumber__of @ D @ B )
              = ( c_Groups_Ozero__class_Ozero @ D ) )
           => ( A
              = ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq__number__of1) ).

thf(2038,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Fields_Ofield__inverse__zero @ D )
        & ( class_Int_Onumber @ D ) )
     => ( ( ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
            = A )
         => ( ( ( ( c_Int_Onumber__class_Onumber__of @ D @ B )
               != ( c_Groups_Ozero__class_Ozero @ D ) )
             => ( C
                = ( c_Groups_Otimes__class_Otimes @ D @ A @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
            & ( ( ( c_Int_Onumber__class_Onumber__of @ D @ B )
                = ( c_Groups_Ozero__class_Ozero @ D ) )
             => ( A
                = ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) )
        & ( ( ( ( ( c_Int_Onumber__class_Onumber__of @ D @ B )
               != ( c_Groups_Ozero__class_Ozero @ D ) )
             => ( C
                = ( c_Groups_Otimes__class_Otimes @ D @ A @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
            & ( ( ( c_Int_Onumber__class_Onumber__of @ D @ B )
                = ( c_Groups_Ozero__class_Ozero @ D ) )
             => ( A
                = ( c_Groups_Ozero__class_Ozero @ D ) ) ) )
         => ( ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
            = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(275,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oordered__ring @ C )
     => ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
            & ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
          | ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
            & ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
       => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).

thf(2085,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oordered__ring @ C )
     => ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
            & ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) )
          | ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
            & ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
       => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(1008,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__cancel__ab__semigroup__add @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).

thf(4444,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__cancel__ab__semigroup__add @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).

thf(1113,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
      = ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc) ).

thf(4814,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
      = ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).

thf(729,axiom,
    class_Groups_Ocomm__monoid__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).

thf(3573,plain,
    class_Groups_Ocomm__monoid__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).

thf(843,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Oordered__ring @ F )
     => ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff1) ).

thf(3935,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Oordered__ring @ F )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C ) @ A ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) @ D ) @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).

thf(968,axiom,
    ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ c_Int_OPls ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I2_J) ).

thf(4320,plain,
    ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ c_Int_OPls ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).

thf(161,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) )
    <=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
        & ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).

thf(1683,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
          & ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) )
      & ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
          & ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(590,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
          = A )
      <=> ( B
          = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).

thf(3141,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
            = A )
         => ( B
            = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) ) )
        & ( ( B
            = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) )
         => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
            = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(848,axiom,
    class_Groups_Ozero @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).

thf(3952,plain,
    class_Groups_Ozero @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).

thf(642,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessD) ).

thf(3311,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(65,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ F @ E ) @ D )
        = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) @ A ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C )
         => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ D )
           => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
             => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ F )
               => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ E @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).

thf(1361,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ F @ E ) @ D )
        = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) @ A ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C )
         => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ D )
           => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
             => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ F )
               => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ E @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(1127,axiom,
    ! [A: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit0 @ A ) )
      = ( c_Int_OBit0 @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ c_Int_OPls @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I3_J) ).

thf(4860,plain,
    ! [A: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit0 @ A ) )
      = ( c_Int_OBit0 @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ c_Int_OPls @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).

thf(241,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).

thf(1964,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(234,axiom,
    class_Rings_Oring__1 @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).

thf(1942,plain,
    class_Rings_Oring__1 @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(839,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
        = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).

thf(3922,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A )
        = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).

thf(1049,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Olinordered__ab__group__add @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
      <=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).

thf(4582,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Olinordered__ab__group__add @ B )
     => ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).

thf(601,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Int_Onumber @ D )
        & ( class_Rings_Osemiring @ D ) )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__distrib__number__of) ).

thf(3179,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Int_Onumber @ D )
        & ( class_Rings_Osemiring @ D ) )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(611,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ B ) @ A )
      = ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__assoc) ).

thf(3210,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ B ) @ A )
      = ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(427,axiom,
    class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).

thf(2561,plain,
    class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(1099,axiom,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__one__gt__zero) ).

thf(4772,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).

thf(518,axiom,
    class_RealVector_Oreal__normed__algebra__1 @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).

thf(2868,plain,
    class_RealVector_Oreal__normed__algebra__1 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(992,axiom,
    ( ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal )
   != ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).

thf(4389,plain,
    ( ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal )
   != ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).

thf(966,axiom,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).

thf(4315,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).

thf(340,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Olinordered__ab__group__add @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).

thf(2312,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Olinordered__ab__group__add @ B )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(556,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
    <=> ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
        | ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__add1__eq) ).

thf(3010,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
          | ( B = A ) ) )
      & ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
          | ( B = A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(1037,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Omonoid__mult @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__left) ).

thf(4545,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Omonoid__mult @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).

thf(1152,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__div__algebra @ B )
     => ( ( A
         != ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
          = ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__norm__inverse) ).

thf(4938,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__div__algebra @ B )
     => ( ( A
         != ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
          = ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).

thf(166,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).

thf(1700,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(232,axiom,
    ( ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INVERSE__ZERO) ).

thf(1937,plain,
    ( ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(196,axiom,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0__right) ).

thf(1810,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(880,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).

thf(4054,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).

thf(17,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).

thf(1214,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(352,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Olinordered__ab__group__add @ B )
     => ( ( ( c_Groups_Ozero__class_Ozero @ B )
          = ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) )
      <=> ( A
          = ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__zero__sym) ).

thf(2349,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Olinordered__ab__group__add @ B )
     => ( ( ( ( c_Groups_Ozero__class_Ozero @ B )
            = ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) )
         => ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_Groups_Ozero__class_Ozero @ B )
            = ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(548,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
     => ( ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
        | ( A
          = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).

thf(2978,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
     => ( ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
        | ( A
          = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(455,axiom,
    ( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
    = ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ c_Int_OPls ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__is__num__zero) ).

thf(2649,plain,
    ( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
    = ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ c_Int_OPls ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(1089,axiom,
    class_Rings_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).

thf(4736,plain,
    class_Rings_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).

thf(178,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
         => ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).

thf(1744,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
         => ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(745,axiom,
    class_Fields_Ofield @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield) ).

thf(3611,plain,
    class_Fields_Ofield @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).

thf(720,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A )
      <=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
          & ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__less__iff) ).

thf(3541,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A )
         => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
            & ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) )
        & ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
            & ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).

thf(337,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
      <=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
          & ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__inverse__iff) ).

thf(2304,plain,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ B )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
         => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
            & ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) )
        & ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
            & ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) )
         => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(566,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Fields_Ofield @ E )
     => ( ( D
         != ( c_Groups_Ozero__class_Ozero @ E ) )
       => ( ( C
           != ( c_Groups_Ozero__class_Ozero @ E ) )
         => ( ( c_Groups_Ominus__class_Ominus @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ D ) @ ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) )
            = ( c_Rings_Oinverse__class_Odivide @ E @ ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ A @ D ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__frac__eq) ).

thf(3059,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Fields_Ofield @ E )
     => ( ( D
         != ( c_Groups_Ozero__class_Ozero @ E ) )
       => ( ( C
           != ( c_Groups_Ozero__class_Ozero @ E ) )
         => ( ( c_Groups_Ominus__class_Ominus @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ D ) @ ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) )
            = ( c_Rings_Oinverse__class_Odivide @ E @ ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ A @ D ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(526,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ c_Int_OPls )
       => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
          = ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ) )
      & ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ c_Int_OPls )
       => ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls )
           => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
              = ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) ) )
          & ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls )
           => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
              = ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nat__number__of) ).

thf(2900,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ c_Int_OPls )
       => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
          = ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ) )
      & ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ c_Int_OPls )
       => ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls )
           => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
              = ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) ) )
          & ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls )
           => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
              = ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(785,axiom,
    ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
    = ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__3__eq__3) ).

thf(3743,plain,
    ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
    = ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).

thf(514,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semidom @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__1__mult) ).

thf(2851,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semidom @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(395,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring @ B )
     => ( ( A
         != ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
          = ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__eq__divide) ).

thf(2465,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring @ B )
     => ( ( A
         != ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
          = ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(407,axiom,
    ! [A: $i,B: $i] :
      ( ( ( class_Int_Onumber__ring @ B )
        & ( class_Rings_Olinordered__idom @ B ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I4_J) ).

thf(2505,plain,
    ! [A: $i,B: $i] :
      ( ( ( class_Int_Onumber__ring @ B )
        & ( class_Rings_Olinordered__idom @ B ) )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Int_OBit1 @ c_Int_OPls ) )
         => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(237,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
        = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
    <=> ( ( B = A )
        | ( C
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel1) ).

thf(1947,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
          = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
       => ( ( B = A )
          | ( C
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
      & ( ( ( B = A )
          | ( C
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
       => ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
          = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(937,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
      = ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__numeral__code_I9_J) ).

thf(4231,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
      = ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).

thf(932,axiom,
    class_Groups_Oone @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).

thf(4223,plain,
    class_Groups_Oone @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).

thf(329,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ F @ E ) @ D )
        = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) @ A ) )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ D @ F )
         => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
           => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
             => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ F )
               => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).

thf(2285,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ F @ E ) @ D )
        = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) @ A ) )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ D @ F )
         => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
           => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
             => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ F )
               => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(406,axiom,
    class_RealVector_Oreal__field @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__field) ).

thf(2504,plain,
    class_RealVector_Oreal__field @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(387,axiom,
    ! [A: $i,B: $i] :
      ( ( B != A )
     => ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).

thf(2450,plain,
    ! [A: $i,B: $i] :
      ( ( B != A )
     => ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(536,axiom,
    ! [A: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).

thf(2932,plain,
    ! [A: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(704,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).

thf(3486,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).

thf(91,axiom,
    class_Groups_Omonoid__mult @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).

thf(1478,plain,
    class_Groups_Omonoid__mult @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(31,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ C )
     => ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
        = ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ominus) ).

thf(1249,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ C )
     => ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
        = ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(108,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
         => ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).

thf(1530,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
         => ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(509,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) @ c_Int_OPls )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I12_J) ).

thf(2836,plain,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) @ c_Int_OPls )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) @ c_Int_OPls ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(353,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).

thf(2355,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(1018,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Int_OBit1 @ B )
        = ( c_Int_OBit1 @ A ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I51_J) ).

thf(4482,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( c_Int_OBit1 @ B )
          = ( c_Int_OBit1 @ A ) )
       => ( B = A ) )
      & ( ( B = A )
       => ( ( c_Int_OBit1 @ B )
          = ( c_Int_OBit1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).

thf(941,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
        = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
    <=> ( ( B
          = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
        & ( A
          = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).

thf(4244,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
          = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
       => ( ( B
            = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
          & ( A
            = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
      & ( ( ( B
            = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
          & ( A
            = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
       => ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
          = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).

thf(791,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__number__of__int__code) ).

thf(3760,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).

thf(678,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ B ) @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).

thf(3409,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ B ) @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(491,axiom,
    ! [A: $i] :
      ( ( c_Int_OBit0 @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__def) ).

thf(2766,plain,
    ! [A: $i] :
      ( ( c_Int_OBit0 @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(1140,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( B
          = ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
      <=> ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).

thf(4902,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( ( B
            = ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
         => ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ C ) ) )
        & ( ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( B
            = ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).

thf(29,axiom,
    ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
    = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__0) ).

thf(1246,plain,
    ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
    = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(647,axiom,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ c_Int_OPls )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls__right) ).

thf(3333,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ c_Int_OPls )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(1159,axiom,
    ? [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_An_O_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_An_096) ).

thf(4953,plain,
    ? [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).

thf(909,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
        <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__iff) ).

thf(4152,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
       => ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
           => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
          & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
           => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).

thf(945,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Int_Onumber @ D )
        & ( class_Rings_Oring @ D ) )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__diff__distrib__number__of) ).

thf(4259,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Int_Onumber @ D )
        & ( class_Rings_Oring @ D ) )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).

thf(1076,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Int_OBit0 @ B )
     != ( c_Int_OBit1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I49_J) ).

thf(4689,plain,
    ! [A: $i,B: $i] :
      ( ( c_Int_OBit0 @ B )
     != ( c_Int_OBit1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).

thf(554,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
     => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).

thf(3005,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
     => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(324,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono1) ).

thf(2272,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(659,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) )
      = ( c_Int_OBit1 @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit1__Bit0) ).

thf(3364,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) )
      = ( c_Int_OBit1 @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(136,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).

thf(1627,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(982,axiom,
    class_Rings_Ono__zero__divisors @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).

thf(4361,plain,
    class_Rings_Ono__zero__divisors @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).

thf(106,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
        = ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).

thf(1525,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
        = ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(700,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
     => ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucE) ).

thf(3476,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
     => ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).

thf(789,axiom,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) @ A )
     != ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__nonzero) ).

thf(3755,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) @ A )
     != ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).

thf(450,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Groups_Ominus__class_Ominus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
          = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__diff__eq__iff) ).

thf(2634,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Groups_Ominus__class_Ominus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
          = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(812,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) ) )
        & ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of1) ).

thf(3834,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) ) )
        & ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).

thf(534,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
      = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).

thf(2926,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
      = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(979,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Nat_OSuc @ B )
        = ( c_Nat_OSuc @ A ) )
     => ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).

thf(4352,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Nat_OSuc @ B )
        = ( c_Nat_OSuc @ A ) )
     => ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).

thf(198,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ E )
     => ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
         => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
           => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
             => ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).

thf(1814,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ E )
     => ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
         => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
           => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
             => ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(164,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oordered__cancel__semiring @ C )
     => ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
            & ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
          | ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
            & ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) )
       => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).

thf(1695,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oordered__cancel__semiring @ C )
     => ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
            & ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
          | ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
            & ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) )
       => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(484,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ C )
     => ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
        = ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__divide) ).

thf(2748,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ C )
     => ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
        = ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(529,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
        = ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__special_I2_J) ).

thf(2915,plain,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
        = ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(815,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leI) ).

thf(3841,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).

thf(8,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field @ B )
     => ( ( A
         != ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Groups_Oabs__class_Oabs @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
          = ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__abs__inverse) ).

thf(1185,plain,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field @ B )
     => ( ( A
         != ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Groups_Oabs__class_Oabs @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
          = ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(252,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ E )
     => ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
           => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
             => ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).

thf(1996,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ E )
     => ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
           => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
             => ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(27,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ogroup__add @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ B @ A @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self) ).

thf(1241,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ogroup__add @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ B @ A @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(726,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Omonoid__add @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).

thf(3563,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Omonoid__add @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).

thf(1043,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
     => ( ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
        | ( A
          = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__2__cases) ).

thf(4567,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
     => ( ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
        | ( A
          = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).

thf(304,axiom,
    c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ c_Int_OPls ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of2) ).

thf(2208,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ c_Int_OPls ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(1104,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
    <=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ A ) )
        & ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__number__of) ).

thf(4782,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
       => ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
           => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ A ) )
          & ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ) )
      & ( ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
           => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ A ) )
          & ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).

thf(632,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) )
    <=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
        & ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).

thf(3279,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
          & ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ) )
      & ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
          & ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(928,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ A )
        = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).

thf(4212,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ A )
        = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).

thf(737,axiom,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__refl) ).

thf(3587,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).

thf(641,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I16_J) ).

thf(3306,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(740,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__neg__neg) ).

thf(3592,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).

thf(861,axiom,
    ! [A: $i] :
      ( ( class_Int_Onumber__ring @ A )
     => ( ( c_Int_Onumber__class_Onumber__of @ A @ c_Int_OPls )
        = ( c_Groups_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Pls) ).

thf(3999,plain,
    ! [A: $i] :
      ( ( class_Int_Onumber__ring @ A )
     => ( ( c_Int_Onumber__class_Onumber__of @ A @ c_Int_OPls )
        = ( c_Groups_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).

thf(544,axiom,
    class_Rings_Oring__no__zero__divisors @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).

thf(2963,plain,
    class_Rings_Oring__no__zero__divisors @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(359,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Omult__zero @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__left) ).

thf(2368,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Omult__zero @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(154,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( ( ( c_Groups_Oabs__class_Oabs @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ B ) )
      <=> ( A
          = ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__eq__0) ).

thf(1663,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( ( ( ( c_Groups_Oabs__class_Oabs @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_Groups_Oabs__class_Oabs @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(606,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
     => ( ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred) ).

thf(3190,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
     => ( ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(102,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring @ B )
     => ( ( A
         != ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
         != ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__imp__inverse__nonzero) ).

thf(1515,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring @ B )
     => ( ( A
         != ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
         != ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(310,axiom,
    class_Groups_Oab__semigroup__mult @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).

thf(2221,plain,
    class_Groups_Oab__semigroup__mult @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(873,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ D @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).

thf(4036,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ D @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).

thf(302,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A )
      <=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
           => ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) )
          & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
           => ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) @ C ) )
              & ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq) ).

thf(2189,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ D )
     => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A )
         => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
             => ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) @ C ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) )
        & ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
             => ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) @ C ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(551,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
      <=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__less__0__iff) ).

thf(2995,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(132,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing) ).

thf(1616,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(683,axiom,
    class_Groups_Oordered__ab__group__add__abs @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).

thf(3422,plain,
    class_Groups_Oordered__ab__group__add__abs @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

thf(226,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Int_Onumber__ring @ C )
     => ( ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__mult) ).

thf(1906,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Int_Onumber__ring @ C )
     => ( ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(255,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonneg__neg) ).

thf(2001,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(172,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Odivision__ring @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( ( c_Groups_Otimes__class_Otimes @ D @ B @ C )
            = A )
         => ( B
            = ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__imp) ).

thf(1727,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Odivision__ring @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( ( c_Groups_Otimes__class_Otimes @ D @ B @ C )
            = A )
         => ( B
            = ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(901,axiom,
    class_Int_Onumber @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).

thf(4131,plain,
    class_Int_Onumber @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).

thf(1082,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).

thf(4708,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).

thf(39,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring__inverse__zero @ C )
     => ( ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
          = ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__imp__eq) ).

thf(1273,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring__inverse__zero @ C )
     => ( ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
          = ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(114,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Olinordered__ab__group__add @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).

thf(1548,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Olinordered__ab__group__add @ B )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(1070,axiom,
    ! [A: $i] :
      ( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__Suc) ).

