TSTP Solution File: SWW229+1 by Leo-III---1.7.12

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SWW229+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n014.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 06:47:50 EDT 2024

% Result   : Theorem 23.39s 6.10s
% Output   : Refutation 24.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      : 1360
% Syntax   : Number of formulae    : 2610 ( 774 unt; 112 typ;   0 def)
%            Number of atoms       : 6261 (1678 equ;   0 cnn)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives : 29831 ( 409   ~; 130   |; 555   &;25659   @)
%                                         ( 254 <=>;2824  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  125 ( 125   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  114 ( 112 usr;  16 con; 0-3 aty)
%            Number of variables   : 4790 (   0   ^4709   !;  81   ?;4790   :)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_Divides_Odiv__class_Odiv_type,type,
    c_Divides_Odiv__class_Odiv: $i > $i > $i > $i ).

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

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

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

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

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

thf(class_Divides_Osemiring__div_type,type,
    class_Divides_Osemiring__div: $i > $o ).

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

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

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

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

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

thf(class_Rings_Ocomm__semiring__0_type,type,
    class_Rings_Ocomm__semiring__0: $i > $o ).

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

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

thf(class_Rings_Ocomm__ring__1_type,type,
    class_Rings_Ocomm__ring__1: $i > $o ).

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

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

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

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

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

thf(class_Groups_Ominus_type,type,
    class_Groups_Ominus: $i > $o ).

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

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

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

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

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

thf(class_Groups_Osgn__if_type,type,
    class_Groups_Osgn__if: $i > $o ).

thf(c_Groups_Osgn__class_Osgn_type,type,
    c_Groups_Osgn__class_Osgn: $i > $i > $i ).

thf(class_Groups_Ouminus_type,type,
    class_Groups_Ouminus: $i > $o ).

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

thf(c_RComplete_Onatceiling_type,type,
    c_RComplete_Onatceiling: $i > $i ).

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

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

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

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

thf(class_Orderings_Oord_type,type,
    class_Orderings_Oord: $i > $o ).

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

thf(tc_fun_type,type,
    tc_fun: $i > $i > $i ).

thf(class_Rings_Ocomm__ring_type,type,
    class_Rings_Ocomm__ring: $i > $o ).

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

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

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

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

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

thf(class_Groups_Ocancel__comm__monoid__add_type,type,
    class_Groups_Ocancel__comm__monoid__add: $i > $o ).

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

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

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

thf(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_type,type,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).

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

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

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

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

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

thf(c_RComplete_Onatfloor_type,type,
    c_RComplete_Onatfloor: $i > $i ).

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

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

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

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

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

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

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

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

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

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

thf(c_Polynomial_Oorder_type,type,
    c_Polynomial_Oorder: $i > $i > $i > $i ).

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

thf(v_s_____type,type,
    v_s____: $i ).

thf(c_Complex_Oii_type,type,
    c_Complex_Oii: $i ).

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

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

thf(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize_type,type,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: $i > $i > $i ).

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

thf(c_SEQ_Odecseq_type,type,
    c_SEQ_Odecseq: $i > $i > $o ).

thf(551,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ 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_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).

thf(3021,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ 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)],[551]) ).

thf(114,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(1586,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)],[114]) ).

thf(46,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(1369,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)],[46]) ).

thf(547,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Opreorder @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).

thf(3008,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Opreorder @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(474,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(2778,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)],[474]) ).

thf(1185,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(4899,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)],[1185]) ).

thf(371,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(2412,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)],[371]) ).

thf(393,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(2480,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)],[393]) ).

thf(863,axiom,
    class_Fields_Ofield__inverse__zero @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).

thf(4015,plain,
    class_Fields_Ofield__inverse__zero @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).

thf(835,axiom,
    class_Orderings_Opreorder @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).

thf(3927,plain,
    class_Orderings_Opreorder @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).

thf(1132,axiom,
    ! [A: $i] :
      ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
      = ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sgn__eq) ).

thf(4728,plain,
    ! [A: $i] :
      ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
      = ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).

thf(589,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(3172,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)],[589]) ).

thf(324,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(2250,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)],[324]) ).

thf(487,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(2822,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)],[487]) ).

thf(820,axiom,
    class_Rings_Olinordered__semiring__strict @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).

thf(3873,plain,
    class_Rings_Olinordered__semiring__strict @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).

thf(1069,axiom,
    class_Rings_Ozero__neq__one @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).

thf(4560,plain,
    class_Rings_Ozero__neq__one @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).

thf(848,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( B = A )
      <=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
          & ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).

thf(3962,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( ( B = A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
            & ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) )
        & ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
            & ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).

thf(152,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(1718,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)],[152]) ).

thf(427,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(2612,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)],[427]) ).

thf(893,axiom,
    class_Groups_Ocancel__comm__monoid__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add) ).

thf(4094,plain,
    class_Groups_Ocancel__comm__monoid__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).

thf(338,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ( B != A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).

thf(2295,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ( B != A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(897,axiom,
    class_Groups_Oab__semigroup__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).

thf(4101,plain,
    class_Groups_Oab__semigroup__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).

thf(257,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Groups_Oordered__ab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).

thf(2072,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Groups_Oordered__ab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(745,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(3661,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)],[745]) ).

thf(170,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(1767,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)],[170]) ).

thf(328,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
      <=> ( ( c_Orderings_Oord__class_Oless @ C @ A @ B )
          | ( B = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).

thf(2263,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
         => ( ( c_Orderings_Oord__class_Oless @ C @ A @ B )
            | ( B = A ) ) )
        & ( ( ( c_Orderings_Oord__class_Oless @ C @ A @ B )
            | ( B = A ) )
         => ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(924,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(4169,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)],[924]) ).

thf(747,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(3666,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)],[747]) ).

thf(157,axiom,
    class_Rings_Olinordered__semidom @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).

thf(1729,plain,
    class_Rings_Olinordered__semidom @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(970,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(4290,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)],[970]) ).

thf(761,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(3698,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)],[761]) ).

thf(851,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(3979,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)],[851]) ).

thf(656,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 @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) )
      <=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ B )
          & ( 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_nonneg1__imp__zdiv__pos__iff) ).

thf(3397,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 @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) )
         => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ B )
            & ( 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 @ A @ 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_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(203,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(1899,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)],[203]) ).

thf(185,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(1840,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)],[185]) ).

thf(713,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
     => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ge__natfloor__plus__one__imp__gt) ).

thf(3581,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
     => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).

thf(25,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(1315,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)],[25]) ).

thf(478,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(2787,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)],[478]) ).

thf(164,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(1750,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)],[164]) ).

thf(1049,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(4500,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)],[1049]) ).

thf(992,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(4339,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)],[992]) ).

thf(815,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(3858,plain,
    class_Rings_Oring__no__zero__divisors @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).

thf(605,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(3230,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)],[605]) ).

thf(514,axiom,
    ! [A: $i] :
      ( ( c_RComplete_Onatfloor @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__real__of__nat) ).

thf(2908,plain,
    ! [A: $i] :
      ( ( c_RComplete_Onatfloor @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(436,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(2659,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)],[436]) ).

thf(529,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(2953,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)],[529]) ).

thf(574,axiom,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ A )
     => ( class_Groups_Ocomm__monoid__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).

thf(3098,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ A )
     => ( class_Groups_Ocomm__monoid__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(441,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Lattices_Oboolean__algebra @ 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_compl__eq__compl__iff) ).

thf(2671,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Lattices_Oboolean__algebra @ 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)],[441]) ).

thf(1209,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(4960,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)],[1209]) ).

thf(1087,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(4603,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)],[1087]) ).

thf(265,axiom,
    ! [A: $i] :
      ( ( class_Fields_Ofield @ A )
     => ( class_Divides_Osemiring__div @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Divides_Osemiring__div) ).

thf(2099,plain,
    ! [A: $i] :
      ( ( class_Fields_Ofield @ A )
     => ( class_Divides_Osemiring__div @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(1091,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 @ ( hAPP @ ( 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(4614,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 @ ( hAPP @ ( 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 @ ( hAPP @ ( 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)],[1091]) ).

thf(69,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(1437,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)],[69]) ).

thf(259,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(2077,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)],[259]) ).

thf(875,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(4043,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)],[875]) ).

thf(700,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(3534,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)],[700]) ).

thf(756,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(3681,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)],[756]) ).

thf(856,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ A )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_RComplete_Onatfloor @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor) ).

thf(3990,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ A )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_RComplete_Onatfloor @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).

thf(566,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Groups_Oordered__cancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).

thf(3072,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Groups_Oordered__cancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(212,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).

thf(1924,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(308,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ B ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg) ).

thf(2210,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ B ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(524,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ 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__1__class_Onormalizing__semiring__rules_I8_J) ).

thf(2940,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ 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)],[524]) ).

thf(58,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(1406,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)],[58]) ).

thf(267,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(2104,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)],[267]) ).

thf(886,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(4075,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)],[886]) ).

thf(16,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Divides_Osemiring__div @ B )
     => ( ( c_Divides_Odiv__class_Odiv @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__by__1) ).

thf(1290,plain,
    ! [A: $i,B: $i] :
      ( ( class_Divides_Osemiring__div @ B )
     => ( ( c_Divides_Odiv__class_Odiv @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(981,axiom,
    class_Rings_Olinordered__semidom @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).

thf(4311,plain,
    class_Rings_Olinordered__semidom @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).

thf(93,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( B != A )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
         => ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I12_J) ).

thf(1522,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( B != A )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
         => ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(785,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(3762,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)],[785]) ).

thf(692,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oorder @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ A @ C )
         => ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).

thf(3509,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oorder @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ A @ C )
         => ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).

thf(620,axiom,
    class_Groups_Ocancel__semigroup__add @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).

thf(3285,plain,
    class_Groups_Ocancel__semigroup__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(651,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(3377,plain,
    class_Groups_Oordered__ab__group__add__abs @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(1012,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(4391,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)],[1012]) ).

thf(109,axiom,
    class_Rings_Ocomm__semiring__0 @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).

thf(1569,plain,
    class_Rings_Ocomm__semiring__0 @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(846,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 @ ( hAPP @ ( 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(3959,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 @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( v_g____ @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).

thf(323,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(2248,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)],[323]) ).

thf(271,axiom,
    class_Groups_Oab__group__add @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).

thf(2114,plain,
    class_Groups_Oab__group__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(9,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_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I1_J) ).

thf(1269,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_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(687,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(3498,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).

thf(937,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(4215,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)],[937]) ).

thf(362,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(2380,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)],[362]) ).

thf(600,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Lattices_Oboolean__algebra @ B )
     => ( ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__compl) ).

thf(3217,plain,
    ! [A: $i,B: $i] :
      ( ( class_Lattices_Oboolean__algebra @ B )
     => ( ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(891,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(4090,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)],[891]) ).

thf(581,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(3120,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)],[581]) ).

thf(1134,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(4739,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)],[1134]) ).

thf(346,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(2316,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)],[346]) ).

thf(1072,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 @ ( hAPP @ ( 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(4564,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 @ ( hAPP @ ( 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)],[1072]) ).

thf(292,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(2168,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)],[292]) ).

thf(383,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(2459,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)],[383]) ).

thf(629,axiom,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ A )
     => ( class_Groups_Oone @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).

thf(3313,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ A )
     => ( class_Groups_Oone @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(39,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(1354,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)],[39]) ).

thf(356,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oorder @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C )
         => ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).

thf(2360,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oorder @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C )
         => ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(303,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(2195,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)],[303]) ).

thf(1065,axiom,
    class_Rings_Ocomm__semiring__0 @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).

thf(4543,plain,
    class_Rings_Ocomm__semiring__0 @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).

thf(139,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(1671,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)],[139]) ).

thf(1233,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(5037,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)],[1233]) ).

thf(121,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(1608,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)],[121]) ).

thf(1017,axiom,
    class_Int_Onumber__ring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).

thf(4403,plain,
    class_Int_Onumber__ring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).

thf(1098,axiom,
    ! [A: $i] :
      ( ( 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_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__le) ).

thf(4647,plain,
    ! [A: $i] :
      ( ( 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_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).

thf(648,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Orderings_Oorder @ B )
     => ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).

thf(3367,plain,
    ! [A: $i,B: $i] :
      ( ( class_Orderings_Oorder @ B )
     => ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(1179,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(4884,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)],[1179]) ).

thf(647,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Olinordered__semidom @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).

thf(3365,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Olinordered__semidom @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(869,axiom,
    class_Rings_Ocomm__semiring__0 @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__0) ).

thf(4026,plain,
    class_Rings_Ocomm__semiring__0 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).

thf(160,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( ( A
            = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
         => ( ( c_Groups_Osgn__class_Osgn @ ( tc_Polynomial_Opoly @ B ) @ A )
            = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
        & ( ( A
           != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
         => ( ( ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
             => ( ( c_Groups_Osgn__class_Osgn @ ( tc_Polynomial_Opoly @ B ) @ A )
                = ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
             => ( ( c_Groups_Osgn__class_Osgn @ ( tc_Polynomial_Opoly @ B ) @ A )
                = ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__poly__def) ).

thf(1735,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( ( A
            = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
         => ( ( c_Groups_Osgn__class_Osgn @ ( tc_Polynomial_Opoly @ B ) @ A )
            = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
        & ( ( A
           != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
         => ( ( ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
             => ( ( c_Groups_Osgn__class_Osgn @ ( tc_Polynomial_Opoly @ B ) @ A )
                = ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
             => ( ( c_Groups_Osgn__class_Osgn @ ( tc_Polynomial_Opoly @ B ) @ A )
                = ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(902,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(4110,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)],[902]) ).

thf(193,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(1867,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)],[193]) ).

thf(1060,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(4528,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)],[1060]) ).

thf(195,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(1872,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)],[195]) ).

thf(457,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(2712,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)],[457]) ).

thf(662,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(3414,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)],[662]) ).

thf(167,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(1761,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)],[167]) ).

thf(972,axiom,
    class_Rings_Ocomm__semiring__0 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).

thf(4294,plain,
    class_Rings_Ocomm__semiring__0 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).

thf(683,axiom,
    ! [A: $i] :
      ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__self__div__2) ).

thf(3481,plain,
    ! [A: $i] :
      ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

thf(223,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(1954,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)],[223]) ).

thf(495,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(2844,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)],[495]) ).

thf(1144,axiom,
    c_Orderings_Oord__class_Oless @ 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 @ ( hAPP @ ( 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_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__096abs_A_Icmod_A_Ipoly_Ap_A_Ig_A_If_A_IN1_A_L_AN2_J_J_J_J_A_N_A_N_As_J_A_060_A1_A_P_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096) ).

thf(4762,plain,
    c_Orderings_Oord__class_Oless @ 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 @ ( hAPP @ ( 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_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)],[1144]) ).

thf(75,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(1458,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)],[75]) ).

thf(638,axiom,
    ! [A: $i] :
      ( ( class_Rings_Oidom @ A )
     => ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

thf(3335,plain,
    ! [A: $i] :
      ( ( class_Rings_Oidom @ A )
     => ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(576,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(3103,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)],[576]) ).

thf(183,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(1835,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)],[183]) ).

thf(643,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(3350,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)],[643]) ).

thf(858,axiom,
    class_Rings_Oordered__cancel__semiring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).

thf(3994,plain,
    class_Rings_Oordered__cancel__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).

thf(468,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(2763,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)],[468]) ).

thf(112,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(1576,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)],[112]) ).

thf(610,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(3249,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)],[610]) ).

thf(789,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(3777,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)],[789]) ).

thf(260,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(2082,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)],[260]) ).

thf(282,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(2136,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)],[282]) ).

thf(1149,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(4775,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)],[1149]) ).

thf(806,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(3836,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)],[806]) ).

thf(733,axiom,
    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 @ ( hAPP @ ( 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__0961_A_P_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096) ).

thf(3629,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 @ ( hAPP @ ( 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)],[733]) ).

thf(533,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(2972,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)],[533]) ).

thf(249,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(2046,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)],[249]) ).

thf(627,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(3308,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)],[627]) ).

thf(216,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(1935,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)],[216]) ).

thf(1158,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(4803,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)],[1158]) ).

thf(774,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(3730,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)],[774]) ).

thf(211,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(1921,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)],[211]) ).

thf(1243,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(5056,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)],[1243]) ).

thf(507,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ( B != A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).

thf(2886,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ( B != A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(1192,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(4916,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)],[1192]) ).

thf(42,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(1359,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)],[42]) ).

thf(871,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(4030,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)],[871]) ).

thf(155,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(1724,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)],[155]) ).

thf(81,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(1475,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)],[81]) ).

thf(796,axiom,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__gt__diff__one) ).

thf(3809,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).

thf(45,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Ofield @ C )
     => ( ( c_Divides_Odiv__class_Odiv @ ( tc_Polynomial_Opoly @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ B ) @ A )
        = ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ ( c_Divides_Odiv__class_Odiv @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__div__minus__left) ).

thf(1366,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Ofield @ C )
     => ( ( c_Divides_Odiv__class_Odiv @ ( tc_Polynomial_Opoly @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ B ) @ A )
        = ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ ( c_Divides_Odiv__class_Odiv @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(367,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oab__group__add @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__poly__code_I2_J) ).

thf(2400,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oab__group__add @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(488,axiom,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring__1 @ A )
     => ( class_Int_Onumber @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Onumber) ).

thf(2825,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring__1 @ A )
     => ( class_Int_Onumber @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(96,axiom,
    ! [A: $i,B: $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 @ B ) )
       => ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) ) )
          = ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) ) ) )
      & ( ~ ( 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 @ B ) )
       => ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) ) )
          = ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__number__of__Bit1) ).

thf(1529,plain,
    ! [A: $i,B: $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 @ B ) )
       => ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) ) )
          = ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) ) ) )
      & ( ~ ( 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 @ B ) )
       => ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit1 @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) ) )
          = ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(919,axiom,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( 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(4156,plain,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( 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)],[919]) ).

thf(1106,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(4665,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)],[1106]) ).

thf(985,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(4322,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)],[985]) ).

thf(126,axiom,
    class_Rings_Olinordered__ring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).

thf(1623,plain,
    class_Rings_Olinordered__ring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(4,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(1254,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)],[4]) ).

thf(802,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(3820,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)],[802]) ).

thf(1024,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(4422,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)],[1024]) ).

thf(351,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(2339,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)],[351]) ).

thf(641,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(3342,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)],[641]) ).

thf(686,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(3495,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)],[686]) ).

thf(562,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(3061,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)],[562]) ).

thf(1150,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(4778,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)],[1150]) ).

thf(444,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(2682,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)],[444]) ).

thf(511,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(2897,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)],[511]) ).

thf(278,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) ) )
      = ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ ( 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_div__Suc__eq__div__add3) ).

thf(2126,plain,
    ! [A: $i,B: $i] :
      ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) ) )
      = ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ ( 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)],[278]) ).

thf(59,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(1409,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)],[59]) ).

thf(946,axiom,
    class_Rings_Ocomm__ring__1 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).

thf(4238,plain,
    class_Rings_Ocomm__ring__1 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).

thf(596,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(3204,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)],[596]) ).

thf(1031,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) @ ( c_RComplete_Onatceiling @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__mono) ).

thf(4439,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) @ ( c_RComplete_Onatceiling @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).

thf(15,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Divides_Osemiring__div @ B )
     => ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__0) ).

thf(1287,plain,
    ! [A: $i,B: $i] :
      ( ( class_Divides_Osemiring__div @ B )
     => ( ( c_Divides_Odiv__class_Odiv @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(602,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(3221,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)],[602]) ).

thf(1183,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(4896,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)],[1183]) ).

thf(65,axiom,
    class_Groups_Ouminus @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).

thf(1430,plain,
    class_Groups_Ouminus @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(738,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
     => ( ( c_RComplete_Onatceiling @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
        = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__add) ).

thf(3644,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
     => ( ( c_RComplete_Onatceiling @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
        = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).

thf(450,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ~ ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
      <=> ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__le) ).

thf(2698,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ( ~ ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ A @ B ) )
        & ( ( c_Orderings_Oord__class_Oless @ C @ A @ B )
         => ~ ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(136,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ B )
     => ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ B ) )
      <=> ( A
          = ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__zero__iff) ).

thf(1660,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ B )
     => ( ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_Groups_Osgn__class_Osgn @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(18,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).

thf(1298,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(207,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(1907,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)],[207]) ).

thf(397,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(2501,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)],[397]) ).

thf(30,axiom,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ A )
     => ( class_Rings_Osemiring @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).

thf(1330,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ A )
     => ( class_Rings_Osemiring @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(7,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(1264,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)],[7]) ).

thf(990,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oord @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( B = A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__le__eq__trans) ).

thf(4334,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oord @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( B = A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).

thf(311,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(2217,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)],[311]) ).

thf(28,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(1323,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)],[28]) ).

thf(726,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Lattices_Oboolean__algebra @ 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_compl__mono) ).

thf(3612,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Lattices_Oboolean__algebra @ 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)],[726]) ).

thf(584,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(3148,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)],[584]) ).

thf(741,axiom,
    class_Groups_Osgn__if @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Osgn__if) ).

thf(3653,plain,
    class_Groups_Osgn__if @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).

thf(12,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).

thf(1279,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(965,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(4275,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)],[965]) ).

thf(299,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( B != A )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).

thf(2185,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( B != A )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(74,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) )
        = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oplus__class_Oplus @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).

thf(1455,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Otimes__class_Otimes @ C @ A @ B ) )
        = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oplus__class_Oplus @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(810,axiom,
    class_Groups_Oone @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).

thf(3845,plain,
    class_Groups_Oone @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).

thf(867,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 @ ( hAPP @ ( 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(4023,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 @ ( hAPP @ ( 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)],[867]) ).

thf(644,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(3353,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)],[644]) ).

thf(1216,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(4984,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)],[1216]) ).

thf(465,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(2745,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)],[465]) ).

thf(767,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(3713,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)],[767]) ).

thf(950,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(4243,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).

thf(452,axiom,
    class_Int_Oring__char__0 @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).

thf(2703,plain,
    class_Int_Oring__char__0 @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(368,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Groups_Osgn__class_Osgn @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Osgn__class_Osgn @ C @ B ) @ ( c_Groups_Osgn__class_Osgn @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__times) ).

thf(2403,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Groups_Osgn__class_Osgn @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Osgn__class_Osgn @ C @ B ) @ ( c_Groups_Osgn__class_Osgn @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(1105,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(4664,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)],[1105]) ).

thf(1207,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(4952,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)],[1207]) ).

thf(765,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(3708,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)],[765]) ).

thf(962,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(4265,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)],[962]) ).

thf(1010,axiom,
    class_Rings_Omult__zero @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).

thf(4383,plain,
    class_Rings_Omult__zero @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).

thf(43,axiom,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ A )
     => ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).

thf(1362,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ A )
     => ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(1142,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(4756,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)],[1142]) ).

thf(907,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__natfloor) ).

thf(4119,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).

thf(695,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(3517,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)],[695]) ).

thf(201,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(1892,plain,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ A )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(50,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(1379,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)],[50]) ).

thf(996,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 @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_s1m) ).

thf(4353,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 @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).

thf(1175,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(4862,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)],[1175]) ).

thf(1152,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(4788,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)],[1152]) ).

thf(1000,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(4358,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)],[1000]) ).

thf(250,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Ofield @ C )
     => ( ( c_Divides_Odiv__class_Odiv @ ( tc_Polynomial_Opoly @ C ) @ B @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ A ) )
        = ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ ( c_Divides_Odiv__class_Odiv @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__div__minus__right) ).

thf(2049,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Ofield @ C )
     => ( ( c_Divides_Odiv__class_Odiv @ ( tc_Polynomial_Opoly @ C ) @ B @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ A ) )
        = ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ ( c_Divides_Odiv__class_Odiv @ ( tc_Polynomial_Opoly @ C ) @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(1043,axiom,
    class_Groups_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).

thf(4492,plain,
    class_Groups_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).

thf(1197,axiom,
    class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).

thf(4928,plain,
    class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).

thf(830,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Lattices_Oboolean__algebra @ 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_compl__le__compl__iff) ).

thf(3919,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Lattices_Oboolean__algebra @ 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)],[830]) ).

thf(1167,axiom,
    class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).

thf(4830,plain,
    class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).

thf(984,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(4317,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)],[984]) ).

thf(1111,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 @ ( hAPP @ ( 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(4675,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 @ ( hAPP @ ( 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)],[1111]) ).

thf(679,axiom,
    ! [A: $i] :
      ( ( class_Rings_Oidom @ A )
     => ( class_Rings_Oring__no__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).

thf(3470,plain,
    ! [A: $i] :
      ( ( class_Rings_Oidom @ A )
     => ( class_Rings_Oring__no__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).

thf(1067,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(4551,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)],[1067]) ).

thf(826,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(3902,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)],[826]) ).

thf(721,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(3602,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)],[721]) ).

thf(1015,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(4400,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)],[1015]) ).

thf(172,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(1778,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)],[172]) ).

thf(1154,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 @ ( hAPP @ ( 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(4793,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 @ ( hAPP @ ( 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)],[1154]) ).

thf(1053,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(4507,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)],[1053]) ).

thf(497,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(2852,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)],[497]) ).

thf(1147,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(4771,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)],[1147]) ).

thf(819,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 @ ( hAPP @ ( 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(3866,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 @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) ) ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).

thf(977,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ A )
     => ( ( c_RComplete_Onatceiling @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) )
        = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__subtract) ).

thf(4302,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ A )
     => ( ( c_RComplete_Onatceiling @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) )
        = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).

thf(1056,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(4514,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)],[1056]) ).

thf(955,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ D )
     => ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__add) ).

thf(4253,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ D )
     => ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).

thf(1210,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( hAPP @ ( c_Polynomial_Opoly @ B @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
        = ( c_Groups_Oone__class_Oone @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__1) ).

thf(4967,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( hAPP @ ( c_Polynomial_Opoly @ B @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
        = ( c_Groups_Oone__class_Oone @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).

thf(1108,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(4669,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)],[1108]) ).

thf(186,axiom,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ A )
     => ( class_Rings_Ocomm__semiring__0 @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).

thf(1847,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ A )
     => ( class_Rings_Ocomm__semiring__0 @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(313,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(2222,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)],[313]) ).

thf(632,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(3322,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)],[632]) ).

thf(698,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(3524,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)],[698]) ).

thf(838,axiom,
    class_Groups_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).

thf(3934,plain,
    class_Groups_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).

thf(263,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(2090,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)],[263]) ).

thf(317,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Groups_Osgn__if @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Osgn__if) ).

thf(2236,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Groups_Osgn__if @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(504,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(2880,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)],[504]) ).

thf(519,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(2925,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)],[519]) ).

thf(914,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(4134,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)],[914]) ).

thf(709,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 @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) )
        = ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mth1) ).

thf(3569,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 @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) )
        = ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).

thf(1156,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(4798,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)],[1156]) ).

thf(239,axiom,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ A )
     => ( class_Groups_Ouminus @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ouminus) ).

thf(2017,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ A )
     => ( class_Groups_Ouminus @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(1119,axiom,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) @ ( c_Rings_Oinverse__class_Odivide @ 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__div4) ).

thf(4696,plain,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) @ ( c_Rings_Oinverse__class_Odivide @ 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)],[1119]) ).

thf(935,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(4205,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)],[935]) ).

thf(1187,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(4903,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)],[1187]) ).

thf(72,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(1450,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)],[72]) ).

thf(958,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(4258,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)],[958]) ).

thf(543,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(2996,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)],[543]) ).

thf(1035,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(4454,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)],[1035]) ).

thf(624,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(3295,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)],[624]) ).

thf(509,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(2893,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)],[509]) ).

thf(387,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(2469,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)],[387]) ).

thf(1164,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(4820,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)],[1164]) ).

thf(587,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
      <=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
          & ( B != A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).

thf(3163,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
            & ( B != A ) ) )
        & ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
            & ( B != A ) )
         => ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(32,axiom,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring__1 @ A )
     => ( class_Int_Onumber__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Onumber__ring) ).

thf(1334,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring__1 @ A )
     => ( class_Int_Onumber__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(699,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(3527,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)],[699]) ).

thf(191,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(1858,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)],[191]) ).

thf(669,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
     => ( ( 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_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__nonpos__pos__le0) ).

thf(3438,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
     => ( ( 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_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(276,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(2122,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)],[276]) ).

thf(905,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(4115,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)],[905]) ).

thf(350,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oord @ D )
     => ( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) @ B @ A )
      <=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A )
          & ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).

thf(2335,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oord @ D )
     => ( ( ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) @ B @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A )
            & ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ A @ B ) ) )
        & ( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A )
            & ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ A @ B ) )
         => ( c_Orderings_Oord__class_Oless @ ( tc_fun @ C @ D ) @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(1161,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(4810,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)],[1161]) ).

thf(922,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(4162,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)],[922]) ).

thf(1130,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(4718,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)],[1130]) ).

thf(379,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(2437,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)],[379]) ).

thf(49,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Opreorder @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).

thf(1377,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Opreorder @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(71,axiom,
    ! [A: $i] :
      ( ( c_RComplete_Onatceiling @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__real__of__nat) ).

thf(1447,plain,
    ! [A: $i] :
      ( ( c_RComplete_Onatceiling @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(472,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(2772,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)],[472]) ).

thf(38,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( ( B != A )
         => ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).

thf(1351,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( ( B != A )
         => ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(335,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(2286,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)],[335]) ).

thf(604,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ( A != B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).

thf(3226,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ( A != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(598,axiom,
    ! [A: $i] :
      ( c_Int_OPls
     != ( c_Int_OBit1 @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I39_J) ).

thf(3211,plain,
    ! [A: $i] :
      ( c_Int_OPls
     != ( c_Int_OBit1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(1093,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(4628,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)],[1093]) ).

thf(652,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(3378,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)],[652]) ).

thf(1239,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(5045,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)],[1239]) ).

thf(654,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(3389,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)],[654]) ).

thf(1245,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(5059,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)],[1245]) ).

thf(872,axiom,
    ( ( c_RComplete_Onatceiling @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
    = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__one) ).

thf(4033,plain,
    ( ( c_RComplete_Onatceiling @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
    = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).

thf(491,axiom,
    class_Rings_Ocomm__semiring__1 @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).

thf(2833,plain,
    class_Rings_Ocomm__semiring__1 @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(592,axiom,
    class_Rings_Olinordered__ring__strict @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).

thf(3189,plain,
    class_Rings_Olinordered__ring__strict @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(333,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(2281,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)],[333]) ).

thf(202,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(1896,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)],[202]) ).

thf(301,axiom,
    ! [A: $i] :
      ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__1) ).

thf(2190,plain,
    ! [A: $i] :
      ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(199,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(1886,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)],[199]) ).

thf(1052,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__eq @ tc_Nat_Onat @ B @ A )
       => ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B )
          = ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__div__geq) ).

thf(4504,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__eq @ tc_Nat_Onat @ B @ A )
       => ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B )
          = ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).

thf(404,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(2523,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)],[404]) ).

thf(555,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(3036,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)],[555]) ).

thf(1003,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 @ ( hAPP @ ( 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(4364,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 @ ( hAPP @ ( 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)],[1003]) ).

thf(889,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(4087,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)],[889]) ).

thf(535,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(2979,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(1063,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 )
       => ~ ! [B: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( 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__096_B_Bthesis_O_A_I_B_Bg_O_A_091_124_AALL_An_O_Acmod_A_Ig_An_J_A_060_061_Ar_059_AALL_An_O_Acmod_A_Ipoly_Ap_A_Ig_An_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_An_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

thf(4536,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 )
       => ~ ! [B: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( 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)],[1063]) ).

thf(608,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(3243,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)],[608]) ).

thf(532,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(2965,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)],[532]) ).

thf(1058,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 @ ( hAPP @ ( 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(4519,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 @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).

thf(717,axiom,
    class_Int_Onumber__ring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber__ring) ).

thf(3588,plain,
    class_Int_Onumber__ring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).

thf(1181,axiom,
    class_Rings_Ocomm__semiring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).

thf(4892,plain,
    class_Rings_Ocomm__semiring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).

thf(659,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(3406,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)],[659]) ).

thf(306,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(2205,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)],[306]) ).

thf(145,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(1696,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)],[145]) ).

thf(506,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(2884,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)],[506]) ).

thf(668,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(3435,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)],[668]) ).

thf(518,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(2922,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)],[518]) ).

thf(814,axiom,
    class_Int_Onumber @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber) ).

thf(3857,plain,
    class_Int_Onumber @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).

thf(1080,axiom,
    class_Rings_Ozero__neq__one @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).

thf(4589,plain,
    class_Rings_Ozero__neq__one @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).

thf(143,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(1691,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)],[143]) ).

thf(274,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(2118,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)],[274]) ).

thf(34,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(1338,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)],[34]) ).

thf(1231,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 @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_calculation) ).

thf(5034,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 @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ A ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).

thf(264,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(2093,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)],[264]) ).

thf(174,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Opreorder @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).

thf(1783,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Opreorder @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(881,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(4059,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)],[881]) ).

thf(1195,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

thf(4925,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).

thf(585,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(3151,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)],[585]) ).

thf(236,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(2011,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)],[236]) ).

thf(1223,axiom,
    ( ( c_RComplete_Onatceiling @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__zero) ).

thf(5012,plain,
    ( ( c_RComplete_Onatceiling @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).

thf(690,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(3503,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)],[690]) ).

thf(676,axiom,
    ! [A: $i] :
      ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
      = ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ ( 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_div2__Suc__Suc) ).

thf(3459,plain,
    ! [A: $i] :
      ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) )
      = ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ ( 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)],[676]) ).

thf(1182,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(4893,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)],[1182]) ).

thf(719,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(3591,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)],[719]) ).

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

thf(1306,plain,
    class_Rings_Oordered__cancel__semiring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(1061,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(4531,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)],[1061]) ).

thf(1225,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oorder @ D )
     => ( ( C = B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I3_J) ).

thf(5017,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oorder @ D )
     => ( ( C = B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).

thf(735,axiom,
    class_Groups_Ominus @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).

thf(3635,plain,
    class_Groups_Ominus @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).

thf(290,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
      = ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zminus2) ).

thf(2164,plain,
    ! [A: $i,B: $i] :
      ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
      = ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

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

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

thf(631,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(3318,plain,
    ! [A: $i,B: $i] :
      ( ( c_Int_OBit0 @ B )
     != ( c_Int_OBit1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(315,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(2232,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)],[315]) ).

thf(1075,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Ominus @ E )
     => ( ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ E ) @ C @ B ) @ A )
        = ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__apply) ).

thf(4576,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Ominus @ E )
     => ( ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ E ) @ C @ B ) @ A )
        = ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).

thf(342,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(2307,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)],[342]) ).

thf(982,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(4312,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)],[982]) ).

thf(479,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(2790,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)],[479]) ).

thf(254,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oab__group__add @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
        = ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__poly__code_I1_J) ).

thf(2061,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Oab__group__add @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
        = ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(925,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(4172,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)],[925]) ).

thf(132,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(1636,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)],[132]) ).

thf(158,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(1730,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)],[158]) ).

thf(755,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ~ ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).

thf(3679,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ~ ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).

thf(776,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(3735,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)],[776]) ).

thf(370,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Groups_Osgn__class_Osgn @ B @ A )
          = ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__neg) ).

thf(2409,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Groups_Osgn__class_Osgn @ B @ A )
          = ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(377,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(2428,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)],[377]) ).

thf(1176,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
         => ( B = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).

thf(4878,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).

thf(137,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Groups_Oabs__if @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oabs__if) ).

thf(1666,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Groups_Oabs__if @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(766,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(3711,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)],[766]) ).

thf(461,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(2733,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)],[461]) ).

thf(864,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 @ ( hAPP @ ( 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(4016,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 @ ( hAPP @ ( 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)],[864]) ).

thf(483,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ominus @ B )
     => ( class_Groups_Ominus @ ( tc_fun @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).

thf(2805,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ominus @ B )
     => ( class_Groups_Ominus @ ( tc_fun @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(1014,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(4397,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)],[1014]) ).

thf(1219,axiom,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_RComplete_Onatceiling @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__natceiling) ).

thf(5002,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_RComplete_Onatceiling @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).

thf(1089,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(4609,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)],[1089]) ).

thf(110,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(1570,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)],[110]) ).

thf(1217,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(4989,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)],[1217]) ).

thf(1238,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(5044,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238]) ).

thf(281,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
     => ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A )
        = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__less) ).

thf(2133,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
     => ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A )
        = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(910,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ B )
     => ( ( hAPP @ ( c_Polynomial_Opoly @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__0) ).

thf(4128,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ B )
     => ( ( hAPP @ ( c_Polynomial_Opoly @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).

thf(565,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oab__group__add @ C )
     => ( ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
        = ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Limits_Ominus__diff__minus) ).

thf(3069,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oab__group__add @ C )
     => ( ( c_Groups_Ominus__class_Ominus @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
        = ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(824,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(3884,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)],[824]) ).