thf(4657,plain,
    ! [A: $i] :
      ( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).

thf(635,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__cancel) ).

thf(3289,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(630,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gt__half__sum) ).

thf(3274,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(1055,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A )
      <=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
          & ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__iff) ).

thf(4599,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ C )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
            & ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) )
        & ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
            & ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).

thf(1145,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I15_J) ).

thf(4919,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).

thf(586,axiom,
    class_Groups_Ocancel__semigroup__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).

thf(3130,plain,
    class_Groups_Ocancel__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(182,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
      <=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__positive__iff__positive) ).

thf(1754,plain,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ B )
     => ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
         => ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
        & ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
         => ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(990,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq3) ).

thf(4380,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).

thf(1131,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
     => ( B != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).

thf(4872,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).

thf(160,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
        <=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__le__divide__eq) ).

thf(1680,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ A ) )
          & ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ A )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(165,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__right__mono__neg) ).

thf(1698,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(239,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ E )
     => ( ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ E @ B @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).

thf(1959,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ E )
     => ( ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ E @ B @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(423,axiom,
    class_Groups_Ocomm__monoid__mult @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).

thf(2556,plain,
    class_Groups_Ocomm__monoid__mult @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(896,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Omonoid__add @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).

thf(4116,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Omonoid__add @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).

thf(657,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__0__less__add__iff) ).

thf(3358,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(824,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
    <=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
        | ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq) ).

thf(3871,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
          | ( B = A ) ) )
      & ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
          | ( B = A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).

thf(627,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
    <=> ( A
        = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zabs__less__one__iff) ).

thf(3257,plain,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
       => ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
      & ( ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(476,axiom,
    ! [A: $i] :
      ( ( c_Int_OBit1 @ A )
     != c_Int_OPls ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I46_J) ).

thf(2717,plain,
    ! [A: $i] :
      ( ( c_Int_OBit1 @ A )
     != c_Int_OPls ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(19,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__inverse__less) ).

thf(1219,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(572,axiom,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__Suc__gt__zero) ).

thf(3079,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(944,axiom,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ A )
      = ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__2__eq__Suc) ).

thf(4256,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ A )
      = ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).

thf(975,axiom,
    ! [A: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__1) ).

thf(4340,plain,
    ! [A: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).

thf(127,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__semidom @ A )
     => ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__one) ).

thf(1595,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__semidom @ A )
     => ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(829,axiom,
    class_Rings_Omult__zero @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).

thf(3888,plain,
    class_Rings_Omult__zero @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).

thf(949,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
        = ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__minus) ).

thf(4269,plain,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
        = ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).

thf(769,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I33_J) ).

thf(3686,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).

thf(868,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ C )
     => ( ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) )
        = ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__minus__commute) ).

thf(4017,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ C )
     => ( ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) )
        = ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).

thf(362,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__trans) ).

thf(2376,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(1012,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A )
      = ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__real__def) ).

thf(4453,plain,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A )
      = ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).

thf(652,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
          = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__eq__iff) ).

thf(3343,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
          = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(594,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__minus__self) ).

thf(3158,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(322,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
        & ( class_Int_Onumber @ D ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ A )
      <=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ A @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
          & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
           => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ C ) )
              & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__eq__number__of1) ).

thf(2260,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
        & ( class_Int_Onumber @ D ) )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ A )
         => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
             => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ A @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ C ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) )
        & ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
             => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ A @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ C ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(604,axiom,
    class_Rings_Olinordered__comm__semiring__strict @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).

thf(3187,plain,
    class_Rings_Olinordered__comm__semiring__strict @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(948,axiom,
    class_Rings_Olinordered__semiring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).

thf(4268,plain,
    class_Rings_Olinordered__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).

thf(547,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) )
      <=> ( ( B
           != ( c_Groups_Ozero__class_Ozero @ C ) )
          | ( A
           != ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).

thf(2970,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ C )
     => ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) )
         => ( ( B
             != ( c_Groups_Ozero__class_Ozero @ C ) )
            | ( A
             != ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
        & ( ( ( B
             != ( c_Groups_Ozero__class_Ozero @ C ) )
            | ( A
             != ( c_Groups_Ozero__class_Ozero @ C ) ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(793,axiom,
    ! [A: $i] :
      ( ( ( class_Fields_Ofield @ A )
        & ( class_Int_Onumber__ring @ A ) )
     => ( ( c_Rings_Oinverse__class_Oinverse @ A @ ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
        = ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__numeral__1) ).

thf(3768,plain,
    ! [A: $i] :
      ( ( ( class_Fields_Ofield @ A )
        & ( class_Int_Onumber__ring @ A ) )
     => ( ( c_Rings_Oinverse__class_Oinverse @ A @ ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
        = ( c_Int_Onumber__class_Onumber__of @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).

thf(619,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ocomm__monoid__add @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).

thf(3240,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ocomm__monoid__add @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(496,axiom,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A )
          = ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) )
      & ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__real__def) ).

thf(2789,plain,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A )
          = ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) )
      & ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(898,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
      = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).

thf(4122,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
      = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).

thf(1014,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
        = ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__def) ).

thf(4465,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
        = ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).

thf(1154,axiom,
    class_Rings_Odivision__ring__inverse__zero @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).

thf(4946,plain,
    class_Rings_Odivision__ring__inverse__zero @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).

thf(612,axiom,
    class_Rings_Olinordered__ring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).

thf(3213,plain,
    class_Rings_Olinordered__ring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(905,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__le__zero) ).

thf(4144,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).

thf(661,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).

thf(3372,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(722,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ E )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ B ) @ A )
         => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult__less) ).

thf(3547,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ E )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ B ) @ A )
         => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).

thf(205,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oab__semigroup__mult @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A )
        = ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).

thf(1833,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oab__semigroup__mult @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A )
        = ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(840,axiom,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ A )
     != A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).

thf(3925,plain,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ A )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).

thf(539,axiom,
    ! [A: $i] :
      ( ( ( c_RealDef_Oreal @ tc_Nat_Onat @ A )
        = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    <=> ( A
        = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__zero__iff) ).

thf(2938,plain,
    ! [A: $i] :
      ( ( ( ( c_RealDef_Oreal @ tc_Nat_Onat @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
      & ( ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( ( c_RealDef_Oreal @ tc_Nat_Onat @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(744,axiom,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ B @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__triangle__sub) ).

thf(3609,plain,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ B @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).

thf(912,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B )
        = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).

thf(4159,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B )
          = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
       => ( B = A ) )
      & ( ( B = A )
       => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B )
          = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).

thf(549,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit0 @ A ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I4_J) ).

thf(2981,plain,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit0 @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(964,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
        <=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__iff) ).

thf(4309,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
       => ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
           => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
          & ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
           => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).

thf(134,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ C @ B ) @ A )
      = ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).

thf(1620,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ C @ B ) @ A )
      = ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(403,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ C )
     => ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) )
        = ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__abs) ).

thf(2489,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ C )
     => ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) )
        = ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(147,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
      <=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__negative__iff__negative) ).

thf(1652,plain,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ B )
     => ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(573,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__field @ C )
     => ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
        = ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Ominus) ).

thf(3081,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__field @ C )
     => ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
        = ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(110,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oordered__cancel__semiring @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).

thf(1535,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oordered__cancel__semiring @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(499,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Groups_Oabs__class_Oabs @ B @ A )
          = ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__neg) ).

thf(2806,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Groups_Oabs__class_Oabs @ B @ A )
          = ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(739,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucI) ).

thf(3590,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).

thf(369,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Ofield @ B )
     => ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
        = ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__class_Onormalizing__field__rules_I2_J) ).

thf(2398,plain,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Ofield @ B )
     => ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
        = ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(971,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
      = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).

thf(4328,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
      = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).

thf(1052,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
      = ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).

thf(4590,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
      = ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).

thf(1167,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ocomm__monoid__add @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).

thf(4975,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ocomm__monoid__add @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).

thf(1058,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) )
    <=> ~ ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
            & ~ ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
          | ? [D: $i] :
              ( ( B
                = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ D ) )
              & ~ ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).

thf(4612,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) )
       => ~ ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
              & ~ ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
            | ? [D: $i] :
                ( ( B
                  = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ D ) )
                & ~ ( hBOOL @ ( hAPP @ C @ D ) ) ) ) )
      & ( ~ ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
              & ~ ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
            | ? [D: $i] :
                ( ( B
                  = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ D ) )
                & ~ ( hBOOL @ ( hAPP @ C @ D ) ) ) )
       => ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).

thf(502,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__order) ).

thf(2817,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(1098,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ A ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).

thf(4769,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ B ) @ A ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ B ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).

thf(1023,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Int_OBit1 @ B )
     != ( c_Int_OBit0 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I50_J) ).

thf(4505,plain,
    ! [A: $i,B: $i] :
      ( ( c_Int_OBit1 @ B )
     != ( c_Int_OBit0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).

thf(742,axiom,
    ! [A: $i] :
      ( ( A
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).

thf(3599,plain,
    ! [A: $i] :
      ( ( ( A
         != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
       => ( A
         != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).

thf(298,axiom,
    class_Rings_Olinordered__ring__strict @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).

thf(2161,plain,
    class_Rings_Olinordered__ring__strict @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(155,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).

thf(1669,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(1168,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
    <=> ( A
        = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc0) ).

thf(4978,plain,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
       => ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
      & ( ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).

thf(50,axiom,
    class_Rings_Olinordered__semiring__1__strict @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).

thf(1312,plain,
    class_Rings_Olinordered__semiring__1__strict @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(585,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ c_Int_OPls )
       => ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
      & ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ c_Int_OPls )
       => ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
          = ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nat__number__of) ).

thf(3123,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ c_Int_OPls )
       => ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
      & ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ c_Int_OPls )
       => ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
          = ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(799,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
      | ( B = A )
      | ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__linear) ).

thf(3783,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
      | ( B = A )
      | ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).

thf(473,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__bin__lemma) ).

thf(2706,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(810,axiom,
    class_Rings_Odivision__ring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).

thf(3832,plain,
    class_Rings_Odivision__ring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).

thf(378,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__field @ D )
     => ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Odiff) ).

thf(2425,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__field @ D )
     => ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(575,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
     => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__gt__half__sum) ).

thf(3091,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
     => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(639,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def) ).

thf(3302,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(354,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ C )
     => ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
        = ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__divide) ).

thf(2358,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ C )
     => ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
        = ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(719,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
    <=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
        | ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).

thf(3532,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
          | ( B = A ) ) )
      & ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
          | ( B = A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).

thf(264,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
        <=> ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).

thf(2029,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
           => ( c_Orderings_Oord__class_Oless @ D @ A @ B ) )
          & ( ( c_Orderings_Oord__class_Oless @ D @ A @ B )
           => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(891,axiom,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A )
          = ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) )
      & ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zabs__def) ).

thf(4096,plain,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A )
          = ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) )
      & ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).

thf(779,axiom,
    class_Rings_Olinordered__semidom @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).

thf(3726,plain,
    class_Rings_Olinordered__semidom @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).

thf(338,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
         => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__left__mono__neg) ).

thf(2308,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
         => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(571,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).

thf(3077,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(646,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( ( c_Groups_Oabs__class_Oabs @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
        = ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__idempotent) ).

thf(3330,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( ( c_Groups_Oabs__class_Oabs @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
        = ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(480,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).

thf(2738,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(908,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
      <=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).

thf(4149,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ C )
     => ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
         => ( c_Orderings_Oord__class_Oless @ C @ A @ B ) )
        & ( ( c_Orderings_Oord__class_Oless @ C @ A @ B )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).

thf(915,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).

thf(4171,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).

thf(939,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I14_J) ).

thf(4236,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).

thf(930,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D @ C )
     => ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C )
          = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).

thf(4218,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ D @ C )
     => ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C )
          = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).

thf(140,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) @ A )
      = ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__assoc) ).

thf(1635,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) @ A )
      = ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(1074,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
       => ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
            = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
        <=> ( B = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__diff__iff) ).

thf(4672,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A )
       => ( ( ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
              = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) )
           => ( B = A ) )
          & ( ( B = A )
           => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C )
              = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).

thf(537,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ B )
     => ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__not__less__zero) ).

thf(2935,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ B )
     => ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(741,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I14_J) ).

thf(3594,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).

thf(1045,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
      | ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__linear) ).

thf(4573,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
      | ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).

thf(26,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Fields_Olinordered__field @ E )
     => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
       => ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
         => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
           => ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
             => ( c_Orderings_Oord__class_Oless @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ A ) @ ( c_Rings_Oinverse__class_Odivide @ E @ C @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__less) ).

thf(1239,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Fields_Olinordered__field @ E )
     => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
       => ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
         => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
           => ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
             => ( c_Orderings_Oord__class_Oless @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ A ) @ ( c_Rings_Oinverse__class_Odivide @ E @ C @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(383,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
       => ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).

thf(2442,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
       => ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(488,axiom,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
      = ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__2__eq__Suc_H) ).

thf(2759,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
      = ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(223,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).

thf(1897,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(424,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
     => ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__le__mono) ).

thf(2557,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
     => ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(141,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Osemiring @ E )
     => ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_combine__common__factor) ).

thf(1638,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Osemiring @ E )
     => ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(1136,axiom,
    ! [A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ A ) )
    <=> ( A
        = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__real__square__gt__zero) ).

thf(4887,plain,
    ! [A: $i] :
      ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ A ) )
       => ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
      & ( ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).

thf(355,axiom,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__square) ).

thf(2361,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(682,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).

thf(3419,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

thf(581,axiom,
    class_Groups_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).

thf(3106,plain,
    class_Groups_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(289,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring__inverse__zero @ B )
     => ( ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ B ) )
      <=> ( A
          = ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonzero__iff__nonzero) ).

thf(2116,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring__inverse__zero @ B )
     => ( ( ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(540,axiom,
    ! [A: $i] :
      ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != ( c_Nat_OSuc @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).

thf(2945,plain,
    ! [A: $i] :
      ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != ( c_Nat_OSuc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(708,axiom,
    ! [A: $i] :
      ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
      = ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__numeral__code_I5_J) ).

thf(3500,plain,
    ! [A: $i] :
      ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
      = ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(961,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).

thf(4300,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).

thf(351,axiom,
    ! [A: $i] :
      ( ( class_Rings_Odivision__ring__inverse__zero @ A )
     => ( ( c_Rings_Oinverse__class_Oinverse @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
        = ( c_Groups_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__zero) ).

thf(2346,plain,
    ! [A: $i] :
      ( ( class_Rings_Odivision__ring__inverse__zero @ A )
     => ( ( c_Rings_Oinverse__class_Oinverse @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
        = ( c_Groups_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(767,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
          = ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).

thf(3678,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
            = ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
            = ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).

thf(413,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__le__0__iff) ).

thf(2521,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(1105,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__pos__pos) ).

thf(4790,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).

thf(15,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
       => ( ( A
           != ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__positive__imp__positive) ).

thf(1209,plain,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
       => ( ( A
           != ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(477,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
    <=> ? [C: $i] :
          ( A
          = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).

thf(2721,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
       => ? [C: $i] :
            ( A
            = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) ) )
      & ( ? [C: $i] :
            ( A
            = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ C ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(655,axiom,
    class_Rings_Odivision__ring__inverse__zero @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) ).

thf(3352,plain,
    class_Rings_Odivision__ring__inverse__zero @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(464,axiom,
    ! [A: $i,B: $i] :
      ( ( ( class_Fields_Ofield @ B )
        & ( class_Int_Onumber__ring @ B ) )
     => ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__numeral__1) ).

thf(2679,plain,
    ! [A: $i,B: $i] :
      ( ( ( class_Fields_Ofield @ B )
        & ( class_Int_Onumber__ring @ B ) )
     => ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(1080,axiom,
    class_Rings_Ocomm__semiring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).

thf(4704,plain,
    class_Rings_Ocomm__semiring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).

thf(860,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc__right) ).

thf(3996,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).

thf(751,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) @ A )
        = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq2) ).

thf(3631,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) @ A )
        = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).

thf(211,axiom,
    class_Int_Onumber @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber) ).

thf(1853,plain,
    class_Int_Onumber @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(399,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
     => ( ( B != A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).

thf(2478,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
     => ( ( B != A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(986,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
     => ( A
        = ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred_H) ).

thf(4369,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
     => ( A
        = ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).

thf(296,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
       => ( ( c_Groups_Oabs__class_Oabs @ B @ A )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).

thf(2151,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
       => ( ( c_Groups_Oabs__class_Oabs @ B @ A )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(314,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).

thf(2229,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(274,axiom,
    class_Rings_Oidom @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).

thf(2084,plain,
    class_Rings_Oidom @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(617,axiom,
    class_Rings_Omult__zero @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).

thf(3238,plain,
    class_Rings_Omult__zero @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(307,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
        <=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__divide__eq) ).

thf(2214,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) ) )
          & ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(365,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).

thf(2383,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(448,axiom,
    class_Rings_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).

thf(2624,plain,
    class_Rings_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(451,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
       => ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
         => ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__inverse) ).

thf(2637,plain,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
       => ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
         => ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(377,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ B )
     => ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) )
        = ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__norm__cancel) ).

thf(2422,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ B )
     => ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) )
        = ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(634,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult__ineq) ).

thf(3287,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(713,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv) ).

thf(3515,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).

thf(1143,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( c_Groups_Ominus__class_Ominus @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).

thf(4914,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( c_Groups_Ominus__class_Ominus @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).

thf(1079,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit1 @ A ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I5_J) ).

thf(4699,plain,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit1 @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ A ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).

thf(61,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( A
           != ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__negative__imp__negative) ).

thf(1349,plain,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( A
           != ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(321,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) )
          = ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__right) ).

thf(2257,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) )
          = ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(782,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).

thf(3732,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).

thf(318,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ C )
     => ( ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) )
          = ( c_Groups_Ozero__class_Ozero @ C ) )
      <=> ( ( B
            = ( c_Groups_Ozero__class_Ozero @ C ) )
          & ( A
            = ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).

thf(2246,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ C )
     => ( ( ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) )
            = ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( ( B
              = ( c_Groups_Ozero__class_Ozero @ C ) )
            & ( A
              = ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
        & ( ( ( B
              = ( c_Groups_Ozero__class_Ozero @ C ) )
            & ( A
              = ( c_Groups_Ozero__class_Ozero @ C ) ) )
         => ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) )
            = ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(94,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).

thf(1492,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(363,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__inverse__le__neg) ).

thf(2378,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(988,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Int_Onumber__ring @ D )
     => ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ominus__class_Ominus @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__diff2) ).

thf(4374,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Int_Onumber__ring @ D )
     => ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ominus__class_Ominus @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).

thf(602,axiom,
    ( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
    = ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__one) ).

thf(3182,plain,
    ( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
    = ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(120,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__pos) ).

thf(1571,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(1024,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__mono2) ).

thf(4509,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).

thf(1017,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).

thf(4477,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).

thf(894,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ E )
     => ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Oabs__class_Oabs @ E @ ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ B @ A ) ) ) @ ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oabs__class_Oabs @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ E @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__diff__triangle__ineq) ).

thf(4107,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ E )
     => ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Oabs__class_Oabs @ E @ ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ B @ A ) ) ) @ ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oabs__class_Oabs @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ E @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).

thf(243,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( A
           != ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
            = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__mult__distrib) ).

thf(1969,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( A
           != ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( ( c_Rings_Oinverse__class_Oinverse @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
            = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(595,axiom,
    class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).

thf(3160,plain,
    class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(924,axiom,
    class_Groups_Omonoid__mult @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).

thf(4203,plain,
    class_Groups_Omonoid__mult @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).

thf(560,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
        = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
    <=> ( ( ( B
            = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
          & ( A
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
        | ( ( B
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
          & ( A
            = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__1) ).

thf(3027,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
          = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
       => ( ( ( B
              = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
            & ( A
              = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
          | ( ( B
              = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
            & ( A
              = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) )
      & ( ( ( ( B
              = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
            & ( A
              = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
          | ( ( B
              = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
            & ( A
              = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
       => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
          = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(287,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring @ B )
     => ( ( A
         != ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
          = ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__minus__eq) ).

thf(2111,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring @ B )
     => ( ( A
         != ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
          = ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(919,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ B ) )
      <=> ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).

thf(4181,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
     => ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ B ) )
         => ( A = B ) )
        & ( ( A = B )
         => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).

thf(438,axiom,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).

thf(2593,plain,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(637,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).

thf(3298,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(959,axiom,
    class_Rings_Oring__1 @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).

thf(4296,plain,
    class_Rings_Oring__1 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).

thf(461,axiom,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
        = ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OPls ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__0__number__of) ).

thf(2664,plain,
    ! [A: $i] :
      ( ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
          = ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OPls ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OPls )
       => ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
          = ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(72,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oordered__ring @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).

thf(1381,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oordered__ring @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(391,axiom,
    class_Rings_Ocomm__semiring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).

thf(2461,plain,
    class_Rings_Ocomm__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(345,axiom,
    class_Groups_Ocancel__ab__semigroup__add @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).

thf(2329,plain,
    class_Groups_Ocancel__ab__semigroup__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(1035,axiom,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th00) ).

thf(4541,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).

thf(482,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Oab__group__add @ E )
     => ( ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Deriv_Oadd__diff__add) ).

thf(2742,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Oab__group__add @ E )
     => ( ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(892,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ A )
      = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).

thf(4103,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ A )
      = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).

thf(117,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__number__of__int__code) ).

thf(1557,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(293,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
        <=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__less__divide__eq) ).

thf(2129,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
           => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ A ) )
          & ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) @ A )
           => ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(350,axiom,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0) ).

thf(2343,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(449,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ A ) )
        = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    <=> ( ( B
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
        & ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__two__squares__add__zero__iff) ).

thf(2625,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ A ) )
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ( ( B
            = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
          & ( A
            = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
      & ( ( ( B
            = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
          & ( A
            = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
       => ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ A ) )
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(137,axiom,
    ! [A: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0) ).

thf(1630,plain,
    ! [A: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(251,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ B )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__antisym) ).

thf(1993,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ B )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(1087,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ B )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__antisym) ).

thf(4731,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ B )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).

thf(871,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).

thf(4028,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).

thf(173,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Odiff) ).

thf(1731,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(802,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ C ) )
      <=> ( A
          = ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__0__iff) ).

thf(3800,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( A
            = ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) )
        & ( ( A
            = ( c_Groups_Ouminus__class_Ouminus @ C @ B ) )
         => ( ( c_Groups_Oplus__class_Oplus @ C @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).

thf(842,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) )
      = ( c_Int_OBit1 @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I9_J) ).

thf(3932,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit0 @ A ) )
      = ( c_Int_OBit1 @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).

thf(227,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( A
           != ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( ( c_Groups_Ominus__class_Ominus @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
            = ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Deriv_Oinverse__diff__inverse) ).

thf(1909,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( A
           != ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( ( c_Groups_Ominus__class_Ominus @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
            = ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(1138,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono) ).

thf(4897,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).

thf(1169,axiom,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ A )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).

thf(4985,plain,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ A )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).

thf(1011,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).

thf(4452,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).

thf(373,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq4) ).

thf(2410,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(532,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ D @ C )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) ) @ C )
       => ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th0) ).

thf(2923,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ D @ C )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) ) @ C )
       => ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(56,axiom,
    class_Rings_Olinordered__ring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).

thf(1325,plain,
    class_Rings_Olinordered__ring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(46,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__imp__inverse__negative) ).

thf(1293,plain,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( c_Orderings_Oord__class_Oless @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(1172,axiom,
    class_Rings_Osemiring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).

thf(4993,plain,
    class_Rings_Osemiring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).

thf(12,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
      <=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).

thf(1198,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ C )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(543,axiom,
    class_Int_Onumber @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber) ).

thf(2962,plain,
    class_Int_Onumber @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(790,axiom,
    class_Rings_Olinordered__semidom @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).

thf(3759,plain,
    class_Rings_Olinordered__semidom @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).

thf(583,axiom,
    ! [A: $i] :
      ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != ( c_Nat_OSuc @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).

thf(3110,plain,
    ! [A: $i] :
      ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != ( c_Nat_OSuc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(837,axiom,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ B ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__minus__mult__self__le) ).

thf(3917,plain,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ B ) ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).

thf(803,axiom,
    ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
    = ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__add__1) ).

thf(3806,plain,
    ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
    = ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).

thf(4,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Odivision__ring @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
        = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__eq__right) ).

thf(1176,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Odivision__ring @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
        = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(849,axiom,
    ? [A: $i] :
    ! [B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ A @ B ) ) @ v_r )
      & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( hAPP @ A @ B ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_Af_O_AALL_Ax_O_Acmod_A_If_Ax_J_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A_If_Ax_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_Ax_J_096) ).

thf(3953,plain,
    ? [A: $i] :
    ! [B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ A @ B ) ) @ v_r )
      & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( hAPP @ A @ B ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).

thf(658,axiom,
    class_Rings_Olinordered__semiring__1 @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).

thf(3363,plain,
    class_Rings_Olinordered__semiring__1 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(282,axiom,
    c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ c_Int_OPls,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I19_J) ).

thf(2101,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ c_Int_OPls,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(96,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring__inverse__zero @ C )
     => ( ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
          = ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__iff__eq) ).

thf(1496,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring__inverse__zero @ C )
     => ( ( ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
            = ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
            = ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(927,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Olinordered__semiring__1__strict @ F )
     => ( ( c_Orderings_Oord__class_Oless @ F @ E @ D )
       => ( ( c_Orderings_Oord__class_Oless @ F @ C @ D )
         => ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ B )
           => ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ A )
             => ( ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
                  = ( c_Groups_Oone__class_Oone @ F ) )
               => ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ E ) @ ( c_Groups_Otimes__class_Otimes @ F @ A @ C ) ) @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__lt) ).

thf(4209,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Olinordered__semiring__1__strict @ F )
     => ( ( c_Orderings_Oord__class_Oless @ F @ E @ D )
       => ( ( c_Orderings_Oord__class_Oless @ F @ C @ D )
         => ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ B )
           => ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ A )
             => ( ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
                  = ( c_Groups_Oone__class_Oone @ F ) )
               => ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ E ) @ ( c_Groups_Otimes__class_Otimes @ F @ A @ C ) ) @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).

thf(271,axiom,
    ! [A: $i] :
      ( ( class_Groups_Ogroup__add @ A )
     => ( ( c_Groups_Ouminus__class_Ouminus @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
        = ( c_Groups_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__zero) ).

thf(2075,plain,
    ! [A: $i] :
      ( ( class_Groups_Ogroup__add @ A )
     => ( ( c_Groups_Ouminus__class_Ouminus @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
        = ( c_Groups_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(1149,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
        = ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__special_I2_J) ).

thf(4933,plain,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
        = ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).

thf(1123,axiom,
    ! [A: $i,B: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).

thf(4844,plain,
    ! [A: $i,B: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).

thf(370,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
     => ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
        = ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_expand__Suc) ).

thf(2401,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
     => ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
        = ( c_Nat_OSuc @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(126,axiom,
    class_Rings_Olinordered__idom @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).

thf(1594,plain,
    class_Rings_Olinordered__idom @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(684,axiom,
    ! [A: $i] :
      ( ( class_Int_Onumber__ring @ A )
     => ( ( c_Groups_Ozero__class_Ozero @ A )
        = ( c_Int_Onumber__class_Onumber__of @ A @ c_Int_OPls ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I112_J) ).

thf(3423,plain,
    ! [A: $i] :
      ( ( class_Int_Onumber__ring @ A )
     => ( ( c_Groups_Ozero__class_Ozero @ A )
        = ( c_Int_Onumber__class_Onumber__of @ A @ c_Int_OPls ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).

thf(400,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).

thf(2481,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ A )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(79,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonpos__neg) ).

thf(1445,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(107,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) @ A ) )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__pos__lemma) ).

thf(1528,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) @ A ) )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(1022,axiom,
    ! [A: $i] :
      ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zminus) ).

thf(4502,plain,
    ! [A: $i] :
      ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).

thf(143,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Oordered__semiring @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono) ).

thf(1643,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Oordered__semiring @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(887,axiom,
    ! [A: $i] :
      ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != ( c_Nat_OSuc @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).

thf(4085,plain,
    ! [A: $i] :
      ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != ( c_Nat_OSuc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).

thf(983,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
     => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incr__lemma) ).

thf(4362,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
     => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).

thf(765,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__D2) ).

thf(3674,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).

thf(1118,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Int_OBit0 @ B )
        = ( c_Int_OBit0 @ A ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I48_J) ).

thf(4827,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( c_Int_OBit0 @ B )
          = ( c_Int_OBit0 @ A ) )
       => ( B = A ) )
      & ( ( B = A )
       => ( ( c_Int_OBit0 @ B )
          = ( c_Int_OBit0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).

thf(330,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

thf(2288,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(187,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ B )
     => ( ( c_Groups_Oabs__class_Oabs @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
        = ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__inverse) ).

thf(1775,plain,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ B )
     => ( ( c_Groups_Oabs__class_Oabs @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
        = ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(486,axiom,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).

thf(2752,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(66,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ogroup__add @ B )
     => ( ( ( c_Groups_Ozero__class_Ozero @ B )
          = ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
      <=> ( ( c_Groups_Ozero__class_Ozero @ B )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).

thf(1364,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ogroup__add @ B )
     => ( ( ( ( c_Groups_Ozero__class_Ozero @ B )
            = ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
         => ( ( c_Groups_Ozero__class_Ozero @ B )
            = A ) )
        & ( ( ( c_Groups_Ozero__class_Ozero @ B )
            = A )
         => ( ( c_Groups_Ozero__class_Ozero @ B )
            = ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(546,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Oring__1 @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ B @ ( c_Groups_Otimes__class_Otimes @ B @ A @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
        = ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__squared__diff__one__factored) ).

thf(2967,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Oring__1 @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ B @ ( c_Groups_Otimes__class_Otimes @ B @ A @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
        = ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(712,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__field @ D )
     => ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Oadd) ).

thf(3512,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__field @ D )
     => ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).

thf(953,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__mono) ).

thf(4282,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).

thf(706,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oab__group__add @ C )
     => ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
        = ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__diff__minus) ).

thf(3490,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oab__group__add @ C )
     => ( ( c_Groups_Ominus__class_Ominus @ C @ B @ A )
        = ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(664,axiom,
    class_Orderings_Olinorder @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).

thf(3380,plain,
    class_Orderings_Olinorder @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(118,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Ofield @ C )
     => ( ( c_Rings_Oinverse__class_Odivide @ C @ B @ A )
        = ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__divide__inverse) ).

thf(1562,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Ofield @ C )
     => ( ( c_Rings_Oinverse__class_Odivide @ C @ B @ A )
        = ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(76,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ D )
     => ( ( C
          = ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
      <=> ( ( ( A
             != ( c_Groups_Ozero__class_Ozero @ D ) )
           => ( ( c_Groups_Otimes__class_Otimes @ D @ C @ A )
              = B ) )
          & ( ( A
              = ( c_Groups_Ozero__class_Ozero @ D ) )
           => ( C
              = ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq) ).

thf(1413,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ D )
     => ( ( ( C
            = ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
         => ( ( ( A
               != ( c_Groups_Ozero__class_Ozero @ D ) )
             => ( ( c_Groups_Otimes__class_Otimes @ D @ C @ A )
                = B ) )
            & ( ( A
                = ( c_Groups_Ozero__class_Ozero @ D ) )
             => ( C
                = ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) )
        & ( ( ( ( A
               != ( c_Groups_Ozero__class_Ozero @ D ) )
             => ( ( c_Groups_Otimes__class_Otimes @ D @ C @ A )
                = B ) )
            & ( ( A
                = ( c_Groups_Ozero__class_Ozero @ D ) )
             => ( C
                = ( c_Groups_Ozero__class_Ozero @ D ) ) ) )
         => ( C
            = ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(972,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ A @ v_z____ ) ) @ v_d____ )
     => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ A ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th1) ).

thf(4331,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ A @ v_z____ ) ) @ v_d____ )
     => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ A ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).

thf(1002,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Odivision__ring @ D )
     => ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__divide__distrib) ).

thf(4426,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Odivision__ring @ D )
     => ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).

thf(692,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
      <=> ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__less__iff) ).

thf(3444,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ C )
     => ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ B ) )
        & ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ B )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).

thf(731,axiom,
    class_Groups_Omonoid__add @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).

thf(3576,plain,
    class_Groups_Omonoid__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).

thf(87,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ A )
      = ( c_Int_OBit0 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Bit0) ).

thf(1467,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ A )
      = ( c_Int_OBit0 @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(596,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__trans__Suc) ).

thf(3161,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(1032,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq2) ).

thf(4529,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).

thf(291,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__left) ).

thf(2124,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) @ A )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(59,axiom,
    ! [A: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1__right) ).

thf(1340,plain,
    ! [A: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(320,axiom,
    class_Rings_Olinordered__semiring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).

thf(2256,plain,
    class_Rings_Olinordered__semiring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(636,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) )
      <=> ( A
         != ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__norm__iff) ).

thf(3292,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ B )
     => ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) )
         => ( A
           != ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( A
           != ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(1084,axiom,
    class_Rings_Oidom @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).

thf(4722,plain,
    class_Rings_Oidom @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).

thf(818,axiom,
    class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

thf(3849,plain,
    class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).

thf(153,axiom,
    class_Groups_Ozero @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).

thf(1662,plain,
    class_Groups_Ozero @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(994,axiom,
    ! [A: $i] :
      ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) )
      = ( c_Int_OBit0 @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Bit0) ).

thf(4394,plain,
    ! [A: $i] :
      ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) )
      = ( c_Int_OBit0 @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).

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

thf(1304,plain,
    class_Rings_Omult__zero @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(217,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Int_Onumber__ring @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__number__of__left) ).

thf(1873,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Int_Onumber__ring @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(607,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ B )
     => ( ( ( c_RealVector_Onorm__class_Onorm @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      <=> ( A
          = ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__eq__zero) ).

thf(3193,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ B )
     => ( ( ( ( c_RealVector_Onorm__class_Onorm @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
         => ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_RealVector_Onorm__class_Onorm @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(867,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
      <=> ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
          & ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__inverse__iff) ).

thf(4013,plain,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ B )
     => ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
         => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
            & ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) )
        & ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
            & ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) )
         => ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).

thf(184,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__left) ).

thf(1758,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(285,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).

thf(2107,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(672,axiom,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ A @ v_z____ ) ) )
        & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ A @ v_z____ ) ) @ v_d____ ) )
     => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ A ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_d_I2_J) ).

thf(3395,plain,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ A @ v_z____ ) ) )
        & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ A @ v_z____ ) ) @ v_d____ ) )
     => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ A ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(323,axiom,
    class_Groups_Ocancel__semigroup__add @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).

thf(2271,plain,
    class_Groups_Ocancel__semigroup__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(1013,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oidom @ C )
     => ( ( ( c_Groups_Otimes__class_Otimes @ C @ B @ B )
          = ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) )
      <=> ( ( B = A )
          | ( B
            = ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__iff) ).

thf(4456,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oidom @ C )
     => ( ( ( ( c_Groups_Otimes__class_Otimes @ C @ B @ B )
            = ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) )
         => ( ( B = A )
            | ( B
              = ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) )
        & ( ( ( B = A )
            | ( B
              = ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) )
         => ( ( c_Groups_Otimes__class_Otimes @ C @ B @ B )
            = ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).

thf(855,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
    <=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
        & ( B != A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__less__def) ).

thf(3981,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
          & ( B != A ) ) )
      & ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
          & ( B != A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).

thf(520,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
    <=> ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
        | ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__real__def) ).

thf(2878,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
       => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
          | ( B = A ) ) )
      & ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
          | ( B = A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(957,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__div__algebra @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bseq__inverse__lemma) ).

thf(4292,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__div__algebra @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).

thf(100,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ E )
     => ( ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).

thf(1509,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ E )
     => ( ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(249,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) )
           => ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__left__mono) ).

thf(1990,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ C ) )
           => ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(564,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__eq__diff) ).

thf(3048,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(440,axiom,
    ! [A: $i,B: $i] :
      ( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) )
      = ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__mult) ).

thf(2597,plain,
    ! [A: $i,B: $i] :
      ( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) )
      = ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(1048,axiom,
    class_Groups_Omonoid__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).

thf(4581,plain,
    class_Groups_Omonoid__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).