thf(523,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Divides_Osemiring__div @ B )
     => ( ( A
         != ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Divides_Odiv__class_Odiv @ B @ A @ A )
          = ( c_Groups_Oone__class_Oone @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__self) ).

thf(2937,plain,
    ! [A: $i,B: $i] :
      ( ( class_Divides_Osemiring__div @ B )
     => ( ( A
         != ( c_Groups_Ozero__class_Ozero @ B ) )
       => ( ( c_Divides_Odiv__class_Odiv @ B @ A @ A )
          = ( c_Groups_Oone__class_Oone @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(1048,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(4499,plain,
    class_Fields_Olinordered__field__inverse__zero @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).

thf(425,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(2606,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)],[425]) ).

thf(586,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(3154,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)],[586]) ).

thf(1034,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(4449,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)],[1034]) ).

thf(1044,axiom,
    class_Fields_Ofield__inverse__zero @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).

thf(4493,plain,
    class_Fields_Ofield__inverse__zero @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).

thf(182,axiom,
    ! [A: $i] :
      ( ( ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( ( c_Groups_Osgn__class_Osgn @ 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_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
           => ( ( c_Groups_Osgn__class_Osgn @ tc_Int_Oint @ A )
              = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
          & ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
           => ( ( c_Groups_Osgn__class_Osgn @ tc_Int_Oint @ A )
              = ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zsgn__def) ).

thf(1824,plain,
    ! [A: $i] :
      ( ( ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( ( c_Groups_Osgn__class_Osgn @ 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_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
           => ( ( c_Groups_Osgn__class_Osgn @ tc_Int_Oint @ A )
              = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
          & ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
           => ( ( c_Groups_Osgn__class_Osgn @ tc_Int_Oint @ A )
              = ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(967,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(4284,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)],[967]) ).

thf(798,axiom,
    class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).

thf(3814,plain,
    class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).

thf(538,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(2986,plain,
    ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ c_Int_OPls @ c_Int_OPls ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(372,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ 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__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono1) ).

thf(2414,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ 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__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(280,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(2132,plain,
    class_Groups_Oordered__ab__group__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(508,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(2890,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)],[508]) ).

thf(406,axiom,
    class_Rings_Olinordered__semiring__strict @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).

thf(2528,plain,
    class_Rings_Olinordered__semiring__strict @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(746,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(3664,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).

thf(640,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(3339,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)],[640]) ).

thf(238,axiom,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ A )
     => ( class_Rings_Omult__zero @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).

thf(2015,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ A )
     => ( class_Rings_Omult__zero @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(621,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).

thf(3286,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
     => ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) )
         => ( 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_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(198,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) @ ( 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_pos__imp__zdiv__neg__iff) ).

thf(1883,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
     => ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) @ ( 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_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(106,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(1560,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)],[106]) ).

thf(931,axiom,
    class_RealVector_Oreal__normed__vector @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).

thf(4192,plain,
    class_RealVector_Oreal__normed__vector @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).

thf(1226,axiom,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__div3) ).

thf(5021,plain,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).

thf(1137,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(4746,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)],[1137]) ).

thf(1214,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(4979,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)],[1214]) ).

thf(739,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(3647,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)],[739]) ).

thf(619,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(3282,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)],[619]) ).

thf(844,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(3948,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)],[844]) ).

thf(381,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(2445,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)],[381]) ).

thf(973,axiom,
    class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).

thf(4295,plain,
    class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).

thf(385,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(2464,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)],[385]) ).

thf(217,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(1938,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)],[217]) ).

thf(467,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(2758,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)],[467]) ).

thf(852,axiom,
    class_Orderings_Oorder @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).

thf(3980,plain,
    class_Orderings_Oorder @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).

thf(616,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
          = ( c_Groups_Oone__class_Oone @ B ) )
      <=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__1__pos) ).

thf(3269,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( ( ( c_Groups_Osgn__class_Osgn @ 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 @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
         => ( ( c_Groups_Osgn__class_Osgn @ B @ A )
            = ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(118,axiom,
    class_Rings_Omult__zero @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).

thf(1602,plain,
    class_Rings_Omult__zero @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(729,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(3618,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)],[729]) ).

thf(1078,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(4585,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)],[1078]) ).

thf(390,axiom,
    class_Divides_Osemiring__div @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).

thf(2477,plain,
    class_Divides_Osemiring__div @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(1131,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(4725,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)],[1131]) ).

thf(226,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oorder @ D )
     => ( ( C = B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ A @ B )
         => ( c_Orderings_Oord__class_Oless @ D @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I1_J) ).

thf(1968,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oorder @ D )
     => ( ( C = B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ A @ B )
         => ( c_Orderings_Oord__class_Oless @ D @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(438,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(2663,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)],[438]) ).

thf(104,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 @ tc_Int_Oint @ B @ A )
       => ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__pos__pos__trivial) ).

thf(1555,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 @ tc_Int_Oint @ B @ A )
       => ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(349,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(2332,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)],[349]) ).

thf(1205,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(4947,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)],[1205]) ).

thf(688,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(3499,plain,
    class_Groups_Oordered__comm__monoid__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(200,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ F )
     => ( ( E
         != ( c_Groups_Ozero__class_Ozero @ F ) )
       => ( ( ( D = C )
            & ( B != A ) )
         => ( ( c_Groups_Oplus__class_Oplus @ F @ D @ ( c_Groups_Otimes__class_Otimes @ F @ E @ B ) )
           != ( c_Groups_Oplus__class_Oplus @ F @ C @ ( c_Groups_Otimes__class_Otimes @ F @ E @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).

thf(1888,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ F )
     => ( ( E
         != ( c_Groups_Ozero__class_Ozero @ F ) )
       => ( ( ( D = C )
            & ( B != A ) )
         => ( ( c_Groups_Oplus__class_Oplus @ F @ D @ ( c_Groups_Otimes__class_Otimes @ F @ E @ B ) )
           != ( c_Groups_Oplus__class_Oplus @ F @ C @ ( c_Groups_Otimes__class_Otimes @ F @ E @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(822,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(3877,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)],[822]) ).

thf(180,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(1819,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)],[180]) ).

thf(127,axiom,
    ! [A: $i] :
      ( ( A
       != ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
     => ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ A )
        = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__self) ).

thf(1624,plain,
    ! [A: $i] :
      ( ( A
       != ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
     => ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ A )
        = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(304,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(2200,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)],[304]) ).

thf(426,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(2609,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)],[426]) ).

thf(1016,axiom,
    class_Rings_Ocomm__ring__1 @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).

thf(4402,plain,
    class_Rings_Ocomm__ring__1 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).

thf(176,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(1787,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)],[176]) ).

thf(1202,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
     => ( ( c_RComplete_Onatceiling @ A )
        = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__neg) ).

thf(4942,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
     => ( ( c_RComplete_Onatceiling @ A )
        = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).

thf(559,axiom,
    ! [A: $i] :
      ( ( class_Groups_Ocomm__monoid__add @ A )
     => ( class_Groups_Ocomm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).

thf(3050,plain,
    ! [A: $i] :
      ( ( class_Groups_Ocomm__monoid__add @ A )
     => ( class_Groups_Ocomm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(834,axiom,
    class_Rings_Ozero__neq__one @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).

thf(3926,plain,
    class_Rings_Ozero__neq__one @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).

thf(352,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(2344,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)],[352]) ).

thf(394,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(2492,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)],[394]) ).

thf(900,axiom,
    ! [A: $i] :
      ( ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A )
        = ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ A @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
        | ( 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 @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
        | ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ A @ c_Complex_Oii ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
        | ( 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 @ c_Complex_Oii ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unimodular__reduce__norm) ).

thf(4104,plain,
    ! [A: $i] :
      ( ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ A )
        = ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ A @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
        | ( 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 @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
        | ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ A @ c_Complex_Oii ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
        | ( 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 @ c_Complex_Oii ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).

thf(13,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(1281,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)],[13]) ).

thf(463,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

thf(2741,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(131,axiom,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring__1 @ A )
     => ( class_Rings_Ocomm__ring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).

thf(1634,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring__1 @ A )
     => ( class_Rings_Ocomm__ring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(53,axiom,
    class_Rings_Oordered__semiring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).

thf(1392,plain,
    class_Rings_Oordered__semiring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(837,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(3931,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)],[837]) ).

thf(208,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(1910,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)],[208]) ).

thf(1113,axiom,
    ! [A: $i] :
      ( ( c_RComplete_Onatfloor @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ A ) )
      = ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__number__of__eq) ).

thf(4680,plain,
    ! [A: $i] :
      ( ( c_RComplete_Onatfloor @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ A ) )
      = ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).

thf(111,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(1573,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)],[111]) ).

thf(795,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(3799,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)],[795]) ).

thf(672,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 @ A @ B )
       => ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B )
          = ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__geq) ).

thf(3445,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 @ A @ B )
       => ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B )
          = ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(870,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(4027,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)],[870]) ).

thf(1248,axiom,
    class_Int_Onumber @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber) ).

thf(5066,plain,
    class_Int_Onumber @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).

thf(116,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(1592,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)],[116]) ).

thf(272,axiom,
    class_Rings_Olinordered__idom @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).

thf(2115,plain,
    class_Rings_Olinordered__idom @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(1107,axiom,
    c_Orderings_Oord__class_Oless @ 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 @ ( hAPP @ ( 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_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( 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 @ ( hAPP @ ( 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_thc1) ).

thf(4668,plain,
    c_Orderings_Oord__class_Oless @ 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 @ ( hAPP @ ( 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_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_s____ ) ) ) @ ( 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 @ ( hAPP @ ( 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)],[1107]) ).

thf(817,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(3862,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)],[817]) ).

thf(455,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(2709,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)],[455]) ).

thf(1118,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(4693,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)],[1118]) ).

thf(894,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 @ ( hAPP @ ( 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(4095,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 @ ( hAPP @ ( 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)],[894]) ).

thf(670,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ 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) ).

thf(3440,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ 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)],[670]) ).

thf(1184,axiom,
    class_Rings_Oidom @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).

thf(4898,plain,
    class_Rings_Oidom @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).

thf(1160,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(4808,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)],[1160]) ).

thf(909,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 @ ( hAPP @ ( 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(4123,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 @ ( hAPP @ ( 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)],[909]) ).

thf(396,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( c_Groups_Osgn__class_Osgn @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) )
        = ( c_Groups_Osgn__class_Osgn @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__sgn) ).

thf(2498,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( c_Groups_Osgn__class_Osgn @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) )
        = ( c_Groups_Osgn__class_Osgn @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(728,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(3615,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)],[728]) ).

thf(1242,axiom,
    ! [A: $i,B: $i,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 @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ D )
          & ! [E: $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 @ E @ 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 @ E @ B ) ) @ 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 @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) @ E ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) @ B ) ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__cont) ).

thf(5053,plain,
    ! [A: $i,B: $i,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 @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ D )
          & ! [E: $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 @ E @ 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 @ E @ B ) ) @ 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 @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) @ E ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) @ B ) ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242]) ).

thf(661,axiom,
    class_Rings_Ocomm__ring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).

thf(3413,plain,
    class_Rings_Ocomm__ring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(188,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(1851,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)],[188]) ).

thf(526,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ B ) ) ) @ A )
      = ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( 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 ) ) ) @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__div__eq__add3__div) ).

thf(2946,plain,
    ! [A: $i,B: $i] :
      ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ B ) ) ) @ A )
      = ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( 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 ) ) ) @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(540,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(2990,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)],[540]) ).

thf(1055,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(4512,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)],[1055]) ).

thf(445,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Oordered__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).

thf(2685,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Oordered__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(1221,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
     => ( ( c_RComplete_Onatceiling @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
        = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__add__one) ).

thf(5006,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
     => ( ( c_RComplete_Onatceiling @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
        = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).

thf(510,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(2895,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)],[510]) ).

thf(953,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(4248,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)],[953]) ).

thf(48,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(1375,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)],[48]) ).

thf(1040,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(4486,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)],[1040]) ).

thf(878,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(4048,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)],[878]) ).

thf(1066,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(4544,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)],[1066]) ).

thf(190,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(1856,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)],[190]) ).

thf(1026,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(4429,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)],[1026]) ).

thf(1095,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(4636,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)],[1095]) ).

thf(448,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Divides_Osemiring__div @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Divides_Odiv__class_Odiv @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ B )
          = ( c_Groups_Oplus__class_Oplus @ C @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add__self1) ).

thf(2692,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Divides_Osemiring__div @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Divides_Odiv__class_Odiv @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) @ B )
          = ( c_Groups_Oplus__class_Oplus @ C @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(86,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Orderings_Oord @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oord) ).

thf(1498,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Orderings_Oord @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(399,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(2509,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)],[399]) ).

thf(943,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(4233,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)],[943]) ).

thf(653,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
      <=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).

thf(3386,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
         => ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(432,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(2631,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)],[432]) ).

thf(740,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(3650,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)],[740]) ).

thf(861,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(4012,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)],[861]) ).

thf(829,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
         => ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).

thf(3916,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).

thf(165,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(1755,plain,
    ! [A: $i] :
      ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != ( c_Nat_OSuc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(1101,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(4653,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)],[1101]) ).

thf(503,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(2877,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)],[503]) ).

thf(1173,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(4860,plain,
    class_Rings_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).

thf(590,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(3179,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)],[590]) ).

thf(811,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(3846,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)],[811]) ).

thf(416,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(2561,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)],[416]) ).

thf(490,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
      <=> ( 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_neg__imp__zdiv__neg__iff) ).

thf(2830,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
     => ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
         => ( 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 @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(773,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Orderings_Oord @ E )
     => ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C @ B )
       => ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).

thf(3728,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Orderings_Oord @ E )
     => ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C @ B )
       => ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).

thf(501,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
        <=> ( B = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).

thf(2868,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
           => ( B = A ) )
          & ( ( B = A )
           => ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(374,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(2419,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)],[374]) ).

thf(1200,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(4938,plain,
    class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).

thf(554,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(3032,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Nat_OSuc @ B )
        = ( c_Nat_OSuc @ A ) )
     => ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(750,axiom,
    class_Groups_Ozero @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).

thf(3671,plain,
    class_Groups_Ozero @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).

thf(705,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oidom @ C )
     => ( ( ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A )
          = ( c_Groups_Ozero__class_Ozero @ C ) )
      <=> ( ( B
            = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
          | ( ( c_Polynomial_Oorder @ C @ A @ B )
           != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__root) ).

thf(3555,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oidom @ C )
     => ( ( ( ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A )
            = ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( ( B
              = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
            | ( ( c_Polynomial_Oorder @ C @ A @ B )
             != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
        & ( ( ( B
              = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
            | ( ( c_Polynomial_Oorder @ C @ A @ B )
             != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
         => ( ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A )
            = ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).

thf(710,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(3573,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)],[710]) ).

thf(225,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Opreorder @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
      <=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
          & ~ ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).

thf(1964,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Opreorder @ C )
     => ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
            & ~ ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) )
        & ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
            & ~ ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) )
         => ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(831,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(3922,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)],[831]) ).

thf(572,axiom,
    ! [A: $i] :
      ( ( class_Groups_Ocancel__comm__monoid__add @ A )
     => ( class_Groups_Ocancel__comm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).

thf(3094,plain,
    ! [A: $i] :
      ( ( class_Groups_Ocancel__comm__monoid__add @ A )
     => ( class_Groups_Ocancel__comm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(76,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(1461,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)],[76]) ).

thf(344,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(2312,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)],[344]) ).

thf(548,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(3010,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)],[548]) ).

thf(1139,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 @ ( hAPP @ ( 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 @ ( hAPP @ ( 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(4750,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 @ ( hAPP @ ( 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 @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).

thf(61,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ( ( B != A )
         => ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).

thf(1414,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ( ( B != A )
         => ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(319,axiom,
    class_Int_Onumber__ring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).

thf(2240,plain,
    class_Int_Onumber__ring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(1174,axiom,
    class_Groups_Ozero @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).

thf(4861,plain,
    class_Groups_Ozero @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).

thf(294,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(2172,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)],[294]) ).

thf(269,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(2108,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)],[269]) ).

thf(246,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
       => ( ( c_RComplete_Onatfloor @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
          = ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__div__nat) ).

thf(2038,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
       => ( ( c_RComplete_Onatfloor @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
          = ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(771,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(3723,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)],[771]) ).

thf(1033,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(4444,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)],[1033]) ).

thf(439,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Oordered__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).

thf(2666,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Oordered__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(388,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Orderings_Oorder @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oorder) ).

thf(2472,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Orderings_Oorder @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(928,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ A ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor__eq__one) ).

thf(4180,plain,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).

thf(839,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(3935,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)],[839]) ).

thf(63,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Osgn__if @ B )
     => ( ( ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_Groups_Osgn__class_Osgn @ B @ 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 ) @ A )
             => ( ( c_Groups_Osgn__class_Osgn @ B @ A )
                = ( c_Groups_Oone__class_Oone @ B ) ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
             => ( ( c_Groups_Osgn__class_Osgn @ B @ A )
                = ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__if) ).

thf(1419,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Osgn__if @ B )
     => ( ( ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_Groups_Osgn__class_Osgn @ B @ 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 ) @ A )
             => ( ( c_Groups_Osgn__class_Osgn @ B @ A )
                = ( c_Groups_Oone__class_Oone @ B ) ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
             => ( ( c_Groups_Osgn__class_Osgn @ B @ A )
                = ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(1011,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(4384,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)],[1011]) ).

thf(582,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(3126,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)],[582]) ).

thf(341,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ocomm__monoid__add @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).

thf(2304,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ocomm__monoid__add @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(321,axiom,
    class_Groups_Ocomm__monoid__mult @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).

thf(2243,plain,
    class_Groups_Ocomm__monoid__mult @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(354,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(2355,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)],[354]) ).

thf(221,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(1947,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)],[221]) ).

thf(580,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(3115,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)],[580]) ).

thf(1022,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(4416,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)],[1022]) ).

thf(762,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(3703,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)],[762]) ).

thf(1247,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(5063,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)],[1247]) ).

thf(171,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).

thf(1776,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(725,axiom,
    class_Groups_Oone @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).

thf(3611,plain,
    class_Groups_Oone @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).

thf(743,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(3656,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)],[743]) ).

thf(382,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ 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__neq__iff) ).

thf(2450,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ( ( B != A )
         => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
            | ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) )
        & ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
            | ( c_Orderings_Oord__class_Oless @ C @ A @ B ) )
         => ( B != A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(277,axiom,
    class_Groups_Ogroup__add @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).

thf(2125,plain,
    class_Groups_Ogroup__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(742,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(3654,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)],[742]) ).

thf(791,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(3787,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)],[791]) ).