thf(1112,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__semidom @ B )
     => ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).

thf(4812,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__semidom @ B )
     => ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).

thf(115,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).

thf(1551,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(430,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).

thf(2567,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(180,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
        <=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__divide__less__eq) ).

thf(1748,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
           => ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) ) )
          & ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) )
           => ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(783,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ A ) @ ( hAPP @ C @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ B ) ) @ B ) )
      = ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ A ) @ ( hAPP @ C @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ B ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__MVT) ).

thf(3737,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ A ) @ ( hAPP @ C @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ B ) ) @ B ) )
      = ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ A ) @ ( hAPP @ C @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ B ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).

thf(1019,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).

thf(4490,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).

thf(460,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ C )
     => ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) )
        = ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__commute) ).

thf(2661,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ C )
     => ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) )
        = ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(1151,axiom,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th000_I1_J) ).

thf(4937,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).

thf(950,axiom,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A )
          = ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) )
      & ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__abs__def) ).

thf(4272,plain,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A )
          = ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) )
      & ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).

thf(613,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oab__group__add @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__left__minus) ).

thf(3214,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oab__group__add @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(145,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Olinordered__ab__group__add @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
      <=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).

thf(1647,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Olinordered__ab__group__add @ B )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(847,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Oordered__ring @ F )
     => ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff2) ).

thf(3949,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Oordered__ring @ F )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) @ D ) @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( c_Groups_Otimes__class_Otimes @ F @ B @ D ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).

thf(412,axiom,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).

thf(2518,plain,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(1028,axiom,
    ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ v_r )
   => ? [A: $i] :
      ! [B: $i] :
        ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_calculation) ).

thf(4517,plain,
    ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ v_r )
   => ? [A: $i] :
      ! [B: $i] :
        ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).

thf(989,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).

thf(4377,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).

thf(513,axiom,
    class_Int_Oring__char__0 @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).

thf(2850,plain,
    class_Int_Oring__char__0 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(1053,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
      = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).

thf(4593,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
      = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).

thf(754,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__ab__semigroup__add @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__mono) ).

thf(3640,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__ab__semigroup__add @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).

thf(516,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
     => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__0__less) ).

thf(2863,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
     => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(259,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Oordered__semiring @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono) ).

thf(2012,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Oordered__semiring @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(834,axiom,
    ! [A: $i] :
      ( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
        = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OPls ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of__0) ).

thf(3904,plain,
    ! [A: $i] :
      ( ( ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OPls ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ c_Int_OPls )
       => ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).

thf(437,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I4_J) ).

thf(2588,plain,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(1157,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono2) ).

thf(4950,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).

thf(811,axiom,
    class_Rings_Ono__zero__divisors @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).

thf(3833,plain,
    class_Rings_Ono__zero__divisors @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).

thf(1034,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_RealDef_Oreal @ tc_Nat_Onat @ B )
        = ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__inject) ).

thf(4534,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( c_RealDef_Oreal @ tc_Nat_Onat @ B )
          = ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
       => ( B = A ) )
      & ( ( B = A )
       => ( ( c_RealDef_Oreal @ tc_Nat_Onat @ B )
          = ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).

thf(32,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Odiff) ).

thf(1252,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(696,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__diff) ).

thf(3462,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).

thf(954,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
      = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel2) ).

thf(4287,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
      = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).

thf(189,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
        = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
    <=> ( ( C
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
        | ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).

thf(1780,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
          = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) )
       => ( ( C
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
          | ( B = A ) ) )
      & ( ( ( C
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
          | ( B = A ) )
       => ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B )
          = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(504,axiom,
    class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).

thf(2821,plain,
    class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(366,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__neg) ).

thf(2386,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(372,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ogroup__add @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__minus) ).

thf(2407,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ogroup__add @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(800,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
    <=> ( ( B
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
        | ? [C: $i] :
            ( ( B
              = ( c_Nat_OSuc @ C ) )
            & ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).

thf(3786,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
       => ( ( B
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
          | ? [C: $i] :
              ( ( B
                = ( c_Nat_OSuc @ C ) )
              & ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ) ) )
      & ( ( ( B
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
          | ? [C: $i] :
              ( ( B
                = ( c_Nat_OSuc @ C ) )
              & ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).

thf(1137,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
     => ( ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ B ) )
          = ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bz_Ax_O_A_091_124_Acmod_Az_A_060_061_Ar_059_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_059_A_126_Ax_A_060_A1_A_124_093_A_061_061_062_AFalse_096) ).

thf(4894,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
     => ( ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ B ) )
          = ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).

thf(1163,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
      = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__0) ).

thf(4961,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
      = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).

thf(431,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ C ) @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) @ C ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).

thf(2569,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ C ) @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(755,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I14_J) ).

thf(3642,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).

thf(531,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Groups_Ominus__class_Ominus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
          = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__divide__eq__iff) ).

thf(2920,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Groups_Ominus__class_Ominus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
          = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(869,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).

thf(4020,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).

thf(863,axiom,
    ! [A: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
      = ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fact__lemma) ).

thf(4003,plain,
    ! [A: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
      = ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).

thf(609,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) @ c_Int_OPls )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I29_J) ).

thf(3202,plain,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) @ c_Int_OPls )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ c_Int_OPls )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) @ c_Int_OPls ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(795,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
        = ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__2__right) ).

thf(3774,plain,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
        = ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).

thf(1090,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mono) ).

thf(4737,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).

thf(123,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) )
    <=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).

thf(1579,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) ) )
      & ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(396,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
        = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__minus__iff) ).

thf(2468,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ( B = A ) )
      & ( ( B = A )
       => ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(458,axiom,
    ( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
    = ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__1) ).

thf(2656,plain,
    ( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
    = ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(557,axiom,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th000_I2_J) ).

thf(3019,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(996,axiom,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_w____ ) @ v_r,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wr) ).

thf(4398,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_w____ ) @ v_r,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).

thf(278,axiom,
    class_Rings_Ono__zero__divisors @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).

thf(2092,plain,
    class_Rings_Ono__zero__divisors @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(190,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
      <=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
            & ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
          | ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
            & ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).

thf(1790,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ C )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
              & ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
            | ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
              & ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) ) )
        & ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
              & ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
            | ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
              & ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A ) ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(845,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
      & ( ( B
         != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
          = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__if) ).

thf(3940,plain,
    ! [A: $i,B: $i] :
      ( ( ( B
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
      & ( ( B
         != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
          = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).

thf(312,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Ofield @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( A
           != ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
            = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__add) ).

thf(2224,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Ofield @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( A
           != ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
            = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(640,axiom,
    class_Fields_Ofield @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).

thf(3305,plain,
    class_Fields_Ofield @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(77,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
        & ( class_Int_Onumber @ D ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
      <=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ A ) @ B ) )
          & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
           => ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ A ) ) )
              & ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__divide__eq__number__of) ).

thf(1432,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
        & ( class_Int_Onumber @ D ) )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
         => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
             => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ A ) @ B ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ A ) ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) )
        & ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
             => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ A ) @ B ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ A ) ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(807,axiom,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sum__of__halves) ).

thf(3818,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).

thf(197,axiom,
    class_Rings_Olinordered__semiring__strict @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).

thf(1813,plain,
    class_Rings_Olinordered__semiring__strict @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(82,axiom,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ v_r,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rp) ).

thf(1452,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ v_r,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(770,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
        = ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__special_I3_J) ).

thf(3691,plain,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
        = ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).

thf(584,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
    <=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
        & ( B != A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).

thf(3114,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
          & ( B != A ) ) )
      & ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
          & ( B != A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(9,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ E )
     => ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
          = ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
        <=> ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).

thf(1188,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ E )
     => ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
          = ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
       => ( ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
           => ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A ) )
          & ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
           => ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(471,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) )
      = ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__add__cancel) ).

thf(2700,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) )
      = ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(36,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
        <=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).

thf(1262,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) )
          & ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(24,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).

thf(1235,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(326,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ono__zero__divisors @ C )
     => ( ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( B
            = ( c_Groups_Ozero__class_Ozero @ C ) )
          | ( A
            = ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divisors__zero) ).

thf(2276,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ono__zero__divisors @ C )
     => ( ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( B
            = ( c_Groups_Ozero__class_Ozero @ C ) )
          | ( A
            = ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(309,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
         => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) )
           => ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__left__mono__neg) ).

thf(2219,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
         => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) )
           => ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(902,axiom,
    class_Rings_Olinordered__ring__strict @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).

thf(4132,plain,
    class_Rings_Olinordered__ring__strict @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).

thf(150,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonpos__pos) ).

thf(1658,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(402,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).

thf(2486,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(940,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).

thf(4241,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).

thf(749,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono2) ).

thf(3623,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).

thf(679,axiom,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th32) ).

thf(3412,plain,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).

thf(176,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
        <=> ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__divide__less__eq) ).

thf(1738,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
           => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ B ) )
          & ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ B )
           => ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(820,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
    <=> ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ c_Int_OPls ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__nat__number__of) ).

thf(3853,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
       => ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ c_Int_OPls ) ) )
      & ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ c_Int_OPls ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).

thf(267,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Odivision__ring @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( B
            = ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
        <=> ( ( c_Groups_Otimes__class_Otimes @ D @ B @ C )
            = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__eq__divide__eq) ).

thf(2056,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Odivision__ring @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( ( B
              = ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
           => ( ( c_Groups_Otimes__class_Otimes @ D @ B @ C )
              = A ) )
          & ( ( ( c_Groups_Otimes__class_Otimes @ D @ B @ C )
              = A )
           => ( B
              = ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(1162,axiom,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) @ ( c_Nat_OSuc @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__Suc) ).

thf(4959,plain,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) @ ( c_Nat_OSuc @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).

thf(681,axiom,
    ~ ! [A: $i] :
        ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_BN2_O_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_AN2_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

thf(3415,plain,
    ~ ! [A: $i] :
        ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).

thf(903,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I3_J) ).

thf(4133,plain,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).

thf(707,axiom,
    ! [A: $i] :
      ( ( ( c_Int_OBit0 @ A )
        = c_Int_OPls )
    <=> ( A = c_Int_OPls ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I44_J) ).

thf(3493,plain,
    ! [A: $i] :
      ( ( ( ( c_Int_OBit0 @ A )
          = c_Int_OPls )
       => ( A = c_Int_OPls ) )
      & ( ( A = c_Int_OPls )
       => ( ( c_Int_OBit0 @ A )
          = c_Int_OPls ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).

thf(167,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).

thf(1702,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(1005,axiom,
    ! [A: $i] :
      ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
      = ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__real__of__nat__cancel) ).

thf(4436,plain,
    ! [A: $i] :
      ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
      = ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).

thf(327,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oring @ C )
     => ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__minus) ).

thf(2279,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oring @ C )
     => ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(668,axiom,
    class_Groups_Oab__group__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).

thf(3388,plain,
    class_Groups_Oab__group__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).

thf(1061,axiom,
    ! [A: $i,B: $i] :
      ( ( ( class_RealVector_Oreal__normed__div__algebra @ B )
        & ( class_Rings_Odivision__ring__inverse__zero @ B ) )
     => ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
        = ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__inverse) ).

thf(4634,plain,
    ! [A: $i,B: $i] :
      ( ( ( class_RealVector_Oreal__normed__div__algebra @ B )
        & ( class_Rings_Odivision__ring__inverse__zero @ B ) )
     => ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
        = ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).

thf(191,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ono__zero__divisors @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( A
           != ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
           != ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_no__zero__divisors) ).

thf(1797,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ono__zero__divisors @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( A
           != ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
           != ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(541,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
        & ( class_Int_Onumber @ D ) )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      <=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
           => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) )
          & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
           => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
              & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq__number__of1) ).

thf(2949,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
        & ( class_Int_Onumber @ D ) )
     => ( ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
         => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
             => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) )
        & ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
             => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) )
         => ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(851,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oone @ B )
     => ( ( ( c_Groups_Oone__class_Oone @ B )
          = A )
      <=> ( A
          = ( c_Groups_Oone__class_Oone @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__reorient) ).

thf(3961,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oone @ B )
     => ( ( ( ( c_Groups_Oone__class_Oone @ B )
            = A )
         => ( A
            = ( c_Groups_Oone__class_Oone @ B ) ) )
        & ( ( A
            = ( c_Groups_Oone__class_Oone @ B ) )
         => ( ( c_Groups_Oone__class_Oone @ B )
            = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).

thf(38,axiom,
    class_Groups_Oab__semigroup__add @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).

thf(1272,plain,
    class_Groups_Oab__semigroup__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(714,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I16_J) ).

thf(3520,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

thf(1027,axiom,
    class_Rings_Oring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).

thf(4516,plain,
    class_Rings_Oring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).

thf(231,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__iff) ).

thf(1934,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ C )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(772,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing) ).

thf(3697,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).

thf(112,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
       => ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_positive__imp__inverse__positive) ).

thf(1543,plain,
    ! [A: $i,B: $i] :
      ( ( class_Fields_Olinordered__field @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
       => ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(1108,axiom,
    class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).

thf(4802,plain,
    class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).

thf(582,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
        = ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__simps_I30_J) ).

thf(3107,plain,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
        = ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(209,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).

thf(1849,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(34,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__le__imp__le) ).

thf(1257,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(20,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Fields_Olinordered__field @ E )
     => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
       => ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
         => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
           => ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
             => ( c_Orderings_Oord__class_Oless @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ A ) @ ( c_Rings_Oinverse__class_Odivide @ E @ C @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__less2) ).

thf(1221,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Fields_Olinordered__field @ E )
     => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
       => ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
         => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
           => ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
             => ( c_Orderings_Oord__class_Oless @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ A ) @ ( c_Rings_Oinverse__class_Odivide @ E @ C @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(43,axiom,
    ! [A: $i] :
      ( ( A
       != ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
     => ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ A ) @ A )
        = ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__inverse__left) ).

thf(1284,plain,
    ! [A: $i] :
      ( ( A
       != ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
     => ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ A ) @ A )
        = ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(244,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).

thf(1972,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(474,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) )
        = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
     => ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ B )
        = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__zmult__eq__1) ).

thf(2711,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) )
        = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
     => ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ B )
        = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(893,axiom,
    class_Fields_Olinordered__field__inverse__zero @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).

thf(4106,plain,
    class_Fields_Olinordered__field__inverse__zero @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).

thf(478,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
      <=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).

thf(2728,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ B )
     => ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
        & ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
         => ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(934,axiom,
    class_Rings_Oordered__semiring @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).

thf(4225,plain,
    class_Rings_Oordered__semiring @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).

thf(1120,axiom,
    class_Groups_Oab__group__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).

thf(4838,plain,
    class_Groups_Oab__group__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).

thf(626,axiom,
    class_Rings_Oordered__cancel__semiring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).

thf(3256,plain,
    class_Rings_Oordered__cancel__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(523,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ C )
        = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).

thf(2892,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ C )
        = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(768,axiom,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__ge__zero) ).

thf(3684,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).

thf(993,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__neg) ).

thf(4392,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__comm__monoid__add @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).

thf(1064,axiom,
    ! [A: $i,B: $i] :
      ( ( ( class_Int_Onumber__ring @ B )
        & ( class_RealVector_Oreal__normed__algebra__1 @ B ) )
     => ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
        = ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__number__of) ).

thf(4639,plain,
    ! [A: $i,B: $i] :
      ( ( ( class_Int_Onumber__ring @ B )
        & ( class_RealVector_Oreal__normed__algebra__1 @ B ) )
     => ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
        = ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).

thf(1038,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ogroup__add @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
        = ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0) ).

thf(4548,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ogroup__add @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
        = ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).

thf(208,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
        = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
    <=> ( ( B
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
        | ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__is__0) ).

thf(1839,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( ( B
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
          | ( A
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
      & ( ( ( B
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
          | ( A
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
       => ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(276,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono) ).

thf(2088,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(469,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__ab__semigroup__add @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__mono) ).

thf(2696,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__ab__semigroup__add @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(507,axiom,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__0962_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096) ).

thf(2828,plain,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(693,axiom,
    ( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
    = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__zero) ).

thf(3447,plain,
    ( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
    = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).

thf(339,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
       => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).

thf(2310,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
       => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(605,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
       => ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).

thf(3188,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oordered__ab__semigroup__add__imp__le @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ ( c_Groups_Oplus__class_Oplus @ D @ A @ B ) )
       => ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(75,axiom,
    class_Groups_Olinordered__ab__group__add @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).

thf(1412,plain,
    class_Groups_Olinordered__ab__group__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

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

thf(2611,plain,
    class_Rings_Oordered__comm__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(305,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ E @ B ) @ A ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ A )
         => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ C )
           => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).

thf(2209,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ E @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ E @ B ) @ A ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ A )
         => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ C )
           => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(83,axiom,
    class_Rings_Oordered__comm__semiring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).

thf(1453,plain,
    class_Rings_Oordered__comm__semiring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(253,axiom,
    ! [A: $i,B: $i] :
      ( ( c_SEQ_Osubseq @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( hAPP @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_seq__suble) ).

thf(1998,plain,
    ! [A: $i,B: $i] :
      ( ( c_SEQ_Osubseq @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( hAPP @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(517,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ C )
     => ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
        = ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__divide) ).

thf(2865,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ C )
     => ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
        = ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(598,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
        = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__right) ).

thf(3168,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) )
        = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(695,axiom,
    ! [A: $i,B: $i] :
      ( ( B != A )
    <=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
        | ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).

thf(3452,plain,
    ! [A: $i,B: $i] :
      ( ( ( B != A )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
          | ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) ) )
      & ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
          | ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B ) )
       => ( B != A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(389,axiom,
    class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).

thf(2458,plain,
    class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(904,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
      <=> ( A
         != ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__abs__iff) ).

thf(4138,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
         => ( A
           != ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( A
           != ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).

thf(53,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oring @ C )
     => ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
        = ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__commute) ).

thf(1316,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oring @ C )
     => ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
        = ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(738,axiom,
    class_Groups_Ogroup__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).

thf(3589,plain,
    class_Groups_Ogroup__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).

thf(970,axiom,
    ! [A: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ A )
     => ( ( c_RealVector_Onorm__class_Onorm @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
        = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__zero) ).

thf(4325,plain,
    ! [A: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ A )
     => ( ( c_RealVector_Onorm__class_Onorm @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
        = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).

thf(200,axiom,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__cube) ).

thf(1817,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(599,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__le__iff) ).

thf(3171,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(542,axiom,
    ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) )
    = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__1__eq__Suc__0) ).

thf(2960,plain,
    ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) )
    = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(272,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__right) ).

thf(2078,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(229,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Fields_Ofield__inverse__zero @ D )
        & ( class_Int_Onumber @ D ) )
     => ( ( C
          = ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      <=> ( ( ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
             != ( c_Groups_Ozero__class_Ozero @ D ) )
           => ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
              = B ) )
          & ( ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
              = ( c_Groups_Ozero__class_Ozero @ D ) )
           => ( C
              = ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of1) ).

thf(1913,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Fields_Ofield__inverse__zero @ D )
        & ( class_Int_Onumber @ D ) )
     => ( ( ( C
            = ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
         => ( ( ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
               != ( c_Groups_Ozero__class_Ozero @ D ) )
             => ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
                = B ) )
            & ( ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
                = ( c_Groups_Ozero__class_Ozero @ D ) )
             => ( C
                = ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) )
        & ( ( ( ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
               != ( c_Groups_Ozero__class_Ozero @ D ) )
             => ( ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
                = B ) )
            & ( ( ( c_Int_Onumber__class_Onumber__of @ D @ A )
                = ( c_Groups_Ozero__class_Ozero @ D ) )
             => ( C
                = ( c_Groups_Ozero__class_Ozero @ D ) ) ) )
         => ( C
            = ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(750,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ B ) @ A )
    <=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) @ B )
        & ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__interval__iff) ).

thf(3625,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ B ) @ A )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) @ B )
          & ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ) )
      & ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) @ B )
          & ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).

thf(1067,axiom,
    class_Rings_Osemiring @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).

thf(4646,plain,
    class_Rings_Osemiring @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).

thf(884,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring @ C )
     => ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).

thf(4078,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring @ C )
     => ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ B ) @ ( c_Groups_Otimes__class_Otimes @ C @ A @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).

thf(301,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__ring @ B )
     => ~ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Otimes__class_Otimes @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__square__less__zero) ).

thf(2187,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__ring @ B )
     => ~ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Otimes__class_Otimes @ B @ A @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(653,axiom,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc3__eq__add__3) ).

thf(3346,plain,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(864,axiom,
    ( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
    = ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__num__one) ).

thf(4006,plain,
    ( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
    = ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit1 @ c_Int_OPls ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).

thf(459,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oab__semigroup__add @ D )
     => ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).

thf(2658,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oab__semigroup__add @ D )
     => ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(841,axiom,
    ! [A: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__2) ).

thf(3929,plain,
    ! [A: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).

thf(174,axiom,
    c_SEQ_Osubseq @ v_f____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fz_I1_J) ).

thf(1734,plain,
    c_SEQ_Osubseq @ v_f____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(195,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ B @ A @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__self) ).

thf(1807,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ B @ A @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(762,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ E )
     => ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
          = ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
        <=> ( c_Orderings_Oord__class_Oless @ E @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).

thf(3665,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ E )
     => ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
          = ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
       => ( ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
           => ( c_Orderings_Oord__class_Oless @ E @ B @ A ) )
          & ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
           => ( c_Orderings_Oord__class_Oless @ E @ D @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).

thf(1075,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
        & ( class_Int_Onumber @ D ) )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
      <=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
           => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ A ) @ B ) )
          & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
           => ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ A ) ) )
              & ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq__number__of) ).

thf(4678,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
        & ( class_Int_Onumber @ D ) )
     => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
         => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
             => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ A ) @ B ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ A ) ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) )
        & ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
             => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ A ) @ B ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ A ) ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).

thf(40,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring__inverse__zero @ B )
     => ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__inverse__eq) ).

thf(1276,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring__inverse__zero @ B )
     => ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(747,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring__inverse__zero @ B )
     => ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
        = ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__minus__eq) ).

thf(3613,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring__inverse__zero @ B )
     => ( ( c_Rings_Oinverse__class_Oinverse @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
        = ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).

thf(775,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit0 @ A ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I21_J) ).

thf(3709,plain,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit0 @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ A ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ ( c_Int_OBit0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).

thf(515,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
       => ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
     => ( ( ( C = B )
         => ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
       => ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ C )
           => ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
         => ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).

thf(2853,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
       => ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
     => ( ( ( C = B )
         => ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
       => ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ C )
           => ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
         => ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(666,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ C )
     => ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
        = ( c_Rings_Oinverse__class_Odivide @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__right) ).

thf(3383,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ C )
     => ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
        = ( c_Rings_Oinverse__class_Odivide @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(648,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq) ).

thf(3336,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(787,axiom,
    class_Groups_Oordered__ab__semigroup__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).

thf(3748,plain,
    class_Groups_Oordered__ab__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).

thf(212,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I16_J) ).

thf(1854,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(443,axiom,
    ? [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
      & ! [B: $i] :
          ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ v_z____ ) ) )
            & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ v_z____ ) ) @ A ) )
         => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ B ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_Ad_0620_O_AALL_Aw_O_A0_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_A_N_N_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096) ).

thf(2608,plain,
    ? [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
      & ! [B: $i] :
          ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ v_z____ ) ) )
            & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ B @ v_z____ ) ) @ A ) )
         => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ B ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(28,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ E )
     => ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
           => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
             => ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).

thf(1244,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ E )
     => ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
           => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
             => ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(1115,axiom,
    class_Rings_Olinordered__semiring__1__strict @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).

thf(4823,plain,
    class_Rings_Olinordered__semiring__1__strict @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).

thf(57,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
      <=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
           => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ B ) )
          & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
           => ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) )
              & ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq) ).

thf(1326,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ D )
     => ( ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
         => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
             => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ B ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) )
        & ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
             => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ B ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) )
         => ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(781,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
      = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).

thf(3729,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
      = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).

thf(835,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
        = B )
     => ( A
        = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).

thf(3911,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A )
        = B )
     => ( A
        = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).

thf(368,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oring__no__zero__divisors @ C )
     => ( ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ C ) )
      <=> ( ( B
            = ( c_Groups_Ozero__class_Ozero @ C ) )
          | ( A
            = ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).

thf(2389,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oring__no__zero__divisors @ C )
     => ( ( ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( ( B
              = ( c_Groups_Ozero__class_Ozero @ C ) )
            | ( A
              = ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
        & ( ( ( B
              = ( c_Groups_Ozero__class_Ozero @ C ) )
            | ( A
              = ( c_Groups_Ozero__class_Ozero @ C ) ) )
         => ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(1110,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ A )
      = ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__commute) ).

thf(4806,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ A )
      = ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).

thf(281,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( A
           != ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( ( c_Groups_Ominus__class_Ominus @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
            = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_division__ring__inverse__diff) ).

thf(2098,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( A
           != ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( ( c_Groups_Ominus__class_Ominus @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
            = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Otimes__class_Otimes @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(703,axiom,
    ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) )
    = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__numeral__1__eq__1) ).

thf(3484,plain,
    ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) )
    = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).

thf(888,axiom,
    class_Groups_Omonoid__mult @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).

thf(4089,plain,
    class_Groups_Omonoid__mult @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).

thf(422,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less) ).

thf(2554,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(1015,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
          = A )
      <=> ( ( c_Groups_Ouminus__class_Ouminus @ C @ A )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__equation__iff) ).

thf(4468,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
            = A )
         => ( ( c_Groups_Ouminus__class_Ouminus @ C @ A )
            = B ) )
        & ( ( ( c_Groups_Ouminus__class_Ouminus @ C @ A )
            = B )
         => ( ( c_Groups_Ouminus__class_Ouminus @ C @ B )
            = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).

thf(615,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) )
    <=> ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
         => ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
        & ! [D: $i] :
            ( ( B
              = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ D ) )
           => ( hBOOL @ ( hAPP @ C @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split) ).

thf(3220,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) )
       => ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
           => ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
          & ! [D: $i] :
              ( ( B
                = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ D ) )
             => ( hBOOL @ ( hAPP @ C @ D ) ) ) ) )
      & ( ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
           => ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
          & ! [D: $i] :
              ( ( B
                = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ D ) )
             => ( hBOOL @ ( hAPP @ C @ D ) ) ) )
       => ( hBOOL @ ( hAPP @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(876,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oabs__if @ B )
     => ( ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_Groups_Oabs__class_Oabs @ B @ A )
            = ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) )
        & ( ~ ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_Groups_Oabs__class_Oabs @ B @ A )
            = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__if) ).

thf(4042,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oabs__if @ B )
     => ( ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_Groups_Oabs__class_Oabs @ B @ A )
            = ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) )
        & ( ~ ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_Groups_Oabs__class_Oabs @ B @ A )
            = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).

thf(1036,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Odivision__ring @ D )
     => ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__distrib) ).

thf(4542,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Odivision__ring @ D )
     => ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).

thf(257,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ozero @ B )
     => ( ( ( c_Groups_Ozero__class_Ozero @ B )
          = A )
      <=> ( A
          = ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__reorient) ).

thf(2004,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ozero @ B )
     => ( ( ( ( c_Groups_Ozero__class_Ozero @ B )
            = A )
         => ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_Groups_Ozero__class_Ozero @ B )
            = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(857,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).

thf(3991,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).

thf(105,axiom,
    ( c_Int_OPls
    = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pls__def) ).

thf(1523,plain,
    ( c_Int_OPls
    = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(1081,axiom,
    ! [A: $i,B: $i] :
      ( ( ( class_Fields_Olinordered__field__inverse__zero @ B )
        & ( class_Int_Onumber__ring @ B ) )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
      <=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_half__gt__zero__iff) ).

thf(4705,plain,
    ! [A: $i,B: $i] :
      ( ( ( class_Fields_Olinordered__field__inverse__zero @ B )
        & ( class_Int_Onumber__ring @ B ) )
     => ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) )
         => ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
        & ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
         => ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).

thf(589,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).

thf(3136,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(1134,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ c_Int_OPls ) @ A )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__numeral__0) ).

thf(4881,plain,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ c_Int_OPls ) @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).

thf(761,axiom,
    ! [A: $i,B: $i] :
      ( ( ( class_Fields_Ofield @ B )
        & ( class_Int_Onumber__ring @ B ) )
     => ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__Numeral1) ).

thf(3662,plain,
    ! [A: $i,B: $i] :
      ( ( ( class_Fields_Ofield @ B )
        & ( class_Int_Onumber__ring @ B ) )
     => ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).

thf(414,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
        & ( class_Int_Onumber @ D ) )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ A )
      <=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
           => ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ A @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
          & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
           => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ C ) )
              & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq__number__of1) ).

thf(2526,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
        & ( class_Int_Onumber @ D ) )
     => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ A )
         => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
             => ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ A @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ C ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) )
        & ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
             => ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ A @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ C ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(375,axiom,
    ! [A: $i,B: $i] :
      ( ( ( class_Fields_Ofield__inverse__zero @ B )
        & ( class_Int_Onumber__ring @ B ) )
     => ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ c_Int_OPls ) )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__Numeral0) ).

thf(2416,plain,
    ! [A: $i,B: $i] :
      ( ( ( class_Fields_Ofield__inverse__zero @ B )
        & ( class_Int_Onumber__ring @ B ) )
     => ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ c_Int_OPls ) )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(798,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Int_Onumber__ring @ D )
     => ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__left) ).

thf(3780,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Int_Onumber__ring @ D )
     => ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ B ) @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).

thf(385,axiom,
    class_Rings_Oordered__semiring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).

thf(2447,plain,
    class_Rings_Oordered__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(214,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
        <=> ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).

thf(1861,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
           => ( c_Orderings_Oord__class_Oless @ D @ B @ A ) )
          & ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
           => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(645,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Ocancel__semigroup__add @ D )
     => ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
          = ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__cancel) ).

thf(3324,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Ocancel__semigroup__add @ D )
     => ( ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
            = ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
            = ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(497,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ A ) ) )
    <=> ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ C )
        = ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__2__times__iff) ).

thf(2796,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C
          = ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ A ) ) )
       => ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ C )
          = ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A ) ) )
      & ( ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ C )
          = ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A ) )
       => ( C
          = ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(1164,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring @ B )
     => ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
        = ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__divide) ).

thf(4964,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring @ B )
     => ( ( c_Rings_Oinverse__class_Oinverse @ B @ A )
        = ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).

thf(917,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ A ) )
      <=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff1) ).

thf(4175,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ A ) )
         => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ B ) @ A ) )
        & ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ B ) @ A )
         => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).

thf(736,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__semidom @ A )
     => ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).

thf(3585,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__semidom @ A )
     => ( c_Orderings_Oord__class_Oless @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).

thf(1094,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ B )
     => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).

thf(4759,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ B )
     => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ A ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).

thf(346,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
      | ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__linear) ).

thf(2330,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
      | ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(831,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).

thf(3896,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).

thf(299,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
       != ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
     => ( ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ B )
          = ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ A ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__left__cancel) ).

thf(2162,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
       != ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
     => ( ( ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ B )
            = ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ A ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ B )
            = ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__semidom @ A )
     => ~ ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).

thf(1212,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__semidom @ A )
     => ~ ( c_Orderings_Oord__class_Oless__eq @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(858,axiom,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( v_g____ @ A ) ) @ v_r ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_g_I1_J) ).

thf(3993,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( v_g____ @ A ) ) @ v_r ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).

thf(152,axiom,
    c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).

thf(1661,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(341,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ogroup__add @ B )
     => ( ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ B ) )
      <=> ( A
          = ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).

thf(2315,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ogroup__add @ B )
     => ( ( ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(1147,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Oring @ E )
     => ( ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__diff__mult) ).

thf(4927,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Oring @ E )
     => ( ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).

thf(870,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Int_Onumber @ D )
        & ( class_Rings_Osemiring @ D ) )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__distrib__number__of) ).

thf(4025,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Int_Onumber @ D )
        & ( class_Rings_Osemiring @ D ) )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).

thf(162,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ogroup__add @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__right) ).

thf(1689,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ogroup__add @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(854,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Int_Onumber__ring @ C )
     => ( ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__add) ).

thf(3978,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Int_Onumber__ring @ C )
     => ( ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).

thf(273,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring @ C )
     => ( ( c_Rings_Oinverse__class_Odivide @ C @ B @ A )
        = ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__inverse) ).

thf(2081,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring @ C )
     => ( ( c_Rings_Oinverse__class_Odivide @ C @ B @ A )
        = ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(397,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ E )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ B ) @ A )
         => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__add__less) ).

thf(2475,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ E )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ B ) @ A )
         => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(771,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ocomm__monoid__mult @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1) ).

thf(3694,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ocomm__monoid__mult @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).

thf(495,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
     => ( ( ( c_Nat_OSuc @ B )
         != A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessI) ).

thf(2786,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
     => ( ( ( c_Nat_OSuc @ B )
         != A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(1100,axiom,
    c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__less__1) ).

thf(4774,plain,
    c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).

thf(392,axiom,
    class_Int_Onumber__ring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber__ring) ).

thf(2462,plain,
    class_Int_Onumber__ring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(434,axiom,
    c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).

thf(2576,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(269,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oordered__cancel__semiring @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).

thf(2066,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oordered__cancel__semiring @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(718,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
      = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__left) ).

thf(3529,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
      = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).

thf(10,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Omult__zero @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__right) ).

thf(1193,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Omult__zero @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(130,axiom,
    class_Groups_Oordered__ab__group__add @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).

thf(1607,plain,
    class_Groups_Oordered__ab__group__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(998,axiom,
    ! [A: $i] :
      ( ? [B: $i] :
          ( ? [C: $i] :
              ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ C ) @ v_r )
              & ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ C ) )
                = ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) )
          & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ B ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ v_s____ ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_s) ).

thf(4404,plain,
    ! [A: $i] :
      ( ( ? [B: $i] :
            ( ? [C: $i] :
                ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ C ) @ v_r )
                & ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ C ) )
                  = ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) )
            & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ B ) )
       => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ v_s____ ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ v_s____ )
       => ? [B: $i] :
            ( ? [C: $i] :
                ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ C ) @ v_r )
                & ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ C ) )
                  = ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) )
            & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).

thf(280,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
      <=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__iff) ).

thf(2095,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oordered__ab__group__add @ C )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ B ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(1009,axiom,
    ! [A: $i,B: $i] :
      ( ( ( class_Int_Onumber__ring @ B )
        & ( class_Rings_Olinordered__idom @ B ) )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
      <=> ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I1_J) ).

thf(4446,plain,
    ! [A: $i,B: $i] :
      ( ( ( class_Int_Onumber__ring @ B )
        & ( class_Rings_Olinordered__idom @ B ) )
     => ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
         => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ A ) )
        & ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ A )
         => ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).

thf(221,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring @ B )
     => ( ( A
         != ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ A )
          = ( c_Groups_Oone__class_Oone @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__inverse) ).

thf(1893,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring @ B )
     => ( ( A
         != ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) @ A )
          = ( c_Groups_Oone__class_Oone @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(332,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring__inverse__zero @ B )
     => ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__zero) ).

thf(2294,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring__inverse__zero @ B )
     => ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(481,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ E )
     => ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).

thf(2739,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ E )
     => ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(1044,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
      = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__commute) ).

thf(4570,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) @ A )
      = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).

thf(1129,axiom,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th2) ).

thf(4869,plain,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ ( hAPP @ v_f____ @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ v_N1____ @ v_N2____ ) ) ) ) @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ v_z____ ) ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).

thf(987,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).

thf(4372,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).

thf(256,axiom,
    class_Orderings_Olinorder @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).

thf(2003,plain,
    class_Orderings_Olinorder @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(875,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ogroup__add @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus) ).

thf(4039,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ogroup__add @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).

thf(101,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring @ B )
     => ( ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__zero__left) ).

thf(1512,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring @ B )
     => ( ( c_Rings_Oinverse__class_Odivide @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(336,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).

thf(2302,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(980,axiom,
    class_Rings_Ono__zero__divisors @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).

thf(4356,plain,
    class_Rings_Ono__zero__divisors @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).

thf(1111,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A )
      = ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__average__minus__second) ).

thf(4809,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) @ A )
      = ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).

thf(943,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).

thf(4254,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ ( c_Nat_OSuc @ A ) )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).