thf(98,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(1539,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)],[98]) ).

thf(493,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Osgn__class_Osgn @ 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_sgn__less) ).

thf(2836,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Osgn__class_Osgn @ 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_Groups_Osgn__class_Osgn @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(1211,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(4970,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)],[1211]) ).

thf(779,axiom,
    ! [A: $i] :
      ( c_Complex_Oii
     != ( c_Int_Onumber__class_Onumber__of @ tc_Complex_Ocomplex @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__i__not__number__of) ).

thf(3743,plain,
    ! [A: $i] :
      ( c_Complex_Oii
     != ( c_Int_Onumber__class_Onumber__of @ tc_Complex_Ocomplex @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).

thf(788,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(3770,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)],[788]) ).

thf(138,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(1668,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)],[138]) ).

thf(228,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(1974,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)],[228]) ).

thf(801,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

thf(3819,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).

thf(945,axiom,
    class_Groups_Omonoid__add @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).

thf(4237,plain,
    class_Groups_Omonoid__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).

thf(235,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(2006,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)],[235]) ).

thf(395,axiom,
    class_Rings_Oordered__ring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).

thf(2497,plain,
    class_Rings_Oordered__ring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(1244,axiom,
    class_Rings_Ocomm__ring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).

thf(5058,plain,
    class_Rings_Ocomm__ring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).

thf(840,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(3937,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)],[840]) ).

thf(942,axiom,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( 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(4231,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( 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)],[942]) ).

thf(994,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(4347,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)],[994]) ).

thf(469,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(2766,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)],[469]) ).

thf(758,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(3692,plain,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).

thf(251,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( ( A != B )
         => ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I11_J) ).

thf(2052,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( ( A != B )
         => ( c_Orderings_Oord__class_Oless @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(150,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
     => ( ( 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_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__neg__pos__less0) ).

thf(1715,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
     => ( ( 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_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(636,axiom,
    class_Rings_Oring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).

thf(3333,plain,
    class_Rings_Oring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(563,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(3064,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)],[563]) ).

thf(153,axiom,
    class_Groups_Ocomm__monoid__add @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).

thf(1720,plain,
    class_Groups_Ocomm__monoid__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(230,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(1979,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)],[230]) ).

thf(567,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(3074,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)],[567]) ).

thf(1228,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Orderings_Oorder @ B )
     => ( ( c_SEQ_Odecseq @ B @ A )
      <=> ! [C: $i,D: $i] :
            ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ D )
           => ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ D ) @ ( hAPP @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_decseq__def) ).

thf(5026,plain,
    ! [A: $i,B: $i] :
      ( ( class_Orderings_Oorder @ B )
     => ( ( ( c_SEQ_Odecseq @ B @ A )
         => ! [C: $i,D: $i] :
              ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ D )
             => ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ D ) @ ( hAPP @ A @ C ) ) ) )
        & ( ! [C: $i,D: $i] :
              ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ D )
             => ( c_Orderings_Oord__class_Oless__eq @ B @ ( hAPP @ A @ D ) @ ( hAPP @ A @ C ) ) )
         => ( c_SEQ_Odecseq @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).

thf(885,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(4069,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)],[885]) ).

thf(595,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( 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 ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__imp__zdiv__nonneg__iff) ).

thf(3201,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( 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 ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ 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 ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(940,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(4223,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)],[940]) ).

thf(166,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ~ ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__leE) ).

thf(1759,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ~ ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(54,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(1393,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)],[54]) ).

thf(128,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(1627,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)],[128]) ).

thf(599,axiom,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ A )
     => ( class_Rings_Ocomm__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).

thf(3215,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ A )
     => ( class_Rings_Ocomm__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(1002,axiom,
    ( c_Complex_Oii
   != ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__i__not__zero) ).

thf(4361,plain,
    ( c_Complex_Oii
   != ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).

thf(94,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__div__less__self) ).

thf(1525,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(782,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(3755,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)],[782]) ).

thf(67,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(1434,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)],[67]) ).

thf(26,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(1318,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)],[26]) ).

thf(305,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(2203,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)],[305]) ).

thf(1097,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(4644,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)],[1097]) ).

thf(1092,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__ring @ C )
     => ( ( hAPP @ ( c_Polynomial_Opoly @ C @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ B ) ) @ A )
        = ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__minus) ).

thf(4625,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__ring @ C )
     => ( ( hAPP @ ( c_Polynomial_Opoly @ C @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ B ) ) @ A )
        = ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).

thf(505,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(2883,plain,
    class_Rings_Oring__no__zero__divisors @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(107,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(1563,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)],[107]) ).

thf(359,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(2368,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)],[359]) ).

thf(77,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(1466,plain,
    ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ c_Int_OPls )
    = c_Int_OPls ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(874,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(4036,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)],[874]) ).

thf(663,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(3422,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)],[663]) ).

thf(437,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(2662,plain,
    class_Rings_Olinordered__comm__semiring__strict @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(980,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(4308,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)],[980]) ).

thf(407,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(2529,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)],[407]) ).

thf(706,axiom,
    class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).

thf(3563,plain,
    class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(933,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(4195,plain,
    class_Groups_Oordered__ab__group__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).

thf(248,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(2043,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)],[248]) ).

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

thf(3587,plain,
    class_Rings_Ocomm__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(1188,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oorder @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).

thf(4906,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oorder @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ C )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).

thf(517,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(2915,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)],[517]) ).

thf(480,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(2793,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)],[480]) ).

thf(593,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(3190,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)],[593]) ).

thf(808,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
        | ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).

thf(3841,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
        | ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).

thf(428,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(2617,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)],[428]) ).

thf(159,axiom,
    ! [A: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ A )
     => ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
        = ( c_Groups_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__zero) ).

thf(1732,plain,
    ! [A: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ A )
     => ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
        = ( c_Groups_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(1074,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(4572,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)],[1074]) ).

thf(316,axiom,
    class_Orderings_Oord @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).

thf(2235,plain,
    class_Orderings_Oord @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(460,axiom,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ A )
     != A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).

thf(2729,plain,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ A )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(234,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
         => ( ( c_Groups_Oabs__class_Oabs @ ( tc_Polynomial_Opoly @ B ) @ A )
            = ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) @ A ) ) )
        & ( ~ ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
         => ( ( c_Groups_Oabs__class_Oabs @ ( tc_Polynomial_Opoly @ B ) @ A )
            = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__poly__def) ).

thf(2001,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
         => ( ( c_Groups_Oabs__class_Oabs @ ( tc_Polynomial_Opoly @ B ) @ A )
            = ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ B ) @ A ) ) )
        & ( ~ ( c_Orderings_Oord__class_Oless @ ( tc_Polynomial_Opoly @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
         => ( ( c_Groups_Oabs__class_Oabs @ ( tc_Polynomial_Opoly @ B ) @ A )
            = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(911,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(4131,plain,
    class_Groups_Ocancel__ab__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).

thf(365,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ C )
     => ( ( B
          = ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
      <=> ( A
          = ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).

thf(2391,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ C )
     => ( ( ( B
            = ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) )
         => ( A
            = ( c_Groups_Ozero__class_Ozero @ C ) ) )
        & ( ( A
            = ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( B
            = ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(414,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(2556,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)],[414]) ).

thf(557,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(3042,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)],[557]) ).

thf(83,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(1483,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)],[83]) ).

thf(956,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 @ ( hAPP @ ( 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(4256,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 @ ( hAPP @ ( 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)],[956]) ).

thf(1240,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(5048,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)],[1240]) ).

thf(1071,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_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ C @ A ) @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__mono) ).

thf(4562,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_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ C @ A ) @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).

thf(622,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(3289,plain,
    ! [A: $i] :
      ( ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(1051,axiom,
    class_Rings_Olinordered__ring__strict @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).

thf(4503,plain,
    class_Rings_Olinordered__ring__strict @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).

thf(865,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(4017,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)],[865]) ).

thf(1084,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(4599,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)],[1084]) ).

thf(1194,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 @ ( hAPP @ ( 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(4921,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 @ ( hAPP @ ( 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)],[1194]) ).

thf(206,axiom,
    class_Rings_Oordered__comm__semiring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).

thf(1906,plain,
    class_Rings_Oordered__comm__semiring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(764,axiom,
    class_Rings_Oordered__comm__semiring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).

thf(3707,plain,
    class_Rings_Oordered__comm__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).

thf(156,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Groups_Oordered__ab__semigroup__add__imp__le @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).

thf(1727,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Groups_Oordered__ab__semigroup__add__imp__le @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(3,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(1251,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)],[3]) ).

thf(1193,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 @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ A ) @ ( hAPP @ ( 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 @ ( hAPP @ ( 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(4919,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 @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ A ) @ ( hAPP @ ( 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 @ ( hAPP @ ( 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)],[1193]) ).

thf(442,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Int_Oring__char__0 @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).

thf(2677,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Int_Oring__char__0 @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(1127,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(4708,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)],[1127]) ).

thf(325,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
        = ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).

thf(2253,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
        = ( c_Groups_Otimes__class_Otimes @ B @ ( c_Groups_Oplus__class_Oplus @ B @ ( c_Groups_Oone__class_Oone @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(245,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(2033,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)],[245]) ).

thf(613,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(3257,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)],[613]) ).

thf(722,axiom,
    class_Orderings_Oord @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).

thf(3607,plain,
    class_Orderings_Oord @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).

thf(101,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Orderings_Olinorder @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).

thf(1548,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Orderings_Olinorder @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(213,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(1927,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)],[213]) ).

thf(777,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Orderings_Opreorder @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ B @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).

thf(3738,plain,
    ! [A: $i,B: $i] :
      ( ( class_Orderings_Opreorder @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ B @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).

thf(243,axiom,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ A )
     => ( class_Rings_Ozero__neq__one @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).

thf(2028,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ A )
     => ( class_Rings_Ozero__neq__one @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(19,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(1301,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)],[19]) ).

thf(650,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(3375,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)],[650]) ).

thf(117,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(1595,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)],[117]) ).

thf(578,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(3111,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)],[578]) ).

thf(617,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(3274,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)],[617]) ).

thf(760,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(3696,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)],[760]) ).

thf(1042,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(4489,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)],[1042]) ).

thf(130,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(1631,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)],[130]) ).

thf(1237,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(5043,plain,
    class_RealVector_Oreal__normed__div__algebra @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).

thf(1104,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(4662,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)],[1104]) ).

thf(797,axiom,
    ! [A: $i] :
      ( ( c_RComplete_Onatceiling @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ A ) )
      = ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__number__of__eq) ).

thf(3811,plain,
    ! [A: $i] :
      ( ( c_RComplete_Onatceiling @ ( c_Int_Onumber__class_Onumber__of @ tc_RealDef_Oreal @ A ) )
      = ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).

thf(696,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(3519,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)],[696]) ).

thf(724,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(3609,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)],[724]) ).

thf(783,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(3758,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)],[783]) ).

thf(51,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 )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2) ).

thf(1388,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 )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(1241,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(5050,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)],[1241]) ).

thf(57,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(1403,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)],[57]) ).

thf(987,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_termination__basic__simps_I1_J) ).

thf(4328,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)],[987]) ).

thf(1008,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(4381,plain,
    class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).

thf(1204,axiom,
    class_Groups_Oab__group__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).

thf(4946,plain,
    class_Groups_Oab__group__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).

thf(449,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(2695,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)],[449]) ).

thf(489,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(2827,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)],[489]) ).

thf(530,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(2959,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)],[530]) ).

thf(736,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(3636,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)],[736]) ).

thf(833,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(3925,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)],[833]) ).

thf(1045,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(4494,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)],[1045]) ).

thf(612,axiom,
    ( ( c_Int_OBit0 @ c_Int_OPls )
    = c_Int_OPls ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__Pls) ).

thf(3255,plain,
    ( ( c_Int_OBit0 @ c_Int_OPls )
    = c_Int_OPls ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(300,axiom,
    ! [A: $i] :
      ( ( class_Groups_Ozero @ A )
     => ( class_Groups_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).

thf(2188,plain,
    ! [A: $i] :
      ( ( class_Groups_Ozero @ A )
     => ( class_Groups_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(536,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(2981,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)],[536]) ).

thf(1249,axiom,
    class_Rings_Osemiring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).

thf(5067,plain,
    class_Rings_Osemiring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).

thf(125,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(1620,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)],[125]) ).

thf(680,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(3472,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)],[680]) ).

thf(1196,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(4926,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)],[1196]) ).

thf(615,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(3266,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)],[615]) ).

thf(1081,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(4590,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)],[1081]) ).

thf(92,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Olinordered__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).

thf(1520,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Olinordered__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(658,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Opreorder @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).

thf(3404,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Opreorder @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(1090,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(4612,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)],[1090]) ).

thf(603,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(3223,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)],[603]) ).

thf(302,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(2193,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)],[302]) ).

thf(1230,axiom,
    class_Rings_Ocomm__ring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring) ).

thf(5033,plain,
    class_Rings_Ocomm__ring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).

thf(348,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ( ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B )
        <=> ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).

thf(2326,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ( ( ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B )
           => ( A = B ) )
          & ( ( A = B )
           => ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(1020,axiom,
    class_Groups_Ozero @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).

thf(4413,plain,
    class_Groups_Ozero @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).

thf(31,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(1332,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)],[31]) ).

thf(380,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(2442,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)],[380]) ).

thf(252,axiom,
    class_Groups_Ominus @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).

thf(2055,plain,
    class_Groups_Ominus @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(454,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(2706,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)],[454]) ).

thf(376,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(2425,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)],[376]) ).

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_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(4273,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)],[964]) ).

thf(389,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(2474,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)],[389]) ).

thf(588,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(3170,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)],[588]) ).

thf(1059,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le) ).

thf(4526,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).

thf(794,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(3796,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)],[794]) ).

thf(88,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(1503,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)],[88]) ).

thf(147,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(1707,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)],[147]) ).

thf(337,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Orderings_Opreorder @ B )
     => ~ ( c_Orderings_Oord__class_Oless @ B @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).

thf(2293,plain,
    ! [A: $i,B: $i] :
      ( ( class_Orderings_Opreorder @ B )
     => ~ ( c_Orderings_Oord__class_Oless @ B @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(1155,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(4796,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)],[1155]) ).

thf(10,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(1271,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)],[10]) ).

thf(568,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Osgn__class_Osgn @ B @ A ) )
      <=> ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__greater) ).

thf(3077,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( c_Groups_Osgn__class_Osgn @ 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_Groups_Osgn__class_Osgn @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(24,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
      = ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zminus__zminus) ).

thf(1312,plain,
    ! [A: $i,B: $i] :
      ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
      = ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(903,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(4112,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)],[903]) ).

thf(759,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(3695,plain,
    class_Groups_Oordered__comm__monoid__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(896,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(4099,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)],[896]) ).

thf(462,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(2738,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)],[462]) ).

thf(917,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(4149,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)],[917]) ).

thf(944,axiom,
    class_Groups_Ocomm__monoid__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).

thf(4236,plain,
    class_Groups_Ocomm__monoid__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).

thf(938,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__ring__1 @ 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_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).

thf(4218,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__ring__1 @ 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)],[938]) ).

thf(1110,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(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_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)],[1110]) ).

thf(545,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 @ A @ B )
         => ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B )
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
        & ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B )
         => ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B )
            = ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__if) ).

thf(3002,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 @ A @ B )
         => ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B )
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
        & ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ B )
         => ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B )
            = ( c_Nat_OSuc @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ B ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(804,axiom,
    class_Int_Oring__char__0 @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).

thf(3832,plain,
    class_Int_Oring__char__0 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).

thf(712,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(3579,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)],[712]) ).

thf(1172,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(4854,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)],[1172]) ).

thf(737,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(3641,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)],[737]) ).

thf(625,axiom,
    ! [A: $i] :
      ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
      = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zero) ).

thf(3302,plain,
    ! [A: $i] :
      ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
      = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(708,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(3568,plain,
    class_Rings_Olinordered__comm__semiring__strict @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(1180,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(4887,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)],[1180]) ).

thf(951,axiom,
    class_Groups_Ogroup__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).

thf(4245,plain,
    class_Groups_Ogroup__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).

thf(355,axiom,
    ! [A: $i] :
      ( ( class_Rings_Oidom @ A )
     => ( class_Rings_Ono__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).

thf(2358,plain,
    ! [A: $i] :
      ( ( class_Rings_Oidom @ A )
     => ( class_Rings_Ono__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(1028,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(4433,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)],[1028]) ).

thf(40,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(1356,plain,
    class_Groups_Oordered__ab__semigroup__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(286,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(2148,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)],[286]) ).

thf(769,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(3719,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)],[769]) ).

thf(402,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(2521,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(1198,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(4929,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)],[1198]) ).

thf(860,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(3996,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)],[860]) ).

thf(845,axiom,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__natfloor) ).

thf(3957,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_RComplete_Onatfloor @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).

thf(513,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Orderings_Opreorder @ B )
     => ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).

thf(2906,plain,
    ! [A: $i,B: $i] :
      ( ( class_Orderings_Opreorder @ B )
     => ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(1121,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oord @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A )
      <=> ! [E: $i] : ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) @ ( hAPP @ A @ E ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).

thf(4699,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oord @ D )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A )
         => ! [E: $i] : ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) @ ( hAPP @ A @ E ) ) )
        & ( ! [E: $i] : ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) @ ( hAPP @ A @ E ) )
         => ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).

thf(916,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(4139,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)],[916]) ).

thf(525,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(2943,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)],[525]) ).

thf(976,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(4300,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)],[976]) ).

thf(1054,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ A )
     => ( ( c_RComplete_Onatfloor @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) )
        = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__subtract) ).

thf(4509,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ A )
     => ( ( c_RComplete_Onatfloor @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) )
        = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).

thf(443,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(2679,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)],[443]) ).

thf(1124,axiom,
    class_Groups_Ocancel__comm__monoid__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add) ).

thf(4704,plain,
    class_Groups_Ocancel__comm__monoid__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).

thf(1047,axiom,
    class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).

thf(4498,plain,
    class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).

thf(391,axiom,
    class_Rings_Ozero__neq__one @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).

thf(2478,plain,
    class_Rings_Ozero__neq__one @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(1005,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(4369,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)],[1005]) ).

thf(314,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(2229,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)],[314]) ).

thf(799,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(3815,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)],[799]) ).

thf(261,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(2084,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)],[261]) ).

thf(310,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(2214,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)],[310]) ).

thf(363,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(2383,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)],[363]) ).

thf(375,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(2422,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)],[375]) ).

thf(978,axiom,
    class_Divides_Osemiring__div @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).

thf(4305,plain,
    class_Divides_Osemiring__div @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).