thf(1054,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
     => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__inverse) ).

thf(4596,plain,
    ! [A: $i,B: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
     => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).

thf(628,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    <=> ( A
        = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__le__zero__cancel__iff) ).

thf(3264,plain,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
      & ( ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(579,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).

thf(3100,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring @ D )
     => ( ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) @ ( c_Groups_Otimes__class_Otimes @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(813,axiom,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__real__of__nat__less__zero) ).

thf(3837,plain,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).

thf(218,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
        & ( class_Int_Onumber @ D ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      <=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) )
          & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
           => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
              & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__divide__eq__number__of1) ).

thf(1876,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Fields_Olinordered__field__inverse__zero @ D )
        & ( class_Int_Onumber @ D ) )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
         => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
             => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) )
        & ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
             => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ B ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(157,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Int_Onumber__ring @ C )
     => ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
        = ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__simps_I32_J) ).

thf(1673,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Int_Onumber__ring @ C )
     => ( ( c_Groups_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
        = ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(1047,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).

thf(4579,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).

thf(985,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).

thf(4367,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).

thf(567,axiom,
    ! [A: $i] :
      ( ( c_Int_OPls
        = ( c_Int_OBit0 @ A ) )
    <=> ( c_Int_OPls = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I38_J) ).

thf(3062,plain,
    ! [A: $i] :
      ( ( ( c_Int_OPls
          = ( c_Int_OBit0 @ A ) )
       => ( c_Int_OPls = A ) )
      & ( ( c_Int_OPls = A )
       => ( c_Int_OPls
          = ( c_Int_OBit0 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(698,axiom,
    class_Groups_Ogroup__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).

thf(3469,plain,
    class_Groups_Ogroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(759,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oab__group__add @ C )
     => ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__diff__eq) ).

thf(3658,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oab__group__add @ C )
     => ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(899,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Int_Onumber__ring @ C )
     => ( ( c_Groups_Ominus__class_Ominus @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
        = ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__number__of__eq) ).

thf(4125,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Int_Onumber__ring @ C )
     => ( ( c_Groups_Ominus__class_Ominus @ C @ ( c_Int_Onumber__class_Onumber__of @ C @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
        = ( c_Int_Onumber__class_Onumber__of @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).

thf(283,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Oordered__comm__semiring @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).

thf(2102,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Oordered__comm__semiring @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(1144,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ v_N1____ @ A )
     => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( v_g____ @ ( hAPP @ v_f____ @ A ) ) @ v_z____ ) ) @ v_d____ ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_N1) ).

thf(4917,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ v_N1____ @ A )
     => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( v_g____ @ ( hAPP @ v_f____ @ A ) ) @ v_z____ ) ) @ v_d____ ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).

thf(238,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__less__imp__less__neg) ).

thf(1957,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Oinverse @ C @ B ) @ ( c_Rings_Oinverse__class_Oinverse @ C @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(997,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I32_J) ).

thf(4399,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) @ ( c_Int_OBit1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).

thf(821,axiom,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ c_Int_OPls @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls) ).

thf(3860,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ c_Int_OPls @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).

thf(159,axiom,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).

thf(1678,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(588,axiom,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ A )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).

thf(3132,plain,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ A )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

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

thf(1248,plain,
    class_Rings_Ocomm__semiring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(183,axiom,
    class_Rings_Oordered__ring__abs @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).

thf(1757,plain,
    class_Rings_Oordered__ring__abs @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(1072,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) )
    <=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
        & ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).

thf(4663,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
          & ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) )
      & ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
          & ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).

thf(981,axiom,
    ! [A: $i,B: $i] :
      ( ( B = A )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).

thf(4357,plain,
    ! [A: $i,B: $i] :
      ( ( B = A )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).

thf(485,axiom,
    class_Groups_Ocomm__monoid__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).

thf(2751,plain,
    class_Groups_Ocomm__monoid__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(918,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring @ C )
     => ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
        = ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__left) ).

thf(4178,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring @ C )
     => ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
        = ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).

thf(52,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__self) ).

thf(1314,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ B @ A @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(199,axiom,
    class_Rings_Ozero__neq__one @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).

thf(1816,plain,
    class_Rings_Ozero__neq__one @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(1060,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__numeral__1__right) ).

thf(4631,plain,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).

thf(819,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Bit0) ).

thf(3850,plain,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).

thf(701,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).

thf(3479,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).

thf(357,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).

thf(2366,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(89,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
         => ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).

thf(1473,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
         => ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(446,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ E )
     => ( ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oprod__diff__prod) ).

thf(2619,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ E )
     => ( ( c_Groups_Ominus__class_Ominus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ A ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(456,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
     => ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).

thf(2651,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Oordered__cancel__ab__semigroup__add @ E )
     => ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ E @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(494,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( class_Fields_Ofield__inverse__zero @ C )
        & ( class_RealVector_Oreal__normed__field @ C ) )
     => ( ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
        = ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__divide) ).

thf(2783,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( class_Fields_Ofield__inverse__zero @ C )
        & ( class_RealVector_Oreal__normed__field @ C ) )
     => ( ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) )
        = ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(420,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) @ C )
        = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc) ).

thf(2549,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) @ C )
        = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(213,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) )
           => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).

thf(1859,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) )
           => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(906,axiom,
    class_Rings_Ozero__neq__one @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).

thf(4146,plain,
    class_Rings_Ozero__neq__one @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).

thf(963,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( ( c_Rings_Oinverse__class_Odivide @ C @ A @ B )
            = ( c_Groups_Oone__class_Oone @ C ) )
        <=> ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__inverse__eq) ).

thf(4303,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( ( ( c_Rings_Oinverse__class_Odivide @ C @ A @ B )
              = ( c_Groups_Oone__class_Oone @ C ) )
           => ( A = B ) )
          & ( ( A = B )
           => ( ( c_Rings_Oinverse__class_Odivide @ C @ A @ B )
              = ( c_Groups_Oone__class_Oone @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).

thf(1102,axiom,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ A ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_g_I2_J) ).

thf(4777,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ A ) ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).

thf(879,axiom,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).

thf(4051,plain,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).

thf(149,axiom,
    class_Int_Onumber__ring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).

thf(1657,plain,
    class_Int_Onumber__ring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(725,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__2) ).

thf(3560,plain,
    ! [A: $i,B: $i] :
      ( ( class_Int_Onumber__ring @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ B @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).

thf(911,axiom,
    ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ c_Int_OPls )
    = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__Pls) ).

thf(4157,plain,
    ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ c_Int_OPls )
    = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).

thf(432,axiom,
    ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
    = ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Numeral1__eq1__nat) ).

thf(2572,plain,
    ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
    = ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit1 @ c_Int_OPls ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(528,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__less) ).

thf(2913,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(371,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
      & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bn_O_AEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_An_J_096) ).

thf(2404,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) @ v_r )
      & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ B ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(475,axiom,
    ! [A: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ c_Int_OPls )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I1_J) ).

thf(2714,plain,
    ! [A: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ c_Int_OPls )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(685,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ B )
     => ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
        = ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__minus__cancel) ).

thf(3426,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ B )
     => ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
        = ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(1007,axiom,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bn_O_A_N_As_A_060_061_Acmod_A_Ipoly_Ap_A_Ig_An_J_J_096) ).

thf(4442,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p @ ( v_g____ @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).

thf(792,axiom,
    ! [A: $i] :
      ( ( class_RealVector_Oreal__normed__algebra__1 @ A )
     => ( ( c_RealVector_Onorm__class_Onorm @ A @ ( c_Groups_Oone__class_Oone @ A ) )
        = ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__one) ).

thf(3765,plain,
    ! [A: $i] :
      ( ( class_RealVector_Oreal__normed__algebra__1 @ A )
     => ( ( c_RealVector_Onorm__class_Onorm @ A @ ( c_Groups_Oone__class_Oone @ A ) )
        = ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).

thf(710,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Olinordered__ab__group__add @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) )
      <=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).

thf(3506,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Olinordered__ab__group__add @ B )
     => ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) )
         => ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) )
        & ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
         => ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).

thf(816,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__antisym) ).

thf(3843,plain,
    ! [A: $i,B: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).

thf(764,axiom,
    class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).

thf(3673,plain,
    class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).

thf(262,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg) ).

thf(2021,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(268,axiom,
    ! [A: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1) ).

thf(2063,plain,
    ! [A: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(203,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring @ B )
     => ( ( A
         != ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
          = ( c_Groups_Oone__class_Oone @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__inverse) ).

thf(1829,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Odivision__ring @ B )
     => ( ( A
         != ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Rings_Oinverse__class_Oinverse @ B @ A ) )
          = ( c_Groups_Oone__class_Oone @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(559,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__trans) ).

thf(3025,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(71,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ) )
       => ( B
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rabs__ratiotest__lemma) ).

thf(1378,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ) )
       => ( B
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(705,axiom,
    class_Groups_Oordered__ab__group__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).

thf(3489,plain,
    class_Groups_Oordered__ab__group__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).

thf(926,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).

thf(4206,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).

thf(827,axiom,
    class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).

thf(3886,plain,
    class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).

thf(1150,axiom,
    class_Groups_Oab__semigroup__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).

thf(4936,plain,
    class_Groups_Oab__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).

thf(170,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A )
      <=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) )
          & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
           => ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) @ C ) )
              & ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__eq) ).

thf(1713,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ D )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A )
         => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
             => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) @ C ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) )
        & ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
             => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) @ C ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(1160,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).

thf(4955,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).

thf(671,axiom,
    class_Groups_Omonoid__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).

thf(3394,plain,
    class_Groups_Omonoid__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(98,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Fields_Olinordered__field @ E )
     => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
       => ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
         => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
           => ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
             => ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ A ) @ ( c_Rings_Oinverse__class_Odivide @ E @ C @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__le) ).

thf(1505,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Fields_Olinordered__field @ E )
     => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
       => ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
         => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
           => ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
             => ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ A ) @ ( c_Rings_Oinverse__class_Odivide @ E @ C @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(931,axiom,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ B @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__triangle__ineq2) ).

thf(4221,plain,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ B @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).

thf(317,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I34_J) ).

thf(2241,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Int_OBit1 @ B ) @ ( c_Int_OBit1 @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(292,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono2) ).

thf(2127,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ C ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(62,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Fields_Ofield @ E )
     => ( ( D
         != ( c_Groups_Ozero__class_Ozero @ E ) )
       => ( ( C
           != ( c_Groups_Ozero__class_Ozero @ E ) )
         => ( ( ( c_Rings_Oinverse__class_Odivide @ E @ B @ D )
              = ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) )
          <=> ( ( c_Groups_Otimes__class_Otimes @ E @ B @ C )
              = ( c_Groups_Otimes__class_Otimes @ E @ A @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__eq__eq) ).

thf(1352,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Fields_Ofield @ E )
     => ( ( D
         != ( c_Groups_Ozero__class_Ozero @ E ) )
       => ( ( C
           != ( c_Groups_Ozero__class_Ozero @ E ) )
         => ( ( ( ( c_Rings_Oinverse__class_Odivide @ E @ B @ D )
                = ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) )
             => ( ( c_Groups_Otimes__class_Otimes @ E @ B @ C )
                = ( c_Groups_Otimes__class_Otimes @ E @ A @ D ) ) )
            & ( ( ( c_Groups_Otimes__class_Otimes @ E @ B @ C )
                = ( c_Groups_Otimes__class_Otimes @ E @ A @ D ) )
             => ( ( c_Rings_Oinverse__class_Odivide @ E @ B @ D )
                = ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(479,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
    <=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
        | ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).

thf(2731,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
          | ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) )
      & ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
          | ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(109,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) @ A )
      = ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zminus) ).

thf(1532,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) @ A )
      = ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(1107,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A )
      = ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__divide__def) ).

thf(4799,plain,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A )
      = ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ B @ ( c_Rings_Oinverse__class_Oinverse @ tc_RealDef_Oreal @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).

thf(512,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) )
     => ( ( A
          = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
        | ( B
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).

thf(2847,plain,
    ! [A: $i,B: $i] :
      ( ( B
        = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ B @ A ) )
     => ( ( A
          = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
        | ( B
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(441,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oabs__class_Oabs @ C @ A ) @ B )
          = ( c_Groups_Oabs__class_Oabs @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__div__pos) ).

thf(2600,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oabs__class_Oabs @ C @ A ) @ B )
          = ( c_Groups_Oabs__class_Oabs @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(991,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B )
        = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).

thf(4382,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B )
          = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) )
       => ( B = A ) )
      & ( ( B = A )
       => ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ B )
          = ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).

thf(728,axiom,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).

thf(3570,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).

thf(111,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
      <=> ( A
          = ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__zero__iff) ).

thf(1537,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ B )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Oabs__class_Oabs @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(1166,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
      = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).

thf(4972,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
      = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).

thf(1132,axiom,
    ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
    = ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__2__eq__2) ).

thf(4876,plain,
    ( ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) )
    = ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).

thf(246,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Olinordered__ab__group__add @ B )
     => ( ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
          = ( c_Groups_Ozero__class_Ozero @ B ) )
      <=> ( A
          = ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).

thf(1976,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Olinordered__ab__group__add @ B )
     => ( ( ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
            = ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
            = ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(63,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oring @ C )
     => ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__right) ).

thf(1357,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oring @ C )
     => ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(883,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A ) )
    <=> ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
          | ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
          | ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__0__le__divide__iff) ).

thf(4066,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A ) )
       => ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
            | ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) )
          & ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
            | ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ) )
      & ( ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
            | ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A ) )
          & ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
            | ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).

thf(621,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
          = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__add__eq__iff) ).

thf(3245,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
          = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(558,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
        | ( B = A ) )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).

thf(3020,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
        | ( B = A ) )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(670,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__neg__pos) ).

thf(3392,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Rings_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).

thf(936,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__diff__ineq) ).

thf(4229,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).

thf(128,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ ( c_RealVector_Onorm__class_Onorm @ D @ A ) ) )
         => ( B
            = ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__ratiotest__lemma) ).

thf(1597,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal @ C @ ( c_RealVector_Onorm__class_Onorm @ D @ A ) ) )
         => ( B
            = ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(784,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
     => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).

thf(3740,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
     => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).

thf(1103,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Ocancel__ab__semigroup__add @ D )
     => ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
          = ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).

thf(4779,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Ocancel__ab__semigroup__add @ D )
     => ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ B )
          = ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).

thf(733,axiom,
    class_Rings_Oring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).

thf(3580,plain,
    class_Rings_Oring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).

thf(240,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Oordered__semiring @ E )
     => ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ C )
           => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
             => ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono) ).

thf(1962,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Oordered__semiring @ E )
     => ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ C )
           => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
             => ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(261,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring @ C )
     => ( ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
          = ( c_Groups_Oone__class_Oone @ C ) )
       => ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__unique) ).

thf(2018,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Odivision__ring @ C )
     => ( ( ( c_Groups_Otimes__class_Otimes @ C @ B @ A )
          = ( c_Groups_Oone__class_Oone @ C ) )
       => ( ( c_Rings_Oinverse__class_Oinverse @ C @ B )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(381,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__0__le__add__iff) ).

thf(2436,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ A ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(81,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) )
      = ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).

thf(1449,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) )
      = ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(563,axiom,
    class_Rings_Ozero__neq__one @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).

thf(3047,plain,
    class_Rings_Ozero__neq__one @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(916,axiom,
    class_Fields_Ofield__inverse__zero @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).

thf(4174,plain,
    class_Fields_Ofield__inverse__zero @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).

thf(228,axiom,
    class_Int_Oring__char__0 @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).

thf(1912,plain,
    class_Int_Oring__char__0 @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(1088,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
     => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ C ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_decr__lemma) ).

thf(4734,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
     => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ C ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).

thf(717,axiom,
    class_Groups_Oab__semigroup__mult @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).

thf(3528,plain,
    class_Groups_Oab__semigroup__mult @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).

thf(1117,axiom,
    class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).

thf(4826,plain,
    class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).

thf(342,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult) ).

thf(2321,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Groups_Oabs__class_Oabs @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(1065,axiom,
    class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).

thf(4642,plain,
    class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).

thf(236,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oordered__cancel__semiring @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).

thf(1945,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oordered__cancel__semiring @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(1085,axiom,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).

thf(4723,plain,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).

thf(1041,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
    <=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
        | ( B
          = ( c_Nat_OSuc @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__eq) ).

thf(4555,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
          | ( B
            = ( c_Nat_OSuc @ A ) ) ) )
      & ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
          | ( B
            = ( c_Nat_OSuc @ A ) ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).

thf(577,axiom,
    class_RealVector_Oreal__normed__div__algebra @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).

thf(3096,plain,
    class_RealVector_Oreal__normed__div__algebra @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(521,axiom,
    ! [A: $i,B: $i] :
      ( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__add) ).

thf(2887,plain,
    ! [A: $i,B: $i] :
      ( ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(1097,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__left__mono) ).

thf(4767,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).

thf(676,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Fields_Ofield @ E )
     => ( ( D
         != ( c_Groups_Ozero__class_Ozero @ E ) )
       => ( ( C
           != ( c_Groups_Ozero__class_Ozero @ E ) )
         => ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ D ) @ ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) )
            = ( c_Rings_Oinverse__class_Odivide @ E @ ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ A @ D ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__eq) ).

thf(3405,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Fields_Ofield @ E )
     => ( ( D
         != ( c_Groups_Ozero__class_Ozero @ E ) )
       => ( ( C
           != ( c_Groups_Ozero__class_Ozero @ E ) )
         => ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ D ) @ ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) )
            = ( c_Rings_Oinverse__class_Odivide @ E @ ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) @ ( c_Groups_Otimes__class_Otimes @ E @ A @ D ) ) @ ( c_Groups_Otimes__class_Otimes @ E @ D @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).

thf(552,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ B )
          = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ A ) )
      <=> ( B
          = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).

thf(2998,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ B )
            = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ A ) )
         => ( B
            = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ A ) ) )
        & ( ( B
            = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) @ C ) @ A ) )
         => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ E @ C ) @ B )
            = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat @ D @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(119,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Olinordered__ab__group__add @ B )
     => ( ( A
          = ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
      <=> ( A
          = ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equal__neg__zero) ).