thf(327,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(2257,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)],[327]) ).

thf(115,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(1589,plain,
    ! [A: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ c_Int_OPls )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(119,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Ouminus @ D )
     => ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ D ) @ B ) @ A )
        = ( c_Groups_Ouminus__class_Ouminus @ D @ ( hAPP @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__apply) ).

thf(1603,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Ouminus @ D )
     => ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ D ) @ B ) @ A )
        = ( c_Groups_Ouminus__class_Ouminus @ D @ ( hAPP @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(339,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(2299,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)],[339]) ).

thf(1085,axiom,
    class_Groups_Oone @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).

thf(4601,plain,
    class_Groups_Oone @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).

thf(577,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(3106,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)],[577]) ).

thf(678,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Opreorder @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).

thf(3468,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Opreorder @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(99,axiom,
    ! [A: $i] :
      ( ( c_Int_OBit1 @ A )
     != c_Int_OPls ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I46_J) ).

thf(1542,plain,
    ! [A: $i] :
      ( ( c_Int_OBit1 @ A )
     != c_Int_OPls ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(273,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(2116,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)],[273]) ).

thf(494,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(2839,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)],[494]) ).

thf(594,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(3197,plain,
    ! [A: $i,B: $i] :
      ( ( c_Int_OBit1 @ B )
     != ( c_Int_OBit0 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(918,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(4154,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)],[918]) ).

thf(499,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(2856,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)],[499]) ).

thf(689,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(3500,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)],[689]) ).

thf(361,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Olinordered__ring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).

thf(2378,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Olinordered__ring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(564,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(3066,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)],[564]) ).

thf(715,axiom,
    class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).

thf(3586,plain,
    class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).

thf(901,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
     => ( ( c_RComplete_Onatfloor @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
        = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__add) ).

thf(4107,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
     => ( ( c_RComplete_Onatfloor @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
        = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).

thf(22,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(1307,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)],[22]) ).

thf(297,axiom,
    ! [A: $i] :
      ( ( class_Groups_Ocancel__comm__monoid__add @ A )
     => ( class_Groups_Ocancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).

thf(2180,plain,
    ! [A: $i] :
      ( ( class_Groups_Ocancel__comm__monoid__add @ A )
     => ( class_Groups_Ocancel__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(298,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(2182,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)],[298]) ).

thf(242,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(2025,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)],[242]) ).

thf(1023,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(4420,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)],[1023]) ).

thf(883,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(4064,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)],[883]) ).

thf(674,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(3451,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)],[674]) ).

thf(974,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(4296,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)],[974]) ).

thf(520,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(2928,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)],[520]) ).

thf(142,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(1688,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)],[142]) ).

thf(196,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(1877,plain,
    ! [A: $i] :
      ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != ( c_Nat_OSuc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(79,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(1471,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)],[79]) ).

thf(780,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(3747,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)],[780]) ).

thf(1064,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(4541,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)],[1064]) ).

thf(464,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(2742,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)],[464]) ).

thf(1178,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_termination__basic__simps_I2_J) ).

thf(4882,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)],[1178]) ).

thf(561,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
        <=> ( B = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).

thf(3055,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ~ ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
           => ( B = A ) )
          & ( ( B = A )
           => ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(899,axiom,
    class_Groups_Omonoid__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).

thf(4103,plain,
    class_Groups_Omonoid__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).

thf(345,axiom,
    ! [A: $i] :
      ( ( class_Groups_Ocomm__monoid__add @ A )
     => ( class_Groups_Oab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).

thf(2314,plain,
    ! [A: $i] :
      ( ( class_Groups_Ocomm__monoid__add @ A )
     => ( class_Groups_Oab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(279,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(2129,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)],[279]) ).

thf(748,axiom,
    class_Groups_Ocomm__monoid__mult @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).

thf(3668,plain,
    class_Groups_Ocomm__monoid__mult @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).

thf(1190,axiom,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natceiling__ge) ).

thf(4911,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).

thf(270,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
        | ( B = A )
        | ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).

thf(2111,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
        | ( B = A )
        | ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(475,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(2780,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)],[475]) ).

thf(1133,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(4731,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)],[1133]) ).

thf(181,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(1821,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)],[181]) ).

thf(961,axiom,
    class_Rings_Oordered__comm__semiring @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).

thf(4264,plain,
    class_Rings_Oordered__comm__semiring @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).

thf(184,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(1838,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)],[184]) ).

thf(727,axiom,
    class_Groups_Oabs__if @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oabs__if) ).

thf(3614,plain,
    class_Groups_Oabs__if @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).

thf(1100,axiom,
    class_Fields_Olinordered__field @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).

thf(4652,plain,
    class_Fields_Olinordered__field @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).

thf(502,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) )
        = ( c_Groups_Otimes__class_Otimes @ 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_I1_J) ).

thf(2874,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Otimes__class_Otimes @ D @ C @ B ) @ ( c_Groups_Otimes__class_Otimes @ D @ A @ B ) )
        = ( c_Groups_Otimes__class_Otimes @ D @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(849,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(3971,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)],[849]) ).

thf(714,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(3583,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)],[714]) ).

thf(410,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(2542,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)],[410]) ).

thf(336,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oord @ D )
     => ( ( C = B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__eq__less__trans) ).

thf(2289,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oord @ D )
     => ( ( C = B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(434,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(2647,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)],[434]) ).

thf(17,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(1293,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)],[17]) ).

thf(332,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Divides_Osemiring__div @ B )
     => ( ( c_Divides_Odiv__class_Odiv @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__by__0) ).

thf(2278,plain,
    ! [A: $i,B: $i] :
      ( ( class_Divides_Osemiring__div @ B )
     => ( ( c_Divides_Odiv__class_Odiv @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(515,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(2911,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)],[515]) ).

thf(1068,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(4554,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)],[1068]) ).

thf(309,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(2212,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)],[309]) ).

thf(807,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(3838,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)],[807]) ).

thf(429,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(2620,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)],[429]) ).

thf(1050,axiom,
    class_Int_Onumber @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).

thf(4502,plain,
    class_Int_Onumber @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).

thf(283,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(2139,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)],[283]) ).

thf(549,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(3016,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)],[549]) ).

thf(322,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(2244,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)],[322]) ).

thf(628,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(3310,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)],[628]) ).

thf(633,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(3325,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)],[633]) ).

thf(934,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(4196,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)],[934]) ).

thf(544,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(2999,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)],[544]) ).

thf(307,axiom,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ A )
     => ( ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__code_I1_J) ).

thf(2207,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ A )
     => ( ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(537,axiom,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ A )
     => ( class_Groups_Omonoid__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).

thf(2984,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ A )
     => ( class_Groups_Omonoid__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(256,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(2069,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)],[256]) ).

thf(888,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
     => ( ( c_RComplete_Onatfloor @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
        = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__add__one) ).

thf(4084,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
     => ( ( c_RComplete_Onatfloor @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
        = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).

thf(701,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(3539,plain,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ A )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).

thf(471,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(2770,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)],[471]) ).

thf(1169,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(4832,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)],[1169]) ).

thf(531,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(2962,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)],[531]) ).

thf(358,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
     => ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
        = ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sgn__pos) ).

thf(2365,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
     => ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
        = ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(255,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(2064,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)],[255]) ).

thf(753,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(3674,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)],[753]) ).

thf(1166,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(4827,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)],[1166]) ).

thf(521,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(2931,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)],[521]) ).

thf(1236,axiom,
    class_Groups_Oab__semigroup__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).

thf(5042,plain,
    class_Groups_Oab__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236]) ).

thf(1123,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(4703,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)],[1123]) ).

thf(266,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(2101,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)],[266]) ).

thf(44,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Opreorder @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).

thf(1364,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Opreorder @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(1,conjecture,
    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 @ tc_Complex_Ocomplex @ ( hAPP @ ( 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_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( hAPP @ ( 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____ ) ) ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( 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 @ tc_Complex_Ocomplex @ ( hAPP @ ( 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_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( hAPP @ ( 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____ ) ) ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(1250,plain,
    ~ ( 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 @ tc_Complex_Ocomplex @ ( hAPP @ ( 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_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Ominus__class_Ominus @ tc_Complex_Ocomplex @ ( hAPP @ ( 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____ ) ) ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ v_z____ ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(694,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(3512,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)],[694]) ).

thf(1046,axiom,
    class_Groups_Omonoid__mult @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).

thf(4497,plain,
    class_Groups_Omonoid__mult @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).

thf(936,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(4207,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)],[936]) ).

thf(113,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(1583,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)],[113]) ).

thf(528,axiom,
    class_Rings_Oidom @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).

thf(2952,plain,
    class_Rings_Oidom @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(665,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(3427,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)],[665]) ).

thf(1186,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(4901,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)],[1186]) ).

thf(711,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(3576,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)],[711]) ).

thf(89,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(1509,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)],[89]) ).

thf(431,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono1__neg) ).

thf(2629,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(997,axiom,
    class_Rings_Odivision__ring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).

thf(4355,plain,
    class_Rings_Odivision__ring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).

thf(623,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(3292,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)],[623]) ).

thf(812,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(3849,plain,
    class_Groups_Olinordered__ab__group__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).

thf(697,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ ( 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_div__2__gt__zero) ).

thf(3522,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A )
     => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ ( 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)],[697]) ).

thf(989,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(4331,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)],[989]) ).

thf(1013,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(4394,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)],[1013]) ).

thf(1032,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(4441,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)],[1032]) ).

thf(915,axiom,
    ( c_Complex_Oii
   != ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__i__not__one) ).

thf(4136,plain,
    ( c_Complex_Oii
   != ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).

thf(959,axiom,
    class_Fields_Ofield @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield) ).

thf(4260,plain,
    class_Fields_Ofield @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).

thf(1162,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(4813,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)],[1162]) ).

thf(542,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(2994,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)],[542]) ).

thf(477,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(2784,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)],[477]) ).

thf(1036,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(4456,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)],[1036]) ).

thf(751,axiom,
    class_Rings_Oordered__ring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).

thf(3672,plain,
    class_Rings_Oordered__ring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).

thf(205,axiom,
    class_Groups_Omonoid__mult @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).

thf(1905,plain,
    class_Groups_Omonoid__mult @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(853,axiom,
    class_Groups_Omonoid__mult @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).

thf(3981,plain,
    class_Groups_Omonoid__mult @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).

thf(398,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(2503,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)],[398]) ).

thf(1116,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(4688,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)],[1116]) ).

thf(326,axiom,
    class_Groups_Ozero @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).

thf(2256,plain,
    class_Groups_Ozero @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(418,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(2564,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)],[418]) ).

thf(923,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 @ ( hAPP @ ( 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(4168,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 @ ( hAPP @ ( 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)],[923]) ).

thf(422,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(2582,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)],[422]) ).

thf(876,axiom,
    class_Fields_Ofield @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).

thf(4045,plain,
    class_Fields_Ofield @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).

thf(163,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Groups_Oordered__comm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).

thf(1748,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Groups_Oordered__comm__monoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(655,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(3391,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)],[655]) ).

thf(873,axiom,
    class_Rings_Olinordered__ring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).

thf(4035,plain,
    class_Rings_Olinordered__ring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).

thf(828,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(3913,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)],[828]) ).

thf(570,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(3082,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)],[570]) ).

thf(108,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(1566,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)],[108]) ).

thf(134,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Opreorder @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).

thf(1647,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Opreorder @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(583,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(3129,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)],[583]) ).

thf(401,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(2518,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)],[401]) ).

thf(1094,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
        <=> ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).

thf(4630,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B )
           => ( A = B ) )
          & ( ( A = B )
           => ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).

thf(1082,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(4593,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)],[1082]) ).

thf(447,axiom,
    ! [A: $i] :
      ( ( class_RealVector_Oreal__normed__algebra__1 @ A )
     => ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Oone__class_Oone @ A ) )
        = ( c_Groups_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__one) ).

thf(2689,plain,
    ! [A: $i] :
      ( ( class_RealVector_Oreal__normed__algebra__1 @ A )
     => ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Oone__class_Oone @ A ) )
        = ( c_Groups_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(855,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_Ominus__class_Ominus @ tc_RealDef_Oreal @ D @ C ) ) @ B )
     => ( 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 @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ D @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ath2) ).

thf(3988,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_Ominus__class_Ominus @ tc_RealDef_Oreal @ D @ C ) ) @ B )
     => ( 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 @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ D @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).

thf(1138,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(4749,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).

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

thf(1516,plain,
    class_Groups_Oab__semigroup__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(500,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(2863,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)],[500]) ).

thf(630,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(3315,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)],[630]) ).

thf(1001,axiom,
    class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

thf(4360,plain,
    class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).

thf(366,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(2397,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)],[366]) ).

thf(534,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(2977,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)],[534]) ).

thf(122,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Divides_Osemiring__div @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Divides_Odiv__class_Odiv @ C @ ( c_Groups_Oplus__class_Oplus @ C @ A @ B ) @ B )
          = ( c_Groups_Oplus__class_Oplus @ C @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add__self2) ).

thf(1611,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Divides_Osemiring__div @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( c_Divides_Odiv__class_Odiv @ C @ ( c_Groups_Oplus__class_Oplus @ C @ A @ B ) @ B )
          = ( c_Groups_Oplus__class_Oplus @ C @ ( c_Divides_Odiv__class_Odiv @ C @ A @ B ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(360,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(2375,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)],[360]) ).

thf(963,axiom,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( 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(4272,plain,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( 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)],[963]) ).

thf(56,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(1400,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)],[56]) ).

thf(161,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Olinordered__semiring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).

thf(1743,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Olinordered__semiring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(1201,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(4939,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)],[1201]) ).

thf(781,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(3754,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).

thf(1206,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(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_Ominus__class_Ominus @ tc_Nat_Onat @ C @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).

thf(805,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(3833,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)],[805]) ).

thf(744,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(3659,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)],[744]) ).

thf(218,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(1941,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)],[218]) ).

thf(677,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(3462,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)],[677]) ).

thf(1057,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(4517,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)],[1057]) ).

thf(1096,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 @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) @ ( hAPP @ ( 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 @ ( hAPP @ ( 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(4641,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 @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ B ) @ ( hAPP @ ( 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 @ ( hAPP @ ( 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)],[1096]) ).

thf(295,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Olinordered__idom @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).

thf(2175,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Olinordered__idom @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(173,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(1780,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)],[173]) ).

thf(597,axiom,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ A )
     => ( class_Groups_Ogroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).

thf(3209,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ A )
     => ( class_Groups_Ogroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(1140,axiom,
    class_Rings_Ocomm__semiring @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).

thf(4754,plain,
    class_Rings_Ocomm__semiring @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).

thf(8,axiom,
    ! [A: $i] :
      ( ( class_Groups_Ocomm__monoid__add @ A )
     => ( class_Groups_Omonoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).

thf(1267,plain,
    ! [A: $i] :
      ( ( class_Groups_Ocomm__monoid__add @ A )
     => ( class_Groups_Omonoid__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(364,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(2386,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)],[364]) ).

thf(723,axiom,
    class_Rings_Ocomm__semiring__1 @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).

thf(3608,plain,
    class_Rings_Ocomm__semiring__1 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).

thf(496,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(2850,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)],[496]) ).

thf(1070,axiom,
    class_Orderings_Oord @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oord) ).

thf(4561,plain,
    class_Orderings_Oord @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).

thf(948,axiom,
    class_Rings_Oring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).

thf(4240,plain,
    class_Rings_Oring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).

thf(175,axiom,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ A )
     => ( class_Rings_Oring @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).

thf(1785,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ A )
     => ( class_Rings_Oring @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(168,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(1763,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)],[168]) ).

thf(912,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 @ ( hAPP @ ( 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____ ) ) ) ) @ ( hAPP @ ( 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 @ ( hAPP @ ( 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(4132,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 @ ( hAPP @ ( 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____ ) ) ) ) @ ( hAPP @ ( 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 @ ( hAPP @ ( 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)],[912]) ).

thf(646,axiom,
    ! [A: $i,B: $i] :
      ( ( ( class_Int_Oring__char__0 @ B )
        & ( class_Rings_Oidom @ B ) )
     => ( ( ( c_Polynomial_Opoly @ B @ A )
          = ( c_Polynomial_Opoly @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
      <=> ( A
          = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__zero) ).

thf(3359,plain,
    ! [A: $i,B: $i] :
      ( ( ( class_Int_Oring__char__0 @ B )
        & ( class_Rings_Oidom @ B ) )
     => ( ( ( ( c_Polynomial_Opoly @ B @ A )
            = ( c_Polynomial_Opoly @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
         => ( A
            = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
        & ( ( A
            = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
         => ( ( c_Polynomial_Opoly @ B @ A )
            = ( c_Polynomial_Opoly @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(435,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(2656,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)],[435]) ).

thf(550,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(3019,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)],[550]) ).

thf(569,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(3080,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)],[569]) ).

thf(419,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(2569,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)],[419]) ).

thf(609,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(3246,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)],[609]) ).

thf(1030,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(4437,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)],[1030]) ).

thf(673,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(3448,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)],[673]) ).

thf(983,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(4314,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)],[983]) ).

thf(177,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(1790,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)],[177]) ).

thf(231,axiom,
    ! [A: $i] :
      ( ( class_Groups_Ocancel__comm__monoid__add @ A )
     => ( class_Groups_Ocancel__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).

thf(1987,plain,
    ! [A: $i] :
      ( ( class_Groups_Ocancel__comm__monoid__add @ A )
     => ( class_Groups_Ocancel__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(842,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(3940,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)],[842]) ).

thf(626,axiom,
    ! [A: $i] :
      ( ( class_Groups_Osgn__if @ A )
     => ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
        = ( c_Groups_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn0) ).

thf(3305,plain,
    ! [A: $i] :
      ( ( class_Groups_Osgn__if @ A )
     => ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
        = ( c_Groups_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(930,axiom,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__add__one__gt) ).

thf(4190,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).

thf(800,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(3818,plain,
    class_RealVector_Oreal__normed__algebra__1 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).

thf(73,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__div__algebra @ C )
     => ( ( c_Groups_Osgn__class_Osgn @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Osgn__class_Osgn @ C @ B ) @ ( c_Groups_Osgn__class_Osgn @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__mult) ).

thf(1452,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__div__algebra @ C )
     => ( ( c_Groups_Osgn__class_Osgn @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) )
        = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Osgn__class_Osgn @ C @ B ) @ ( c_Groups_Osgn__class_Osgn @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(637,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(3334,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)],[637]) ).

thf(793,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(3791,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)],[793]) ).

thf(681,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(3475,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)],[681]) ).

thf(553,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(3026,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)],[553]) ).

thf(331,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(2276,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)],[331]) ).

thf(1229,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(5030,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)],[1229]) ).

thf(312,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(2219,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)],[312]) ).

thf(451,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Groups_Olinordered__ab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).

thf(2701,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Groups_Olinordered__ab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(949,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(4241,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)],[949]) ).

thf(411,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(2545,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)],[411]) ).

thf(512,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(2903,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)],[512]) ).

thf(1215,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(4982,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)],[1215]) ).

thf(660,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(3412,plain,
    class_Groups_Ocancel__ab__semigroup__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(707,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oorder @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( C = A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I4_J) ).

thf(3564,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oorder @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( C = A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).

thf(33,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(1336,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)],[33]) ).

thf(787,axiom,
    class_Rings_Olinordered__idom @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).

thf(3769,plain,
    class_Rings_Olinordered__idom @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).

thf(253,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(2056,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)],[253]) ).

thf(215,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(1934,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)],[215]) ).

thf(146,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
          = ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) )
      <=> ( c_Orderings_Oord__class_Oless @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__1__neg) ).

thf(1702,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
            = ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ 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_Groups_Osgn__class_Osgn @ B @ A )
            = ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(1213,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
     => ? [B: $i] :
          ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A )
          & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reals__Archimedean6) ).

thf(4976,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
     => ? [B: $i] :
          ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) @ A )
          & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213]) ).

thf(285,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(2145,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)],[285]) ).

thf(421,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(2579,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)],[421]) ).

thf(1027,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(4431,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)],[1027]) ).

thf(400,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(2511,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)],[400]) ).

thf(847,axiom,
    class_Groups_Ocancel__semigroup__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).

thf(3961,plain,
    class_Groups_Ocancel__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).

thf(47,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(1372,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)],[47]) ).

thf(546,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(3007,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ c_Int_OPls @ c_Int_OPls,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(1021,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(4414,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)],[1021]) ).

thf(124,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ocomm__monoid__add @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).

thf(1617,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ocomm__monoid__add @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ B ) @ A @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(1157,axiom,
    class_Groups_Omonoid__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).

thf(4802,plain,
    class_Groups_Omonoid__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).

thf(169,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(1766,plain,
    class_Groups_Olinordered__ab__group__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(880,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(4057,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)],[880]) ).

thf(187,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(1849,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)],[187]) ).

thf(5,axiom,
    ! [A: $i] :
      ( A
     != ( c_Nat_OSuc @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).

thf(1257,plain,
    ! [A: $i] :
      ( A
     != ( c_Nat_OSuc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(415,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(2558,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)],[415]) ).

thf(803,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(3829,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)],[803]) ).

thf(913,axiom,
    class_Groups_Ouminus @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ouminus) ).

thf(4133,plain,
    class_Groups_Ouminus @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).

thf(97,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(1536,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)],[97]) ).

thf(1029,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(4436,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).

thf(952,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(4246,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)],[952]) ).

thf(645,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(3356,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)],[645]) ).

thf(1041,axiom,
    class_Rings_Omult__zero @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).

thf(4488,plain,
    class_Rings_Omult__zero @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).

thf(14,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(1284,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)],[14]) ).

thf(227,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(1972,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)],[227]) ).

thf(456,axiom,
    class_Orderings_Oorder @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).

thf(2711,plain,
    class_Orderings_Oorder @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(1218,axiom,
    ? [A: $i] :
    ! [B: $i] :
      ( ? [C: $i] :
          ( ? [D: $i] :
              ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ D ) @ v_r )
              & ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ D ) )
                = ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ C ) ) )
          & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ C ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_As_O_AALL_Ay_O_A_IEX_Ax_O_A_IEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_J_A_G_Ay_A_060_Ax_J_A_061_A_Iy_A_060_As_J_096) ).

thf(4991,plain,
    ? [A: $i] :
    ! [B: $i] :
      ( ( ? [C: $i] :
            ( ? [D: $i] :
                ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ D ) @ v_r )
                & ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ D ) )
                  = ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ C ) ) )
            & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ C ) )
       => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
       => ? [C: $i] :
            ( ? [D: $i] :
                ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ D ) @ v_r )
                & ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ D ) )
                  = ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ C ) ) )
            & ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).

thf(877,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(4046,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)],[877]) ).

thf(64,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(1427,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)],[64]) ).

thf(178,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(1797,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)],[178]) ).

thf(552,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(3024,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)],[552]) ).

thf(892,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(4093,plain,
    class_Rings_Odivision__ring__inverse__zero @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).

thf(527,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(2949,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)],[527]) ).

thf(459,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(2722,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)],[459]) ).

thf(843,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(3943,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)],[843]) ).

thf(941,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( class_Int_Oring__char__0 @ C )
        & ( class_Rings_Oidom @ C ) )
     => ( ( ( c_Polynomial_Opoly @ C @ B )
          = ( c_Polynomial_Opoly @ C @ A ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__iff) ).

thf(4225,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( class_Int_Oring__char__0 @ C )
        & ( class_Rings_Oidom @ C ) )
     => ( ( ( ( c_Polynomial_Opoly @ C @ B )
            = ( c_Polynomial_Opoly @ C @ A ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( ( c_Polynomial_Opoly @ C @ B )
            = ( c_Polynomial_Opoly @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).

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

thf(1717,plain,
    class_Groups_Ocancel__comm__monoid__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(244,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(2030,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ c_Int_OPls )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(197,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).

thf(1881,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
       => ~ ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(484,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(2807,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)],[484]) ).

thf(423,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(2584,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)],[423]) ).

thf(957,axiom,
    c_SEQ_Osubseq @ v_f____,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fz_I1_J) ).

thf(4257,plain,
    c_SEQ_Osubseq @ v_f____,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).

thf(1109,axiom,
    class_Rings_Oidom @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).

thf(4671,plain,
    class_Rings_Oidom @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).

thf(730,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le__eq__one) ).

thf(3620,plain,
    ! [A: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).

thf(657,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(3401,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)],[657]) ).

thf(1203,axiom,
    class_Orderings_Opreorder @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).

thf(4945,plain,
    class_Orderings_Opreorder @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).

thf(1146,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(4770,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)],[1146]) ).

thf(103,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Orderings_Oord @ B )
     => ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).

thf(1553,plain,
    ! [A: $i,B: $i] :
      ( ( class_Orderings_Oord @ B )
     => ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(60,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Orderings_Opreorder @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Opreorder) ).

thf(1412,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Orderings_Opreorder @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(91,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(1517,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)],[91]) ).

thf(898,axiom,
    class_Groups_Oab__group__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).

thf(4102,plain,
    class_Groups_Oab__group__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).

thf(473,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(2775,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)],[473]) ).

thf(882,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(4061,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)],[882]) ).

thf(233,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ B )
     => ( ( c_Groups_Osgn__class_Osgn @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
        = ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__minus) ).

thf(1998,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ B )
     => ( ( c_Groups_Osgn__class_Osgn @ B @ ( c_Groups_Ouminus__class_Ouminus @ B @ A ) )
        = ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(237,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Olinordered__comm__semiring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).

thf(2013,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Olinordered__comm__semiring__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(682,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(3478,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)],[682]) ).

thf(667,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(3433,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)],[667]) ).

thf(969,axiom,
    class_Int_Oring__char__0 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).

thf(4289,plain,
    class_Int_Oring__char__0 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).

thf(430,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(2626,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)],[430]) ).

thf(210,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).

thf(1918,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( c_Groups_Otimes__class_Otimes @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(675,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(3457,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)],[675]) ).

thf(135,axiom,
    ! [A: $i] :
      ( ( ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ 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 ) @ A )
           => ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
              = ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
          & ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
           => ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
              = ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__real__def) ).

thf(1649,plain,
    ! [A: $i] :
      ( ( ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ 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 ) @ A )
           => ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
              = ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
          & ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
           => ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
              = ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(1120,axiom,
    class_Rings_Ono__zero__divisors @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).

thf(4698,plain,
    class_Rings_Ono__zero__divisors @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).

thf(392,axiom,
    class_Groups_Omonoid__add @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).

thf(2479,plain,
    class_Groups_Omonoid__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(1171,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(4851,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)],[1171]) ).

thf(1088,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(4606,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)],[1088]) ).

thf(718,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(3589,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)],[718]) ).

thf(986,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ A )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
       => ( ( c_RComplete_Onatfloor @ A )
          = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__eq) ).

thf(4325,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ A )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
       => ( ( c_RComplete_Onatfloor @ A )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).

thf(1079,axiom,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) @ B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__dividend) ).

thf(4587,plain,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) @ B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).

thf(222,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(1949,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)],[222]) ).

thf(1145,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(4763,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)],[1145]) ).

thf(27,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ 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_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__less__dividend) ).

thf(1321,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ 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_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(1103,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(4656,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)],[1103]) ).

thf(343,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(2310,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)],[343]) ).

thf(821,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(3874,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)],[821]) ).

thf(836,axiom,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
     => ( ( c_RComplete_Onatfloor @ A )
        = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__neg) ).

thf(3928,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
     => ( ( c_RComplete_Onatfloor @ A )
        = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).

thf(929,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(4185,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)],[929]) ).

thf(731,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

thf(3625,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).

thf(887,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(4078,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)],[887]) ).

thf(772,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(3725,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)],[772]) ).

thf(52,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Oordered__comm__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).

thf(1390,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Oordered__comm__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(1037,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(4463,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)],[1037]) ).

thf(1112,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_termination__basic__simps_I4_J) ).

thf(4678,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)],[1112]) ).

thf(556,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(3039,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)],[556]) ).

thf(11,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(1276,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)],[11]) ).

thf(1191,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( hAPP @ B @ C )
          = ( hAPP @ A @ C ) )
     => ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).

thf(4913,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( hAPP @ B @ C )
          = ( hAPP @ A @ C ) )
     => ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).

thf(369,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(2406,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)],[369]) ).

thf(408,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(2532,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)],[408]) ).

thf(1114,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(4683,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)],[1114]) ).

thf(954,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(4250,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)],[954]) ).

thf(162,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(1745,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)],[162]) ).

thf(734,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(3630,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)],[734]) ).

thf(611,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(3252,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)],[611]) ).

thf(29,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(1326,plain,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ A )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(908,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 @ ( hAPP @ ( 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 @ ( hAPP @ ( 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 @ ( hAPP @ ( 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(4121,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 @ ( hAPP @ ( 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 @ ( hAPP @ ( 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 @ ( hAPP @ ( 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)],[908]) ).

thf(1128,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(4710,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)],[1128]) ).

thf(539,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Opreorder @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).

thf(2988,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Opreorder @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(818,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(3864,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)],[818]) ).

thf(154,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(1721,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)],[154]) ).

thf(291,axiom,
    class_Rings_Osemiring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).

thf(2167,plain,
    class_Rings_Osemiring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(330,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(2273,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)],[330]) ).

thf(334,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(2283,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)],[334]) ).

thf(1159,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(4806,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).

thf(35,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(1341,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)],[35]) ).

thf(684,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(3484,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)],[684]) ).

thf(792,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(3789,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)],[792]) ).

thf(498,axiom,
    class_Orderings_Olinorder @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).

thf(2855,plain,
    class_Orderings_Olinorder @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(890,axiom,
    class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).

thf(4089,plain,
    class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).

thf(413,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Lattices_Oboolean__algebra @ B )
     => ( class_Lattices_Oboolean__algebra @ ( tc_fun @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).

thf(2554,plain,
    ! [A: $i,B: $i] :
      ( ( class_Lattices_Oboolean__algebra @ B )
     => ( class_Lattices_Oboolean__algebra @ ( tc_fun @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(649,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ B ) )
      <=> ( A
          = ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__0__0) ).

thf(3369,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) ) )
        & ( ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_Groups_Osgn__class_Osgn @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(601,axiom,
    class_Groups_Osgn__if @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osgn__if) ).

thf(3220,plain,
    class_Groups_Osgn__if @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(1129,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(4715,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)],[1129]) ).

thf(1153,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(4791,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)],[1153]) ).

thf(129,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(1629,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)],[129]) ).

thf(189,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(1854,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)],[189]) ).

thf(991,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(4338,plain,
    class_Groups_Oordered__ab__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).

thf(607,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(3235,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)],[607]) ).

thf(378,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(2431,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)],[378]) ).

thf(1125,axiom,
    class_Groups_Ocancel__comm__monoid__add @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).

thf(4705,plain,
    class_Groups_Ocancel__comm__monoid__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).

thf(816,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(3859,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)],[816]) ).

thf(635,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(3331,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)],[635]) ).

thf(1177,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(4881,plain,
    class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).

thf(405,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(2526,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)],[405]) ).

thf(373,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(2416,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)],[373]) ).

thf(790,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(3780,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)],[790]) ).

thf(105,axiom,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ A )
     => ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).

thf(1558,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ A )
     => ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(522,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(2934,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)],[522]) ).

thf(960,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ A )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
       => ( ( c_RComplete_Onatceiling @ A )
          = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__eq) ).

thf(4261,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ A )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
       => ( ( c_RComplete_Onatceiling @ A )
          = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).

thf(571,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
     => ( ( ( c_Groups_Oplus__class_Oplus @ 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 @ A ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) ) )
      <=> ( ( D = B )
          | ( C = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__eq) ).

thf(3085,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
     => ( ( ( ( c_Groups_Oplus__class_Oplus @ 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 @ A ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) ) )
         => ( ( D = B )
            | ( C = A ) ) )
        & ( ( ( D = B )
            | ( C = A ) )
         => ( ( c_Groups_Oplus__class_Oplus @ 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 @ A ) @ ( c_Groups_Otimes__class_Otimes @ E @ B @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(1136,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 @ ( hAPP @ ( 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(4745,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 @ ( hAPP @ ( 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)],[1136]) ).

thf(192,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ B )
     => ( ( ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) )
            = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
        & ( ( A
           != ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) )
            = ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__sgn) ).

thf(1861,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ B )
     => ( ( ( A
            = ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) )
            = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
        & ( ( A
           != ( c_Groups_Ozero__class_Ozero @ B ) )
         => ( ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Groups_Osgn__class_Osgn @ B @ A ) )
            = ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(850,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(3978,plain,
    class_Rings_Olinordered__comm__semiring__strict @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).

thf(1099,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(4649,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)],[1099]) ).

thf(247,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(2041,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)],[247]) ).

thf(666,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
          | ( B = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).

thf(3430,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
       => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
          | ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(1143,axiom,
    ! [A: $i,B: $i] :
      ( ( 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_Nat_Onat @ A @ ( c_RComplete_Onatfloor @ B ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor__eq) ).

thf(4759,plain,
    ! [A: $i,B: $i] :
      ( ( 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_Nat_Onat @ A @ ( c_RComplete_Onatfloor @ B ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ B ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( c_RComplete_Onatfloor @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).

thf(420,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(2576,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ c_Int_OPls @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(1018,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ozero @ B )
     => ( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      <=> ( A
          = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psize__eq__0__iff) ).

thf(4404,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ozero @ B )
     => ( ( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
         => ( A
            = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) )
        & ( ( A
            = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
         => ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).

thf(275,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 @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__nonneg__neg__le0) ).

thf(2120,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 @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(23,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(1309,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)],[23]) ).

thf(895,axiom,
    class_Orderings_Olinorder @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).

thf(4098,plain,
    class_Orderings_Olinorder @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).

thf(123,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) ) )
      = ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__number__of__Bit0) ).

thf(1614,plain,
    ! [A: $i,B: $i] :
      ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit0 @ B ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Int_Oint @ ( c_Int_OBit0 @ A ) ) )
      = ( c_Divides_Odiv__class_Odiv @ 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)],[123]) ).

thf(591,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(3181,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)],[591]) ).

thf(1086,axiom,
    class_Rings_Oordered__semiring @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).

thf(4602,plain,
    class_Rings_Oordered__semiring @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).

thf(481,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(2796,plain,
    ! [A: $i] :
      ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != ( c_Nat_OSuc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(971,axiom,
    class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).

thf(4293,plain,
    class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).

thf(926,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(4175,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)],[926]) ).

thf(823,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(3879,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)],[823]) ).

thf(1148,axiom,
    class_Rings_Oring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).

thf(4774,plain,
    class_Rings_Oring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).

thf(720,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Opreorder @ C )
     => ( ( B = A )
       => ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).

thf(3598,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Opreorder @ C )
     => ( ( B = A )
       => ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).

thf(384,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Groups_Oordered__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).

thf(2462,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Groups_Oordered__ab__semigroup__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(1234,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(5040,plain,
    class_Rings_Odivision__ring__inverse__zero @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).

thf(70,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(1440,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)],[70]) ).

thf(1227,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(5023,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)],[1227]) ).

thf(754,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(3677,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)],[754]) ).

thf(357,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(2362,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)],[357]) ).

thf(289,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(2162,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)],[289]) ).

thf(1006,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(4372,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)],[1006]) ).

thf(784,axiom,
    class_Groups_Ocomm__monoid__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).

thf(3761,plain,
    class_Groups_Ocomm__monoid__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).

thf(979,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(4306,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)],[979]) ).

thf(703,axiom,
    class_Rings_Oordered__semiring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).

thf(3552,plain,
    class_Rings_Oordered__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).

thf(868,axiom,
    class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).

thf(4025,plain,
    class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).

thf(240,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(2019,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)],[240]) ).

thf(37,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(1348,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)],[37]) ).

thf(763,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 @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ A ) @ ( hAPP @ ( 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 @ ( hAPP @ ( 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(3705,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 @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_p ) @ A ) @ ( hAPP @ ( 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 @ ( hAPP @ ( 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)],[763]) ).

thf(458,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(2719,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)],[458]) ).

thf(1083,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(4596,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)],[1083]) ).

thf(100,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(1546,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)],[100]) ).

thf(55,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(1395,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)],[55]) ).

thf(999,axiom,
    class_Rings_Odivision__ring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).

thf(4357,plain,
    class_Rings_Odivision__ring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).

thf(1004,axiom,
    ( ( c_RComplete_Onatfloor @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__zero) ).

thf(4367,plain,
    ( ( c_RComplete_Onatfloor @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).

thf(1235,axiom,
    class_RealVector_Oreal__normed__field @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__field) ).

thf(5041,plain,
    class_RealVector_Oreal__normed__field @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).

thf(857,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Orderings_Oord @ E )
     => ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C @ B )
       => ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).

thf(3992,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Orderings_Oord @ E )
     => ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C @ B )
       => ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).

thf(284,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
       => ( ( c_Groups_Osgn__class_Osgn @ B @ A )
          = ( c_Groups_Oone__class_Oone @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__pos) ).