thf(1565,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Olinordered__ab__group__add @ B )
     => ( ( ( A
            = ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
         => ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( A
            = ( c_Groups_Ouminus__class_Ouminus @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(316,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
          = ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__left) ).

thf(2238,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ C @ A ) )
          = ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(333,axiom,
    ! [A: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ A )
     => ( ( c_Groups_Oabs__class_Oabs @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
        = ( c_Groups_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__zero) ).

thf(2297,plain,
    ! [A: $i] :
      ( ( class_Groups_Oordered__ab__group__add__abs @ A )
     => ( ( c_Groups_Oabs__class_Oabs @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
        = ( c_Groups_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(1001,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ A )
      = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).

thf(4423,plain,
    ! [A: $i,B: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).

thf(1141,axiom,
    class_Groups_Oab__semigroup__mult @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).

thf(4908,plain,
    class_Groups_Oab__semigroup__mult @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).

thf(388,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
     => ( A
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).

thf(2453,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
     => ( A
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(881,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Oab__group__add @ E )
     => ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
          = ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
       => ( ( D = C )
        <=> ( B = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).

thf(4056,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Oab__group__add @ E )
     => ( ( ( c_Groups_Ominus__class_Ominus @ E @ D @ C )
          = ( c_Groups_Ominus__class_Ominus @ E @ B @ A ) )
       => ( ( ( D = C )
           => ( B = A ) )
          & ( ( B = A )
           => ( D = C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).

thf(753,axiom,
    ! [A: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ A )
      = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).

thf(3637,plain,
    ! [A: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ A )
      = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).

thf(1128,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( class_Int_Onumber__ring @ C )
        & ( class_Int_Oring__char__0 @ C ) )
     => ( ( ( c_Int_Onumber__class_Onumber__of @ C @ B )
          = ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of) ).

thf(4863,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( class_Int_Onumber__ring @ C )
        & ( class_Int_Oring__char__0 @ C ) )
     => ( ( ( ( c_Int_Onumber__class_Onumber__of @ C @ B )
            = ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( ( c_Int_Onumber__class_Onumber__of @ C @ B )
            = ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).

thf(644,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Nat_OSuc @ B )
        = ( c_Nat_OSuc @ A ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).

thf(3316,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( c_Nat_OSuc @ B )
          = ( c_Nat_OSuc @ A ) )
       => ( B = A ) )
      & ( ( B = A )
       => ( ( c_Nat_OSuc @ B )
          = ( c_Nat_OSuc @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(921,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__less__0__iff) ).

thf(4189,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ B ) )
       => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).

thf(1040,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__cancel) ).

thf(4552,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ogroup__add @ C )
     => ( ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).

thf(862,axiom,
    class_Rings_Oring__1__no__zero__divisors @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).

thf(4002,plain,
    class_Rings_Oring__1__no__zero__divisors @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).