thf(2142,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
       => ( ( c_Groups_Osgn__class_Osgn @ B @ A )
          = ( c_Groups_Oone__class_Oone @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(133,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(1642,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)],[133]) ).

thf(1163,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(4816,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)],[1163]) ).

thf(340,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(2302,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)],[340]) ).

thf(1222,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(5009,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)],[1222]) ).

thf(862,axiom,
    class_Rings_Omult__zero @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).

thf(4014,plain,
    class_Rings_Omult__zero @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).

thf(224,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(1957,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)],[224]) ).

thf(904,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(4114,plain,
    class_Groups_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).

thf(1038,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(4472,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)],[1038]) ).

thf(1115,axiom,
    class_Rings_Ono__zero__divisors @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).

thf(4687,plain,
    class_Rings_Ono__zero__divisors @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).

thf(1126,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ ( c_RComplete_Onatfloor @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__mono) ).

thf(4706,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatfloor @ B ) @ ( c_RComplete_Onatfloor @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).

thf(141,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(1678,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)],[141]) ).

thf(693,axiom,
    class_Groups_Oabs__if @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oabs__if) ).

thf(3511,plain,
    class_Groups_Oabs__if @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).

thf(287,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(2155,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)],[287]) ).

thf(1007,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(4378,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)],[1007]) ).

thf(606,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(3232,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)],[606]) ).

thf(998,axiom,
    class_Rings_Ono__zero__divisors @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).

thf(4356,plain,
    class_Rings_Ono__zero__divisors @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).

thf(827,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(3907,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)],[827]) ).

thf(424,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A )
        = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
    <=> ( ( 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 ) @ B )
          & ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
        | ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
          & ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__eq__0__iff) ).

thf(2587,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( ( 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 ) @ B )
            & ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
          | ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
            & ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ 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 ) @ B )
            & ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) )
          | ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
            & ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ B ) ) )
       => ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(1220,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(5004,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)],[1220]) ).

thf(775,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_termination__basic__simps_I5_J) ).

thf(3733,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)],[775]) ).

thf(403,axiom,
    class_Orderings_Opreorder @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).

thf(2522,plain,
    class_Orderings_Opreorder @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(575,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ B )
       => ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__neg__neg__trivial) ).

thf(3100,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ B )
       => ( ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(486,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(2815,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)],[486]) ).

thf(1151,axiom,
    class_Rings_Osemiring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).

thf(4787,plain,
    class_Rings_Osemiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).

thf(20,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(1303,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)],[20]) ).

thf(95,axiom,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ A )
     => ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).

thf(1527,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ A )
     => ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(639,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(3337,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)],[639]) ).

thf(140,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(1673,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)],[140]) ).

thf(1076,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(4579,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)],[1076]) ).

thf(757,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(3690,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)],[757]) ).

thf(82,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(1480,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)],[82]) ).

thf(1224,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(5014,plain,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).

thf(470,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(2768,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)],[470]) ).

thf(68,axiom,
    class_Rings_Ocomm__semiring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).

thf(1436,plain,
    class_Rings_Ocomm__semiring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(1141,axiom,
    class_Groups_Ominus @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ominus) ).

thf(4755,plain,
    class_Groups_Ominus @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).

thf(1025,axiom,
    ( ( c_RComplete_Onatfloor @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
    = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__one) ).

thf(4427,plain,
    ( ( c_RComplete_Onatfloor @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
    = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).

thf(148,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(1710,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)],[148]) ).

thf(516,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(2913,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)],[516]) ).

thf(1232,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(5036,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)],[1232]) ).

thf(786,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(3765,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)],[786]) ).

thf(80,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(1473,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)],[80]) ).

thf(440,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(2668,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)],[440]) ).

thf(476,axiom,
    class_Groups_Oone @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).

thf(2783,plain,
    class_Groups_Oone @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(412,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(2549,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)],[412]) ).

thf(854,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(3982,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)],[854]) ).

thf(433,axiom,
    ! [A: $i] :
      ( ( ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ 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 ) @ A )
           => ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
              = ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
          & ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
           => ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
              = ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sgn__def) ).

thf(2636,plain,
    ! [A: $i] :
      ( ( ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ 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 ) @ A )
           => ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
              = ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
          & ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
           => ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ A )
              = ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(466,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
      <=> ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
          | ( B = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).

thf(2751,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Oorder @ C )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
         => ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
            | ( B = A ) ) )
        & ( ( ( c_Orderings_Oord__class_Oless @ C @ B @ A )
            | ( B = A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(482,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(2800,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)],[482]) ).

thf(927,axiom,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__div2) ).

thf(4178,plain,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_RealDef_Oreal @ tc_Nat_Onat @ B ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) @ ( c_RealDef_Oreal @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).

thf(634,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(3328,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)],[634]) ).

thf(1073,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(4565,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)],[1073]) ).

thf(232,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
     => ( ( ( D != C )
          & ( B != A ) )
      <=> ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) )
         != ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ A ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).

thf(1989,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ E )
     => ( ( ( ( D != C )
            & ( B != A ) )
         => ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) )
           != ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ A ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ B ) ) ) )
        & ( ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ B ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ A ) )
           != ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Otimes__class_Otimes @ E @ D @ A ) @ ( c_Groups_Otimes__class_Otimes @ E @ C @ B ) ) )
         => ( ( D != C )
            & ( B != A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(879,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(4051,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)],[879]) ).

thf(995,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__ring @ D )
     => ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__diff) ).

thf(4350,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__ring @ D )
     => ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).

thf(179,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ A )
        = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).

thf(1816,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( ( c_Groups_Oplus__class_Oplus @ C @ ( c_Groups_Otimes__class_Otimes @ C @ B @ A ) @ A )
        = ( c_Groups_Otimes__class_Otimes @ C @ ( c_Groups_Oplus__class_Oplus @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(85,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(1495,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)],[85]) ).

thf(966,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(4281,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)],[966]) ).

thf(642,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(3347,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)],[642]) ).

thf(968,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(4286,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)],[968]) ).

thf(618,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(3277,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)],[618]) ).

thf(920,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 @ ( hAPP @ ( 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(4157,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 @ ( hAPP @ ( 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 @ ( hAPP @ ( 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)],[920]) ).

thf(144,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(1693,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)],[144]) ).

thf(768,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(3716,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)],[768]) ).

thf(813,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(3850,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)],[813]) ).

thf(453,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(2704,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)],[453]) ).

thf(932,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(4193,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)],[932]) ).

thf(664,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(3424,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)],[664]) ).

thf(558,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(3045,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)],[558]) ).

thf(691,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(3506,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)],[691]) ).

thf(809,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(3843,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)],[809]) ).

thf(752,axiom,
    class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).

thf(3673,plain,
    class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).

thf(241,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oorder @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( C = A )
         => ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I2_J) ).

thf(2021,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oorder @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( C = A )
         => ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(36,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(1346,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)],[36]) ).

thf(214,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oord @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( B = A )
         => ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__less__eq__trans) ).

thf(1930,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oord @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( B = A )
         => ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(229,axiom,
    ( c_Int_OPls
    = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pls__def) ).

thf(1977,plain,
    ( c_Int_OPls
    = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(6,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(1261,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)],[6]) ).

thf(702,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(3543,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)],[702]) ).

thf(906,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(4118,plain,
    class_Groups_Oordered__ab__group__add__abs @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).

thf(386,axiom,
    ! [A: $i] :
      ( ( 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_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( 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_Suc__n__div__2__gt__zero) ).

thf(2467,plain,
    ! [A: $i] :
      ( ( 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_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( 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)],[386]) ).

thf(825,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(3886,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)],[825]) ).

thf(1199,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(4936,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)],[1199]) ).

thf(1117,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(4691,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)],[1117]) ).

thf(993,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(4345,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)],[993]) ).

thf(329,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(2270,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)],[329]) ).

thf(939,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Opreorder @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).

thf(4221,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Opreorder @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).

thf(320,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(2241,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)],[320]) ).

thf(1170,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(4848,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)],[1170]) ).

thf(288,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(2159,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)],[288]) ).

thf(485,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(2810,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)],[485]) ).

thf(1009,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(4382,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)],[1009]) ).

thf(1212,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(4972,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)],[1212]) ).

thf(1246,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(5061,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)],[1246]) ).

thf(102,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(1550,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)],[102]) ).

thf(41,axiom,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ A )
     => ( class_Groups_Ominus @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ominus) ).

thf(1357,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ A )
     => ( class_Groups_Ominus @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(614,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(3259,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)],[614]) ).

thf(884,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(4066,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)],[884]) ).

thf(1039,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(4484,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)],[1039]) ).

thf(685,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(3489,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)],[685]) ).

thf(87,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(1500,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)],[87]) ).

thf(1019,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_RealVector_Oreal__normed__vector @ D )
        & ( class_Orderings_Oord @ C ) )
     => ( ! [E: $i] :
            ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ E )
           => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ D @ ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ A @ B ) @ ( hAPP @ A @ E ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
       => ! [E: $i] :
            ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ E )
           => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ D @ ( hAPP @ A @ E ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ D @ ( hAPP @ A @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemmaCauchy) ).

thf(4410,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_RealVector_Oreal__normed__vector @ D )
        & ( class_Orderings_Oord @ C ) )
     => ( ! [E: $i] :
            ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ E )
           => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ D @ ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ A @ B ) @ ( hAPP @ A @ E ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) )
       => ! [E: $i] :
            ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ E )
           => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ D @ ( hAPP @ A @ E ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ D @ ( hAPP @ A @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).

thf(947,axiom,
    class_Orderings_Oorder @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).

thf(4239,plain,
    class_Orderings_Oorder @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).

thf(1168,axiom,
    class_Rings_Osemiring @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).

thf(4831,plain,
    class_Rings_Osemiring @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).

thf(988,axiom,
    class_Rings_Olinordered__semidom @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).

thf(4330,plain,
    class_Rings_Olinordered__semidom @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).

thf(841,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(3939,plain,
    class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).

thf(409,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(2539,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)],[409]) ).

thf(149,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ouminus @ B )
     => ( class_Groups_Ouminus @ ( tc_fun @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).

thf(1713,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ouminus @ B )
     => ( class_Groups_Ouminus @ ( tc_fun @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(446,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Oordered__cancel__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).

thf(2687,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Oordered__cancel__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(778,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(3740,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)],[778]) ).

thf(66,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ B ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
      = ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( 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 ) ) ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__div__eq__add3__div__number__of) ).

thf(1431,plain,
    ! [A: $i,B: $i] :
      ( ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ B ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) )
      = ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( 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 ) ) ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ tc_Nat_Onat @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(1208,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(4955,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)],[1208]) ).

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

thf(4019,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oord @ D )
     => ( ( C = B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).

thf(579,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 @ B )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B ) @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__mono2) ).

thf(3113,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 @ B )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ B ) @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(204,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ 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 ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).

thf(1902,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ 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 ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ 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 ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Divides_Odiv__class_Odiv @ tc_Int_Oint @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(1062,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(4533,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)],[1062]) ).

thf(120,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(1606,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)],[120]) ).

thf(1165,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(4826,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)],[1165]) ).

thf(1102,axiom,
    class_Groups_Ouminus @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ouminus) ).

thf(4655,plain,
    class_Groups_Ouminus @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).

thf(1077,axiom,
    class_Groups_Omonoid__mult @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).

thf(4584,plain,
    class_Groups_Omonoid__mult @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).

thf(220,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oorder @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ A @ C )
         => ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).

thf(1945,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Orderings_Oorder @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ A @ C )
         => ( c_Orderings_Oord__class_Oless @ D @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(573,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(3096,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)],[573]) ).

thf(258,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(2074,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)],[258]) ).

thf(921,axiom,
    class_Groups_Ogroup__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).

thf(4161,plain,
    class_Groups_Ogroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).

thf(1189,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(4908,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)],[1189]) ).

thf(560,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(3052,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)],[560]) ).

thf(541,axiom,
    class_Rings_Ono__zero__divisors @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).

thf(2993,plain,
    class_Rings_Ono__zero__divisors @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(78,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(1468,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)],[78]) ).

thf(770,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(3721,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)],[770]) ).

thf(209,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(1912,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)],[209]) ).

thf(347,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(2321,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)],[347]) ).

thf(219,axiom,
    class_Rings_Ocomm__ring__1 @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).

thf(1944,plain,
    class_Rings_Ocomm__ring__1 @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(1122,axiom,
    class_Orderings_Olinorder @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).

thf(4702,plain,
    class_Orderings_Olinorder @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).

thf(417,axiom,
    class_Int_Onumber @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber) ).

thf(2563,plain,
    class_Int_Onumber @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(832,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(3924,plain,
    class_RealVector_Oreal__normed__div__algebra @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).

thf(732,axiom,
    ! [A: $i,B: $i] :
      ( ( 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_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) @ A )
      <=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le__eq) ).

thf(3626,plain,
    ! [A: $i,B: $i] :
      ( ( 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_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_RealDef_Oreal @ tc_Nat_Onat @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_RComplete_Onatceiling @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).

thf(318,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
        | ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).

thf(2238,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Orderings_Olinorder @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
        | ( c_Orderings_Oord__class_Oless @ C @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(84,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(1490,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)],[84]) ).

thf(1135,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(4742,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)],[1135]) ).

thf(671,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Groups_Oordered__ab__group__add__abs @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs) ).

thf(3443,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Groups_Oordered__ab__group__add__abs @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(353,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(2351,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)],[353]) ).

thf(293,axiom,
    ! [A: $i] :
      ( ( class_Rings_Oidom @ A )
     => ( class_Rings_Oidom @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).

thf(2170,plain,
    ! [A: $i] :
      ( ( class_Rings_Oidom @ A )
     => ( class_Rings_Oidom @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(492,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(2834,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)],[492]) ).

thf(268,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(2106,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)],[268]) ).

thf(262,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(2087,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)],[262]) ).

thf(704,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_termination__basic__simps_I3_J) ).

thf(3553,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)],[704]) ).

thf(296,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(2177,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)],[296]) ).

thf(975,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(4298,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)],[975]) ).

thf(62,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(1417,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)],[62]) ).

thf(194,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(1870,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)],[194]) ).

thf(749,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(3669,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)],[749]) ).