thf(5035,plain,
    $false,
    inference(cvc4,[status(thm)],[1322,2822,1586,1337,3883,2612,4835,1633,3434,2412,4290,3863,1982,2544,1179,3566,1295,4992,1554,4166,3053,2341,3008,1454,4909,2109,4824,4262,3661,3399,4169,4899,3798,2463,3397,3581,4852,2559,3449,2363,3990,2512,3072,2104,4339,1290,2644,3813,3549,1401,1939,2282,2114,3402,1692,1305,1173,4226,4500,2231,2622,1443,2776,3509,1618,3285,2671,2676,2014,4711,4603,4215,2380,1705,3217,1608,3429,4575,4011,1735,1867,4638,4564,2168,3313,2844,3577,4762,3276,4234,1671,4090,1655,3745,4418,4739,3004,4839,4647,3367,4884,4870,2918,2448,3338,3616,1233,4279,3253,3826,2459,1761,4294,3481,1507,3717,4941,4792,3545,3634,3249,3777,4803,4198,2516,4948,1623,1196,4047,1746,3103,4343,3236,2763,3915,2227,1576,1650,1645,1724,1475,2825,1967,4322,2819,1803,3880,1904,1518,1265,4775,2869,4511,1887,4637,3248,3046,2755,4761,3821,2501,2274,2745,2703,4439,1287,2603,4524,3938,4348,2814,1985,2698,1660,3131,4956,4415,3342,4224,3574,4654,2444,2217,3612,3148,2682,1826,1313,1279,4349,3749,2562,1832,2897,1992,3353,1462,3043,1545,2691,1800,4119,1479,4952,1641,4265,4669,3840,3374,4194,2552,1319,1890,2373,3919,1741,4317,3084,2929,3470,4551,3902,3657,1931,2301,1494,3557,1778,4302,2388,3866,1232,4253,4967,4008,4756,2829,2222,1465,3431,3199,3075,2090,1373,4297,3670,3163,4847,2540,2335,3152,1183,3771,1489,4696,3887,2324,3527,3702,3438,4147,4050,2122,3525,1864,2925,3973,2291,1383,2254,3300,3093,4660,2367,1377,4033,4842,1896,3808,3676,4924,1600,4628,3389,2508,2964,1447,2483,4364,2371,3243,2809,4038,2639,4643,1943,1201,2804,4519,3606,2154,1521,4588,3184,4475,2586,1975,4082,2762,3378,3435,3899,1206,3503,2910,2646,4531,3995,4312,2000,3151,2011,3097,4853,3582,2574,3720,1470,1708,2093,2441,1900,1223,2428,2541,4878,1217,4091,3207,1343,2560,2596,4397,1255,4434,4609,4989,1174,1676,2133,1502,1751,4128,3239,3069,4204,2937,4449,4493,3816,1370,2032,2986,3250,2132,2890,3339,3778,1238,3889,3948,1837,2200,4187,1836,2327,4740,2211,1634,3408,1573,2769,3271,3958,2464,4280,4585,2433,2477,4725,2565,2332,4155,4947,3349,2068,1819,2547,2492,3727,1281,3647,4080,4063,2653,3413,2685,1804,2895,2841,1375,4429,1587,2509,3386,3650,4109,3440,3968,1360,3467,3699,2300,1851,1772,1259,2577,3381,2694,4525,4693,4930,2537,3176,4817,4291,4333,2023,3846,1182,3714,2419,4513,2038,2085,4444,4814,3573,3935,4320,1683,3141,3952,3311,1361,4860,1964,1942,3922,4582,3179,3210,2561,4772,2868,4389,4315,2312,3010,4545,4938,1700,1937,1810,4054,1214,2349,2978,2649,4736,1744,3611,3541,2304,3059,2900,3743,2851,2465,2505,1947,4231,4223,2285,2504,2450,2932,3486,1478,1249,1530,2836,2355,4482,4244,3760,3409,2766,4902,1246,3333,4953,4152,4259,4689,3005,2272,3364,1627,4361,1525,3476,3755,2634,3834,2926,4352,1814,1695,2748,2915,3841,1185,1996,1241,3563,4567,2208,4782,3279,4212,3587,3306,3592,3999,2963,2368,1663,3190,1515,2221,4036,2189,2995,1616,3422,1906,2001,1727,4131,4708,1273,1548,4657,3289,3274,4599,4919,3130,1754,4380,4872,1680,1698,1959,2556,4116,3358,3871,3257,2717,1219,3079,4256,4340,1595,3888,4269,3686,4017,2376,4453,3343,3158,2260,3187,4268,2970,3768,3240,2789,4122,4465,4946,3213,4144,3372,3547,1833,3925,2938,3609,4159,2981,4309,1620,2489,1652,3081,1535,2806,3590,2398,4328,4590,4975,4612,2817,4769,4505,3599,2161,1669,4978,1312,3123,3783,2706,3832,2425,3091,3302,2358,3532,2029,4096,3726,2308,3077,3330,2738,4149,4171,4236,4218,1635,4672,2935,3594,4573,1239,2442,2759,1897,2557,1638,4887,2361,3419,3106,2116,2945,3500,4300,2346,3678,2521,4790,1209,2721,3352,2679,4704,3996,3631,1853,2478,4369,2151,2229,2084,3238,2214,2383,2624,2637,2422,3287,3515,4914,4699,1349,2257,3732,2246,1492,2378,4374,3182,1571,4509,4477,4107,1969,3160,4203,3027,2111,4181,2593,3298,4296,2664,1381,2461,2329,4541,2742,4103,1557,2129,2343,2625,1630,1993,4731,4028,1731,3800,3932,1909,4897,4985,4452,2410,2923,1325,1293,4993,1198,2962,3759,3110,3917,3806,1176,3953,3363,2101,1496,4209,2075,4933,4844,2401,1594,3423,2481,1445,1528,4502,1643,4085,4362,3674,4827,2288,1775,2752,1364,2967,3512,4282,3490,3380,1562,1413,4331,4426,3444,3576,1467,3161,4529,2124,1340,2256,3292,4722,3849,1662,4394,1304,1873,3193,4013,1758,2107,3395,2271,4456,3981,2878,4292,1509,1990,3048,2597,4581,4812,1551,2567,1748,3737,4490,2661,4937,4272,3214,1647,3949,2518,4517,4377,2850,4593,3640,2863,2012,3904,2588,4950,3833,4534,1252,3462,4287,1780,2821,2386,2407,3786,4894,4961,2569,3642,2920,4020,4003,3202,3774,4737,1579,2468,2656,3019,4398,2092,1790,3940,2224,3305,1432,3818,1813,1452,3691,3114,1188,2700,1262,1235,2276,2219,4132,1658,2486,4241,3623,3412,1738,3853,2056,4959,3415,4133,3493,1702,4436,2279,3388,4634,1797,2949,3961,1272,3520,4516,1934,3697,1543,4802,3107,1849,1257,1221,1284,1972,2711,4106,2728,4225,4838,3256,2892,3684,4392,4639,4548,1839,2088,2696,2828,3447,2310,3188,1412,2611,2209,1453,1998,2865,3168,3452,2458,4138,1316,3589,4325,1817,3171,2960,2078,1913,3625,4646,4078,2187,3346,4006,2658,3929,1734,1807,3665,4678,1276,3613,3709,2853,3383,3336,3748,1854,2608,1244,4823,1326,3729,3911,2389,4806,2098,3484,4089,2554,4468,3220,4042,4542,2004,3991,1523,4705,3136,4881,3662,2526,2416,3780,2447,1861,3324,2796,4964,4175,3585,4759,2330,3896,2162,1212,3993,1661,2315,4927,4025,1689,3978,2081,2475,3694,2786,4774,2462,2576,2066,3529,1193,1607,4404,2095,4446,1893,2294,2739,4570,4869,4372,2003,4039,1512,2302,4356,4809,4254,4596,3264,3100,3837,1876,1673,4579,4367,3062,3469,3658,4125,2102,4917,1957,4399,3860,1678,3132,1248,1757,4663,4357,2751,4178,1314,1816,4631,3850,3479,2366,1473,2619,2651,2783,2549,1859,4146,4303,4777,4051,1657,3560,4157,2572,2913,2404,2714,3426,4442,3765,3506,3843,3673,2021,2063,1829,3025,1378,3489,4206,3886,4936,1713,4955,3394,1505,4221,2241,2127,1352,2731,1532,4799,2847,2600,4382,3570,1537,4972,4876,1976,1357,4066,3245,3020,3392,4229,1597,3740,4779,3580,1962,2018,2436,1449,3047,4174,1912,4734,3528,4826,2321,4642,1945,4723,4555,3096,2887,4767,3405,2998,1565,2238,2297,4423,4908,2453,4056,3637,4863,3316,4189,4552,4002]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWW227+1 : TPTP v8.1.2. Released v5.2.0.
% 0.15/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.37  % Computer : n005.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Thu May 18 22:05:24 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 0.93/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.85/1.21  % [INFO] 	 Parsing done (332ms). 
% 1.85/1.22  % [INFO] 	 Running in sequential loop mode. 
% 2.62/1.46  % [INFO] 	 eprover registered as external prover. 
% 2.70/1.46  % [INFO] 	 cvc4 registered as external prover. 
% 2.70/1.47  % [INFO] 	 Scanning for conjecture ... 
% 3.01/1.62  % [INFO] 	 Found a conjecture and 1170 axioms. Running axiom selection ... 
% 4.27/1.85  % [INFO] 	 Axiom selection finished. Selected 1170 axioms (removed 0 axioms). 
% 5.59/2.25  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 5.59/2.28  % [INFO] 	 Type checking passed. 
% 5.59/2.29  % [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 ... 
% 30.18/7.83  % External prover 'cvc4' found a proof!
% 30.18/7.83  % [INFO] 	 Killing All external provers ... 
% 30.18/7.83  % Time passed: 7291ms (effective reasoning time: 6605ms)
% 30.18/7.83  % Solved by 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)>
% 30.18/7.84  % Axioms used in derivation (1170): fact_less__eq__int__code_I14_J, fact_le__SucI, arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra, fact_numeral__2__eq__2, fact_le__imp__diff__is__add, fact_Numeral1__eq1__nat, fact_minus__Bit0, fact_complex__diff__def, fact_zle__refl, fact_neg__le__0__iff__le, fact_add__le__less__mono, fact_mult__strict__left__mono__neg, fact_pos2, fact_zero__le__divide__iff, fact_Nat_Oadd__0__right, fact_right__inverse__eq, fact_real__squared__diff__one__factored, fact_abs__of__pos, fact_real__le__refl, fact_abs__le__D2, arity_Complex__Ocomplex__Rings_Oidom, fact_nat_Osimps_I3_J, fact_real__less__def, fact_number__of__diff, fact_mult__right__le__imp__le, arity_Nat__Onat__Groups_Ocancel__semigroup__add, fact_real__le__trans, fact_neg__le__divide__eq, arity_Complex__Ocomplex__Groups_Omonoid__add, arity_Int__Oint__Rings_Ocomm__semiring, fact_pos__add__strict, arity_Int__Oint__Rings_Osemiring, fact_nonzero__inverse__inverse__eq, fact_add__strict__right__mono, arity_Int__Oint__Orderings_Olinorder, fact__096_B_Bthesis_O_A_I_B_Bd_O_A_091_124_A0_A_060_Ad_059_AALL_Aw_O_A0_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_A_N_N_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_mult__1__left, fact_diff__0__eq__0, fact_minus__mult__left, fact_neg__divide__le__eq, fact_inverse__1, fact_neg__equal__0__iff__equal, fact_fz_I2_J, fact_semiring__norm_I112_J, fact_diff__add__inverse, fact_diff__bin__simps_I10_J, fact_abs__minus__commute, fact_abs__if, fact_bin__less__0__simps_I4_J, fact_le__eq__less__or__eq, arity_RealDef__Oreal__Groups_Ozero, fact_trans__less__add1, fact_mult__nonneg__nonpos, fact_q__pos__lemma, fact_one__is__num__one, fact_abs__ge__self, arity_RealDef__Oreal__Rings_Oordered__comm__semiring, arity_Complex__Ocomplex__Groups_Oab__group__add, fact_th000_I1_J, fact_diff__0__right, fact_mult__less__cancel__left__disj, fact_nat__add__left__commute, fact_real__mult__left__cancel, fact_mult__nonpos__nonpos, fact_less__imp__inverse__less, arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors, fact_real__of__nat__zero, fact_mult__left_Ominus, fact_number__of__minus, arity_Nat__Onat__Rings_Ono__zero__divisors, fact_nat__less__cases, fact_divide__nonpos__neg, fact_one__is__add, fact_diff__le__mono2, fact_mult__nat__number__of, arity_Int__Oint__Rings_Olinordered__semiring__strict, fact_minus__mult__right, fact_real__of__nat__diff, fact_norm__mult__less, fact_odd__nonzero, fact_add__nat__number__of, fact_zminus__zminus, fact_norm__diff__triangle__ineq, fact_less__int__code_I14_J, fact_mult__eq__0__iff, fact__096_B_By_O_A_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_A_N_A_I_N_Acmod_A_Ipoly_Ap_Az_J_J_A_060_Ay_J_A_061_A_I_N_As_A_060_Ay_J_096, fact_less__imp__le__nat, fact_combine__common__factor, fact_le__imp__0__less, fact_add__leD1, fact_diff__number__of__eq, fact_inverse__inverse__eq, fact_abs__div__pos, arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le, fact_add__less__mono, fact_th2, fact_real__0__less__add__iff, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J, fact_mult__right__less__imp__less, fact_positive__imp__inverse__positive, fact_abs__eq__mult, fact_split__mult__neg__le, fact_real__gt__half__sum, fact_rel__simps_I49_J, fact_rel__simps_I27_J, fact_n__less__m__mult__n, fact_eq__divide__eq__number__of, fact_divide__numeral__1, fact_numeral__1__eq__Suc__0, fact_Suc__mono, fact_inverse__add, fact_inverse__negative__iff__negative, arity_Nat__Onat__Groups_Oordered__comm__monoid__add, fact_less__nat__zero__code, fact_one__less__inverse__iff, arity_RealDef__Oreal__Rings_Olinordered__ring, fact_mult__le__less__imp__less, fact_zadd__commute, arity_Nat__Onat__Groups_Omonoid__mult, fact_diff__Suc__less, fact_real__add__le__0__iff, fact_divide__inverse, fact_mult__0, fact_inverse__zero__imp__zero, fact_abs__triangle__ineq2__sym, fact__096EX_AN_O_AALL_An_062_061N_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_096, fact_eq__neg__iff__add__eq__0, fact_add__right__imp__eq, arity_Complex__Ocomplex__Groups_Oab__semigroup__mult, fact_zero__less__diff, fact_nonzero__inverse__eq__imp__eq, fact_diff__diff__cancel, fact_mult__mono, fact_gr0__conv__Suc, fact_abs__diff__triangle__ineq, fact_inverse__zero, arity_Complex__Ocomplex__Int_Onumber__ring, fact_Suc__le__mono, fact_le__number__of__eq__not__less, fact_norm__add__less, arity_Nat__Onat__Rings_Ozero__neq__one, fact_nat__number__of__Pls, fact_nat__add__right__cancel, fact_neg__le__iff__le, arity_RealDef__Oreal__Groups_Omonoid__add, fact_neg__0__less__iff__less, fact_less__special_I4_J, arity_RealDef__Oreal__Rings_Oidom, fact_int__pos__lt__two__imp__zero__or__one, fact_mult__le__mono2, fact_Suc__diff__diff, fact_le__neq__implies__less, arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add, fact_lemma__NBseq__def2, fact_zero__le__one, fact_diff__bin__simps_I7_J, fact_Bit1__def, fact_int__0__less__1, fact_le__minus__iff, fact_pos__le__divide__eq, fact_left__diff__distrib__number__of, fact_linorder__neqE__linordered__idom, fact_rel__simps_I31_J, fact__096_B_Bthesis_O_A_I_B_BN2_O_A2_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_AN2_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_mult_Oadd__right, fact_mult_Ominus__right, fact_le__add__iff2, fact_mult__eq__self__implies__10, fact_mult__left__le__imp__le, fact_divide__pos__neg, fact_minus__add__cancel, fact_add__pos__nonneg, fact_expand__Suc, fact_mult__numeral__1__right, fact_zle__linear, fact_nat__add__left__cancel__less, fact_add__Bit0__Bit1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_add__strict__increasing2, fact_inverse__positive__imp__positive, fact_minus__number__of__mult, fact_mult__imp__le__div__pos, fact_abs__of__neg, arity_Complex__Ocomplex__Rings_Ocomm__semiring__1, arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero, fact_abs__triangle__ineq2, fact_neg__less__0__iff__less, fact_divide__right__mono, fact_rel__simps_I5_J, arity_RealDef__Oreal__Fields_Ofield__inverse__zero, arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add, fact_add__nonneg__eq__0__iff, fact_mult_Ozero__left, fact_real__mult__commute, fact_real__of__nat__zero__iff, fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096, fact_seq__suble, fact_zadd__left__mono, fact_sum__squares__le__zero__iff, fact_divide__1, fact_mult__strict__left__mono, fact_number__of__is__id, arity_Int__Oint__Rings_Olinordered__semiring__1__strict, fact_mult__right_Ozero, fact_mult__le__cancel__left__neg, fact_minus__real__def, fact_add__le__imp__le__left, fact_sum__squares__ge__zero, fact_add__increasing2, fact_zero__le__mult__iff, arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero, arity_Int__Oint__Groups_Ozero, arity_RealDef__Oreal__Groups_Oabs__if, fact_divide__le__eq, fact_add__mono, fact_gr0I, arity_Int__Oint__Rings_Olinordered__ring, fact_N1, fact_add__right__mono, fact_norm__triangle__ineq3, fact_nat__less__real__le, fact_real__mult__assoc, fact_mult__eq__1__iff, fact_even__less__0__iff, fact_self__quotient__aux1, arity_Int__Oint__Groups_Ocomm__monoid__add, fact_eq__divide__2__times__iff, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, arity_RealDef__Oreal__Groups_Omonoid__mult, fact_add__0__left, fact_add__eq__if, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_le__nat__number__of, fact_less__int__code_I13_J, fact_minus__add, fact_divide__eq__imp, fact_abs__add__one__gt__zero, fact_lemma__NBseq__def, fact_th1, fact_real__of__nat__less__iff, fact_rabs__ratiotest__lemma, fact_diff__le__self, fact_minus__less__iff, fact_half__gt__zero__iff, fact_less__add__eq__less, fact_nat__mult__1__right, fact_divide__strict__left__mono__neg, fact__096_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_J_A_061_A_I_N_As_A_060_A_N_As_J_096, fact_number__of__add, fact_divide__le__eq__number__of, fact_less__eq__nat_Osimps_I1_J, fact_add__numeral__0__right, fact_inverse__less__imp__less, fact__0962_A_P_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_060_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096, fact_add__numeral__0, arity_RealDef__Oreal__Rings_Olinordered__idom, fact_le__iff__add, fact_one__reorient, fact_le__number__of, fact_diff__commute, fact_rel__simps_I44_J, arity_Nat__Onat__Rings_Oordered__comm__semiring, fact_less__eq__number__of__int__code, fact_negative__imp__inverse__negative, fact_diff__Suc__eq__diff__pred, fact_less__divide__eq__number__of1, fact_divide__add__eq__iff, fact_minus__mult__commute, fact_division__ring__inverse__add, fact_mult__left_Odiff, fact_eq__iff__diff__eq__0, fact_add__lessD1, fact_add__le__mono1, arity_Int__Oint__Rings_Oidom, fact_divide__less__eq__number__of1, arity_Complex__Ocomplex__Fields_Ofield, fact_mult__numeral__1, fact_lessI, fact_zero__le__square, fact_nat__1__add__1, fact_zero__reorient, fact_rel__simps_I15_J, arity_Int__Oint__Groups_Oordered__ab__group__add, fact_mult__right_Odiff, fact_inverse__numeral__1, fact_minus__le__iff, fact_less__0__number__of, fact_Suc__less__SucD, fact_mth2, fact_field__divide__inverse, fact_zadd__zless__mono, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_nat__eq__add__iff2, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_split__mult__pos__le, fact_le__special_I1_J, fact_nat_Oinject, fact_mult__left__le__one__le, arity_Int__Oint__Rings_Oring__no__zero__divisors, fact_nat__le__real__less, fact_not__add__less2, fact_less__or__eq__imp__le, fact_Suc__diff__eq__diff__pred, arity_Int__Oint__Rings_Oordered__cancel__semiring, fact_real__add__minus__iff, fact_incr__lemma, arity_RealDef__Oreal__Groups_Ocancel__semigroup__add, fact_minus__divide__divide, fact_zadd__strict__right__mono, arity_Int__Oint__Int_Onumber__ring, arity_Complex__Ocomplex__RealVector_Oreal__field, fact_complex__mod__triangle__sub, fact_q__neg__lemma, fact_inverse__le__1__iff, fact_add__0__right, fact_mult__pos__neg, fact_pos__less__divide__eq, fact_add__number__of__diff2, fact_real__le__eq__diff, fact_mult__less__mono1, fact_Suc__leI, fact_add__neg__nonpos, fact_unique__quotient__lemma__neg, arity_RealDef__Oreal__Rings_Ozero__neq__one, fact_diff__less, fact_mult__pos__neg2, fact_convex__bound__lt, fact_abs__minus__add__cancel, fact_zadd__assoc, fact_pos__divide__le__eq, fact_real__0__le__divide__iff, fact_less__irrefl__nat, arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs, fact_Suc__lessD, arity_RealDef__Oreal__RealVector_Oreal__normed__algebra, fact_not__less__less__Suc__eq, fact_diff__def, arity_RealDef__Oreal__RealVector_Oreal__field, fact_nat__mult__1, fact_diff__is__0__eq_H, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, fact_mult__right__mono__neg, fact_rel__simps_I48_J, fact_rel__simps_I12_J, fact_DERIV__inverse__lemma, fact_divide__strict__right__mono__neg, fact_le__add2, fact_minus__divide__right, fact_abs__eq__0, fact_th, fact_diff__self, fact_minus__nat_Odiff__0, fact_pos__zmult__eq__1__iff, arity_Int__Oint__Groups_Ocancel__semigroup__add, fact_nonzero__inverse__mult__distrib, fact_mult_Oprod__diff__prod, fact_zle__diff1__eq, fact_divide__eq__eq__number__of, fact_Suc__n__not__le__n, fact_add__diff__assoc, fact_inverse__less__1__iff, fact_g_I2_J, fact_diff__0, fact_add__left__imp__eq, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_add__leD2, fact_mult__mono_H, fact_real__add__mult__distrib, fact_divide__left__mono, fact_real__of__nat__le__zero__cancel__iff, fact_abs__ge__minus__self, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, fact_ab__semigroup__mult__class_Omult__ac_I1_J, fact_not__less0, fact_mult__Pls, fact_trans__less__add2, fact_minus__numeral__code_I5_J, fact_less__Suc__eq__le, fact_Suc3__eq__add__3, fact_nat__diff__split, fact_norm__one, fact_zadd__0, fact_add__frac__eq, fact_divide__left__mono__neg, fact_real__zero__not__eq__one, fact_abs__of__nonneg, arity_RealDef__Oreal__Rings_Omult__zero, arity_Complex__Ocomplex__Groups_Oab__semigroup__add, arity_Complex__Ocomplex__Fields_Ofield__inverse__zero, fact_inverse__divide, arity_Int__Oint__Int_Onumber, fact_rel__simps_I21_J, arity_Nat__Onat__Rings_Ocomm__semiring__1, fact_divide_Ominus, fact_s1m, fact_nat_Osimps_I2_J, fact_th00, fact_mult__divide__mult__cancel__left, fact_zero__le__double__add__iff__zero__le__single__add, fact_times__numeral__code_I5_J, arity_Int__Oint__Groups_Oab__semigroup__mult, fact_mult__left__less__imp__less, fact_diff__mult__distrib2, fact_abs__le__D1, fact_semiring__norm_I115_J, fact_neg__less__iff__less, fact_add__Bit0__Bit0, arity_Complex__Ocomplex__Rings_Osemiring, fact_rel__simps_I34_J, fact_real__mult__right__cancel, fact_less__zeroE, fact_minus__zero, arity_Complex__Ocomplex__Groups_Ogroup__add, fact_not__one__less__zero, fact_abs__diff__less__iff, fact_zero__less__norm__iff, fact_one__le__mult__iff, arity_RealDef__Oreal__Rings_Olinordered__semiring, fact_rel__simps_I51_J, fact_not__less__eq, arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, fact_complex__mod__minus__le__complex__mod, fact_norm__le__zero__iff, fact_mult__imp__div__pos__less, fact_less__nat__number__of, fact_mult__le__cancel1, fact_nat__neq__iff, fact_nat__1__eq__mult__iff, fact_nonzero__inverse__eq__divide, fact_less__eq__real__def, fact_eq__add__iff1, fact_less__not__refl3, arity_Complex__Ocomplex__Rings_Ozero__neq__one, fact_nat__diff__split__asm, fact_frac__le, fact_add__left__cancel, fact_divide__real__def, fact_neg__less__nonneg, fact_nat__add__left__cancel__le, fact_add__number__of__diff1, arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict, fact_norm__triangle__ineq4, fact_add__mult__distrib2, arity_Int__Oint__Groups_Ocancel__ab__semigroup__add, fact_add__Bit1__Bit0, fact_arith__simps_I32_J, fact_abs__real__def, fact_norm__eq__zero, fact_add__right__cancel, fact_mult__strict__mono_H, fact_mult__Bit1, fact_one__less__mult, fact_zle__antisym, fact_abs__less__iff, fact_mult__nonneg__nonneg, fact_add__less__cancel__left, fact_real__mult__inverse__cancel, fact_zero__less__mult__pos2, arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add, fact_nonzero__norm__inverse, arity_Int__Oint__Rings_Oordered__ring__abs, fact_frac__eq__eq, fact_zmult__assoc, fact_one__less__inverse, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_abs__not__less__zero, arity_Int__Oint__Rings_Oordered__semiring, arity_Complex__Ocomplex__Rings_Ocomm__semiring, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J, arity_Complex__Ocomplex__RealVector_Oreal__normed__field, fact_double__zero__sym, fact_divide__pos__pos, fact_le__imp__inverse__le__neg, fact_neg__0__equal__iff__equal, fact_zminus__zadd__distrib, fact_le__diff__conv, fact_divide__neg__neg, fact_mult__left__mono, fact_abs__zmult__eq__1, fact_less__Suc__eq__0__disj, fact_mult__left_Oadd, fact_frac__less, fact_mult__imp__less__div__pos, fact_add__divide__eq__iff, fact_norm__ge__zero, fact_zmult__1, fact_mult__left_Ozero, fact_one__neq__zero, fact_left__minus, fact_divide__neg__pos, fact_diff__cancel, fact_norm__divide, fact_divide__Numeral0, arity_RealDef__Oreal__Fields_Olinordered__field, fact_right__minus, fact_real__less__half__sum, fact_le__add__iff1, fact_norm__minus__commute, fact_divide__nonneg__pos, fact_minus__numeral__code_I6_J, fact_le__Suc__eq, fact_real__minus__mult__self__le, fact_add__Pls, fact_less__add__iff2, fact_add__strict__mono, fact_diff__divide__eq__iff, fact_norm__diff__ineq, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, arity_RealDef__Oreal__Orderings_Olinorder, fact_mult__number__of__left, fact_le__add__diff__inverse2, fact_Suc__mult__less__cancel1, fact_add__num__frac, fact_not__one__le__zero, fact_mult__cancel2, fact_complex__mod__triangle__ineq2, arity_RealDef__Oreal__Rings_Ocomm__semiring, arity_RealDef__Oreal__RealVector_Oreal__normed__vector, fact_mult__2__right, arity_Int__Oint__Rings_Olinordered__semidom, fact_nat__number__of__mult__left, fact_equation__minus__iff, fact_inverse__eq__divide, fact_rel__simps_I39_J, fact_nat__diff__add__eq2, fact_mult__neg__pos, arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult, fact_diff__int__def__symmetric, arity_Nat__Onat__Groups_Ocomm__monoid__add, fact_nat__mult__le__cancel1, fact__0961_A_P_Areal_A_ISuc_A_If_A_IN1_A_L_AN2_J_J_J_A_060_061_A1_A_P_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096, fact_less__divide__eq__number__of, fact_less__antisym, fact_not__real__square__gt__zero, fact_Suc__le__eq, arity_Int__Oint__Groups_Ogroup__add, fact_add__diff__cancel, fact_eq__divide__eq__number__of1, arity_Nat__Onat__Rings_Ocomm__semiring, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_mult__less__le__imp__less, fact_nat__mult__assoc, fact_equal__neg__zero, fact_diff__int__def, arity_Nat__Onat__Groups_Omonoid__add, fact_not__sum__squares__lt__zero, fact_less__add__Suc2, fact_semiring__norm_I110_J, fact_le__imp__inverse__le, fact_mult_Ominus__left, fact_diff__add__cancel, arity_Complex__Ocomplex__Rings_Oring, arity_Int__Oint__Groups_Oab__group__add, fact_divide__nonpos__pos, fact_real__mult__1, fact_less__eq__Suc__le, fact_divide__eq__eq, fact_inverse__nonnegative__iff__nonnegative, fact_mult__nonneg__nonpos2, fact_less__imp__diff__less, arity_RealDef__Oreal__Rings_Oordered__cancel__semiring, fact_number__of__mult, fact_inverse__eq__imp__eq, arity_RealDef__Oreal__Rings_Odivision__ring, fact_nat__mult__eq__cancel1, arity_Int__Oint__Rings_Oring__1__no__zero__divisors, fact_Suc__pred_H, fact_abs__ge__zero, fact_add__special_I2_J, fact_rel__simps_I19_J, fact_zmult__commute, fact_norm__number__of, fact_less__eq__int__code_I15_J, fact_nat__mult__2, fact_abs__idempotent, arity_RealDef__Oreal__Rings_Oring, fact_comm__mult__strict__left__mono, fact_minus__minus, fact_rel__simps_I38_J, fact_real__mult__inverse__left, fact_th0, fact_minus__add__distrib, arity_Complex__Ocomplex__Groups_Ocomm__monoid__add, fact_diff__diff__left, fact_left__distrib__number__of, arity_Complex__Ocomplex__Groups_Oone, fact_add__is__1, arity_Nat__Onat__Groups_Oordered__ab__semigroup__add, fact_less__minus__iff, fact_inverse__unique, fact_fz_I1_J, fact_real__of__nat__Suc, fact_linorder__neqE__nat, fact_mult__less__mono2, arity_RealDef__Oreal__Rings_Osemiring, fact_rel__simps_I17_J, fact_number__of__Bit0, fact_diffs0__imp__equal, fact_nonzero__divide__eq__eq, fact__096_B_Bn_O_A_N_As_A_060_061_Acmod_A_Ipoly_Ap_A_Ig_An_J_J_096, fact_less__number__of__int__code, arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add, fact_zero__is__num__zero, fact_divide__less__0__iff, fact_norm__not__less__zero, 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fact__096_B_Bthesis_O_A_I_B_BN1_O_AALL_An_062_061N1_O_Acmod_A_Ig_A_If_An_J_A_N_Az_J_A_060_Ad_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_right__distrib__number__of, fact_neg__less__divide__eq, fact_le__trans, arity_Int__Oint__Groups_Oabs__if, fact_add__Pls__right, fact_zmult__zless__mono2, fact_diff__Suc__diff__eq1, fact_comm__mult__left__mono, fact_divide__eq__eq__number__of1, fact_plus__numeral__code_I9_J, fact_fact__lemma, fact_divide__less__eq, fact_gr__implies__not0, fact_mult__strict__right__mono__neg, fact_abs__triangle__ineq, fact__096cmod_A_Ipoly_Ap_A_Ig_A_If_A_IN1_A_L_AN2_J_J_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_A_If_A_IN1_A_L_AN2_J_J_J_096, fact_real__two__squares__add__zero__iff, arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero, fact_less__add__one, fact_int__one__le__iff__zero__less, fact_mult__less__imp__less__right, fact_zero__neq__one, fact_less__Suc__eq, fact_divide__strict__left__mono, fact_add__leE, fact_th31, fact_mult_Odiff__left, 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arity_RealDef__Oreal__Rings_Oordered__semiring, fact_le__SucE, fact_divide_Odiff, fact_nat__mult__commute, fact_divide__Numeral1, fact_add1__zle__eq, fact_th000_I2_J, fact__096cmod_A0_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A0_J_A_061_A_N_A_I_N_Acmod_A_Ipoly_Ap_A0_J_J_096, fact_eq__imp__le, fact_diff__add__inverse2, arity_Complex__Ocomplex__Int_Oring__char__0, arity_Int__Oint__Rings_Olinordered__semiring__1, fact_plus__nat_Oadd__0, fact_subseq__Suc__iff, arity_RealDef__Oreal__Int_Onumber, fact_neg__divide__less__eq, fact_diff__eq__diff__eq, fact_minus__le__self__iff, fact_less__int__code_I16_J, fact_add__strict__increasing, fact__096EX_Af_O_AALL_Ax_O_Acmod_A_If_Ax_J_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A_If_Ax_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_Ax_J_096, fact_real__mult__order, fact_le__less__Suc__eq, fact_real__norm__def, fact_d_I2_J, fact_mult__left__mono__neg, fact_le__antisym, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, 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% 30.18/7.84  % No. of inferences in proof: 2344
% 30.18/7.84  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7291 ms resp. 6605 ms w/o parsing
% 31.58/8.36  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 31.58/8.37  % [INFO] 	 Killing All external provers ... 
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