thf(5071,plain,
    $false,
    inference(cvc4,[status(thm)],[3021,1586,1369,3008,2778,4899,2412,2480,4015,3927,4728,3172,2250,2822,3873,4560,3962,1718,2612,4094,2295,4101,2072,3661,1767,2263,4169,3666,1729,4290,3698,3979,3397,1899,1840,3581,1315,2787,1750,4500,4339,3858,3230,2908,2659,2953,3098,2671,4960,4603,2099,4614,1437,2077,4043,3534,3681,3990,3072,1924,2210,2940,1406,2104,4075,1290,4311,1522,3762,3509,3285,3377,4391,1569,3959,2248,2114,1269,3498,4215,2380,3217,4090,3120,4739,2316,4564,2168,2459,3313,1354,2360,2195,4543,1671,5037,1608,4403,4647,3367,4884,3365,4026,1735,4110,1867,4528,1872,2712,3414,1761,4294,3481,1954,2844,4762,1458,3335,3103,1835,3350,3994,2763,1576,3249,3777,2082,2136,4775,3836,3629,2972,2046,3308,1935,4803,3730,1921,5056,2886,4916,1359,4030,1724,1475,3809,1366,2400,2825,1529,4156,4665,4322,1623,1254,3820,4422,2339,3342,3495,3061,4778,2682,2897,2126,1409,4238,3204,4439,1287,3221,4896,1430,3644,2698,1660,1298,1907,2501,1330,1264,4334,2217,1323,3612,3148,3653,1279,4275,2185,1455,3845,4023,3353,4984,2745,3713,4243,2703,2403,4664,4952,3708,4265,4383,1362,4756,4119,3517,1892,1379,4353,4862,4788,4358,2049,4492,4928,3919,4830,4317,4675,3470,4551,3902,3602,4400,1778,4793,4507,2852,4771,3866,4302,4514,4253,4967,4669,1847,2222,3322,3524,3934,2090,2236,2880,2925,4134,3569,4798,2017,4696,4205,4903,1450,4258,2996,4454,3295,2893,2469,4820,3163,1334,3527,1858,3438,2122,4115,2335,4810,4162,4718,2437,1377,1447,2772,1351,2286,3226,3211,4628,3378,5045,3389,5059,4033,2833,3189,2281,1896,2190,1886,4504,2523,3036,4364,4087,2979,4536,3243,2965,4519,3588,4892,3406,2205,1696,2884,3435,2922,3857,4589,1691,2118,1338,5034,2093,1783,4059,4925,3151,2011,5012,3503,3459,4893,3591,1306,4531,5017,3635,2164,3995,3318,2232,4576,2307,4312,2790,2061,4172,1636,1730,3679,3735,2409,2428,4878,1666,3711,2733,4016,2805,4397,5002,4609,1570,4989,5044,2133,4128,3069,3884,2937,4499,2606,3154,4449,4493,1824,4284,3814,2986,2414,2132,2890,2528,3664,3339,2015,3286,1883,1560,4192,5021,4746,4979,3647,3282,3948,2445,4295,2464,1938,2758,3980,3269,1602,3618,4585,2477,4725,1968,2663,1555,2332,4947,3499,1888,3877,1819,1624,2200,2609,4402,1787,4942,3050,3926,2344,2492,4104,1281,2741,1634,1392,3931,1910,4680,1573,3799,3445,4027,5066,1592,2115,4668,3862,2709,4693,4095,3440,4898,4808,4123,2498,3615,5053,3413,1851,2946,2990,4512,2685,5006,2895,4248,1375,4486,4048,4544,1856,4429,4636,2692,1498,2509,4233,3386,2631,3650,4012,3916,1755,4653,2877,4860,3179,3846,2561,2830,3728,2868,2419,4938,3032,3671,3555,3573,1964,3922,3094,1461,2312,3010,4750,1414,2240,4861,2172,2108,2038,3723,4444,2666,2472,4180,3935,1419,4384,3126,2304,2243,2355,1947,3115,4416,3703,5063,1776,3611,3656,2450,2125,3654,3787,1539,2836,4970,3743,3770,1668,1974,3819,4237,2006,2497,5058,3937,4231,4347,2766,3692,2052,1715,3333,3064,1720,1979,3074,5026,4069,3201,4223,1759,1393,1627,3215,4361,1525,3755,1434,1318,2203,4644,4625,2883,1563,2368,1466,4036,3422,2662,4308,2529,3563,4195,2043,3587,4906,2915,2793,3190,3841,2617,1732,4572,2235,2729,2001,4131,2391,2556,3042,1483,4256,5048,4562,3289,4503,4017,4599,4921,1906,3707,1727,1251,4919,2677,4708,2253,2033,3257,3607,1548,1927,3738,2028,1301,3375,1595,3111,3274,3696,4489,1631,5043,4662,3811,3519,3609,3758,1388,5050,1403,4328,4381,4946,2695,2827,2959,3636,3925,4494,3255,2188,2981,5067,1620,3472,4926,3266,4590,1520,3404,4612,3223,2193,5033,2326,4413,1332,2442,2055,2706,2425,4273,2474,3170,4526,3796,1503,1707,2293,4796,1271,3077,1312,4112,3695,4099,2738,4149,4236,4218,4672,3002,3832,3579,4854,3641,3302,3568,4887,4245,2358,4433,1356,2148,3719,2521,4929,3996,3957,2906,4699,4139,2943,4300,4509,2679,4704,4498,2478,4369,2229,3815,2084,2214,2383,2422,4305,2257,1589,1603,2299,4601,3106,3468,1542,2116,2839,3197,4154,2856,3500,2378,3066,3586,4107,1307,2180,2182,2025,4420,4064,3451,4296,2928,1688,1877,1471,3747,4541,2742,4882,3055,4103,2314,2129,3668,4911,2111,2780,4731,1821,4264,1838,3614,4652,2874,3971,3583,2542,2289,2647,1293,2278,2911,4554,2212,3838,2620,4502,2139,3016,2244,3310,3325,4196,2999,2207,2984,2069,4084,3539,2770,4832,2962,2365,2064,3674,4827,2931,5042,4703,2101,1364,1250,3512,4497,4207,1583,2952,3427,4901,3576,1509,2629,4355,3292,3849,3522,4331,4394,4441,4136,4260,4813,2994,2784,4456,3672,1905,3981,2503,4688,2256,2564,4168,2582,4045,1748,3391,4035,3913,3082,1566,1647,3129,2518,4630,4593,2689,3988,4749,1516,2863,3315,4360,2397,2977,1611,2375,4272,1400,1743,4939,3754,4950,3833,3659,1941,3462,4517,4641,2175,1780,3209,4754,1267,2386,3608,2850,4561,4240,1785,1763,4132,3359,2656,3019,3080,2569,3246,4437,3448,4314,1790,1987,3940,3305,4190,3818,1452,3334,3791,3475,3026,2276,5030,2219,2701,4241,2545,2903,4982,3412,3564,1336,3769,2056,1934,1702,4976,2145,2579,4431,2511,3961,1372,3007,4414,1617,4802,1766,4057,1849,1257,2558,3829,4133,1536,4436,4246,3356,4488,1284,1972,2711,4991,4046,1427,1797,3024,4093,2949,2722,3943,4225,1717,2030,1881,2807,2584,4257,4671,3620,3401,4945,4770,1553,1412,1517,4102,2775,4061,1998,2013,3478,3433,4289,2626,1918,3457,1649,4698,2479,4851,4606,3589,4325,4587,1949,4763,1321,4656,2310,3874,3928,4185,3625,4078,3725,1390,4463,4678,3039,1276,4913,2406,2532,4683,4250,1745,3630,3252,1326,4121,4710,2988,3864,1721,2167,2273,2283,4806,1341,3484,3789,2855,4089,2554,3369,3220,4715,4791,1629,1854,4338,3235,2431,4705,3859,3331,4881,2526,2416,3780,1558,2934,4261,3085,4745,1861,3978,4649,2041,3430,4759,2576,4404,2120,1309,4098,1614,3181,4602,2796,4293,4175,3879,4774,3598,2462,5040,1440,5023,3677,2362,2162,4372,3761,4306,3552,4025,2019,1348,3705,2719,4596,1546,1395,4357,4367,5041,3992,2142,1642,4816,2302,5009,4014,1957,4114,4472,4687,4706,1678,3511,2155,4378,3232,4356,3907,2587,5004,3733,2522,3100,2815,4787,1303,1527,3337,1673,4579,3690,1480,5014,2768,1436,4755,4427,1710,2913,5036,3765,1473,2668,2783,2549,3982,2636,2751,2800,4178,3328,4565,1989,4051,4350,1816,1495,4281,3347,4286,3277,4157,1693,3716,3850,2704,4193,3424,3045,3506,3843,3673,2021,1346,1930,1977,1261,3543,4118,2467,3886,4936,4691,4345,2270,4221,2241,4848,2159,2810,4382,4972,5061,1550,1357,3259,4066,4484,3489,1500,4410,4239,4831,4330,3939,2539,1713,2687,3740,1431,4955,4019,3113,1902,4533,1606,4826,4655,4584,1945,3096,2074,4161,4908,3052,2993,1468,3721,1912,2321,1944,4702,2563,3924,3626,2238,1490,4742,3443,2351,2170,2834,2106,2087,3553,2177,4298,1417,1870,3669]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SWW229+1 : TPTP v8.2.0. Released v5.2.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n014.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Sat May 18 20:26:24 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.97/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.98/1.14  % [INFO] 	 Parsing done (278ms). 
% 1.98/1.15  % [INFO] 	 Running in sequential loop mode. 
% 2.54/1.35  % [INFO] 	 eprover registered as external prover. 
% 2.54/1.35  % [INFO] 	 cvc4 registered as external prover. 
% 2.54/1.36  % [INFO] 	 Scanning for conjecture ... 
% 3.02/1.49  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1253 axioms. Running axiom selection ... 
% 3.82/1.67  % [INFO] 	 Axiom selection finished. Selected 1247 axioms (removed 6 axioms). 
% 4.96/1.97  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 5.16/2.00  % [INFO] 	 Type checking passed. 
% 5.16/2.00  % [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 ... 
% 23.39/6.09  % External prover 'cvc4' found a proof!
% 23.39/6.10  % [INFO] 	 Killing All external provers ... 
% 23.39/6.10  % Time passed: 5573ms (effective reasoning time: 4947ms)
% 23.39/6.10  % 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)>
% 23.39/6.10  % Axioms used in derivation (1247): fact_zero__le__divide__iff, fact_le__SucI, arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra, fact_numeral__2__eq__2, arity_fun__Orderings_Oorder, fact_le__imp__diff__is__add, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_Numeral1__eq1__nat, fact_minus__Bit0, fact_complex__diff__def, fact_zle__refl, fact_minus__mult__left, fact_neg__le__0__iff__le, fact_add__le__less__mono, fact_mult__strict__left__mono__neg, fact_order__le__neq__trans, fact_Nat_Oadd__0__right, fact_right__inverse__eq, fact_xt1_I1_J, fact_less__eq__int__code_I14_J, 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, arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_number__of__diff, arity_Nat__Onat__Groups_Ocancel__semigroup__add, fact_real__le__trans, arity_Complex__Ocomplex__Groups_Omonoid__add, arity_Int__Oint__Rings_Ocomm__semiring, fact_natfloor__real__of__nat, fact_pos__add__strict, arity_Int__Oint__Rings_Osemiring, arity_RealDef__Oreal__Orderings_Oord, fact_nonzero__inverse__inverse__eq, fact_add__strict__right__mono, arity_Int__Oint__Orderings_Olinorder, fact_natfloor__add, fact_mult__1__left, fact_diff__0__eq__0, fact_inverse__1, fact_zdiv__eq__0__iff, 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, fact_xt1_I4_J, arity_Polynomial__Opoly__Int_Onumber, arity_RealDef__Oreal__Groups_Ozero, fact_trans__less__add1, fact_mult__nonneg__nonpos, fact_one__is__num__one, fact_add__poly__code_I2_J, 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_order__le__less__trans, fact_less__imp__inverse__less, fact_real__of__nat__zero, fact_mult__left_Ominus, fact_number__of__minus, arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors, fact_real__sgn__eq, arity_Nat__Onat__Rings_Ono__zero__divisors, fact_nat__less__cases, fact_divide__nonpos__neg, fact_one__is__add, fact_diff__le__mono2, arity_Int__Oint__Rings_Olinordered__semiring__strict, arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add, fact_minus__mult__right, fact_real__of__nat__diff, fact_termination__basic__simps_I5_J, arity_Polynomial__Opoly__Rings_Ocomm__semiring__0, 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_less__imp__le__nat, fact_combine__common__factor, fact_le__imp__0__less, fact_add__leD1, fact_diff__number__of__eq, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_abs__div__pos, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, arity_RealDef__Oreal__Rings_Olinordered__ring, fact_add__less__mono, fact_th2, fact_real__0__less__add__iff, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, arity_RealDef__Oreal__Groups_Ominus, 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, arity_Nat__Onat__Orderings_Oorder, fact_positive__imp__inverse__positive, fact_split__mult__neg__le, fact_real__gt__half__sum, fact_rel__simps_I49_J, fact_rel__simps_I27_J, fact_divide__numeral__1, fact_numeral__1__eq__Suc__0, fact_Suc__mono, fact_inverse__add, arity_Nat__Onat__Rings_Ocomm__semiring__0, fact_psize__eq__0__iff, fact_inverse__negative__iff__negative, arity_Nat__Onat__Groups_Oordered__comm__monoid__add, fact_less__nat__zero__code, fact_linorder__not__le, arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le, fact_zadd__commute, fact_natceiling__le, arity_Nat__Onat__Groups_Omonoid__mult, fact_diff__Suc__less, fact_real__add__le__0__iff, 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_order__less__asym_H, arity_Polynomial__Opoly__Rings_Olinordered__ring__strict, fact_div__nonpos__pos__le0, fact_eq__neg__iff__add__eq__0, fact_add__right__imp__eq, arity_Polynomial__Opoly__Rings_Oidom, fact_linorder__antisym__conv2, fact_nonzero__inverse__eq__imp__eq, fact_diff__diff__cancel, fact_mult__mono, fact_linorder__neqE, fact_abs__diff__triangle__ineq, fact_Suc__diff__diff, fact_Suc__le__mono, fact_zero__le__natfloor, fact_order__eq__refl, fact_le__number__of__eq__not__less, fact_norm__add__less, arity_Nat__Onat__Rings_Ozero__neq__one, fact_poly__zero, fact_nat__number__of__Pls, fact_zero__less__diff, fact_abs__poly__def, fact_nat__add__right__cancel, fact_neg__le__iff__le, fact_gr0__conv__Suc, arity_Polynomial__Opoly__Groups_Ominus, arity_RealDef__Oreal__Groups_Omonoid__add, fact_neg__0__less__iff__less, fact_div__le__dividend, fact_inverse__zero, fact_leI, fact_natceiling__le__eq__one, arity_Complex__Ocomplex__Int_Onumber__ring, fact_less__special_I4_J, arity_RealDef__Oreal__Rings_Oidom, fact_int__pos__lt__two__imp__zero__or__one, fact_le__neq__implies__less, fact_divide__pos__neg, arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add, arity_Polynomial__Opoly__Rings_Ocomm__ring, fact_zle__linear, fact_lemma__NBseq__def2, fact_zero__le__one, fact_poly__add, arity_RealDef__Oreal__Rings_Ocomm__ring__1, fact_diff__bin__simps_I7_J, fact_Bit1__def, fact_int__0__less__1, fact_le__minus__iff, fact_left__diff__distrib__number__of, fact_abs__of__neg, 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_minus__add__cancel, fact_add__pos__nonneg, fact_expand__Suc, arity_Int__Oint__Orderings_Oord, arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add, fact_nat__add__left__cancel__less, fact_add__Bit0__Bit1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_linorder__antisym__conv3, fact_add__strict__increasing2, fact_order__less__imp__not__eq, fact_inverse__positive__imp__positive, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_linorder__neqE__linordered__idom, arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero, arity_Polynomial__Opoly__Rings_Olinordered__semidom, fact_neg__less__0__iff__less, fact_divide__right__mono, fact_zadd__left__mono, fact_rel__simps_I5_J, fact_add__increasing2, arity_RealDef__Oreal__Fields_Ofield__inverse__zero, fact_natceiling__mono, fact_add__nonneg__eq__0__iff, fact_real__of__nat__zero__iff, arity_Complex__Ocomplex__Rings_Ocomm__semiring__1, arity_Polynomial__Opoly__Orderings_Olinorder, fact_div__1, fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096, fact_seq__suble, fact_div__if, fact_abs__triangle__ineq2, fact_divide__1, fact_mult__strict__left__mono, fact_number__of__is__id, fact_mult__right_Ozero, fact_Suc__div__eq__add3__div__number__of, fact_minus__real__def, fact_add__le__imp__le__left, fact_zero__le__mult__iff, arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero, fact_ath2, fact_linorder__antisym__conv1, arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add, arity_Int__Oint__Groups_Ozero, arity_RealDef__Oreal__Groups_Oabs__if, fact_zdiv__zero, fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J, fact_mult_Ozero__left, fact_poly__0, arity_Int__Oint__Rings_Olinordered__ring, fact_add__0__iff, fact_N1, fact_le__funD, fact_add__right__mono, arity_Polynomial__Opoly__Orderings_Oord, arity_Int__Oint__Groups_Ocancel__comm__monoid__add, fact_nat__less__real__le, fact_diff__le__self, fact_even__less__0__iff, fact_sgn__neg, fact_complex__i__not__zero, fact_le__natfloor__eq__one, arity_Int__Oint__Groups_Ocomm__monoid__add, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, arity_RealDef__Oreal__Groups_Omonoid__mult, fact_add__0__left, fact_add__mono, fact_nonneg1__imp__zdiv__pos__iff, fact_gr0I, fact_sgn__minus, 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_le__fun__def, fact_minus__add, fact_divide__eq__imp, arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add, fact_norm__triangle__ineq3, fact_abs__add__one__gt__zero, fact_lemma__NBseq__def, fact_th1, fact_real__of__nat__less__iff, fact_half__gt__zero__iff, 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fact_real__diff__def, fact_div__add__self2, arity_Nat__Onat__Rings_Oordered__cancel__semiring, fact_int__0__neq__1, fact_le__natfloor__eq, fact_add__less__imp__less__right, fact_le__Suc__ex__iff, arity_RealDef__Oreal__Rings_Oring__no__zero__divisors, fact_th000_I3_J, fact_norm__sgn, fact_subseq__def, fact_Suc__n__div__2__gt__zero, arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le, fact_diff__less__mono, fact_Suc__leD, fact_neg__equal__zero, fact_nonzero__inverse__minus__eq, fact_add__number__of__eq, fact_add__minus__cancel, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_zero__less__divide__iff, fact_real__of__nat__1, fact_add_Ocomm__neutral, fact_less__number__of, fact_nonzero__imp__inverse__nonzero, fact_s, arity_Int__Oint__Groups_Osgn__if, fact_Bit0__def, fact_xt1_I6_J, fact_le__minus__self__iff, fact_rel__simps_I50_J, fact_eq__add__iff2, fact_zdiv__number__of__Bit1, fact_le__special_I3_J, arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra, arity_Nat__Onat__Rings_Oordered__semiring, fact_linorder__linear, fact_diff__bin__simps_I3_J, fact_natfloor__eq, fact_mult__zero__left, fact_abs__sum__triangle__ineq, fact_less__trans__Suc, arity_Int__Oint__Groups_Oordered__ab__semigroup__add, fact_add__scale__eq__noteq, fact_natfloor__div__nat, fact_Nat_Odiff__diff__eq, fact_complex__i__not__one, fact_le__refl, fact_nat__add__assoc, fact_abs__add__one__not__less__self, fact_norm__minus__cancel, fact_less__not__refl2, fact_field__class_Onormalizing__field__rules_I2_J, fact_le__add1, fact_div__2__gt__zero, fact_trans__le__add2, fact_abs__le__zero__iff, fact_sgn__1__neg, fact_rel__simps_I4_J, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_nonzero__minus__divide__divide, fact_linorder__not__less, fact_semiring__norm_I113_J, fact_rel__simps_I46_J, fact_mult__diff__mult, arity_RealDef__Oreal__Groups_Ouminus, fact_rel__simps_I16_J, fact_add__less__imp__less__left, fact_abs__triangle__ineq4, fact_le__imp__less__Suc, fact_d_I1_J, arity_RealDef__Oreal__Groups_Oone, fact_Suc__div__eq__add3__div, fact_numeral__3__eq__3, fact_abs__zero, fact_less__add__Suc1, fact_ab__left__minus, fact_sgn0, fact_add__neg__neg, arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict, fact_less__fun__def, fact_One__nat__def, fact_minus__diff__eq, fact_less__imp__inverse__less__neg, fact_comm__semiring__class_Odistrib, fact_add__number__of__left, fact_square__eq__iff, fact_zero__less__abs__iff, fact_abs__add__abs, fact_nonzero__minus__divide__right, fact_add__is__0, fact_rel__simps_I10_J, fact_eq__number__of, fact_neg__imp__zdiv__nonneg__iff, fact_termination__basic__simps_I3_J, arity_Int__Oint__Rings_Oordered__ring, fact_abs__le__iff, fact_eq__number__of__0, fact_sgn__pos, fact_add__self__div__2, fact_divide_Oadd, fact_inverse__less__imp__less__neg, fact_ab__diff__minus, fact_right__diff__distrib__number__of, fact_sgn__zero__iff, fact_Bseq__inverse__lemma, fact_Deriv_Oadd__diff__add, fact_mult__right__mono, fact_xt1_I2_J, fact_abs__minus__cancel, arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add, fact_add__0, arity_Polynomial__Opoly__Rings_Oordered__ring, fact_diff__minus__eq__add, fact_add__nonneg__nonneg, fact_lemmaCauchy, fact_diff__self__eq__0, fact_add__eq__0__iff, fact_Divides_Otransfer__nat__int__function__closures_I1_J, arity_RealDef__Oreal__Rings_Olinordered__semidom, fact_neg__equal__iff__equal, fact_compl__eq__compl__iff, arity_RealDef__Oreal__Groups_Ocomm__monoid__mult, fact_diff__add__0, fact_add__pos__pos, fact_diff__cancel2, fact_Suc__eq__plus1, arity_RealDef__Oreal__Groups_Oab__group__add, arity_Int__Oint__Rings_Olinordered__idom, arity_Int__Oint__Rings_Ocomm__semiring__1, fact_sgn__greater, fact_inverse__minus__eq, fact_div__neg__pos__less0, arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1, fact_mult__nonpos__nonneg, fact_Suc__diff__le, arity_Polynomial__Opoly__Rings_Osemiring, fact_Zero__neq__Suc, fact_less__eq__int__code_I16_J, fact_order__eq__iff, fact_less__special_I3_J, arity_Nat__Onat__Groups_Oab__semigroup__add, fact_not__less__eq__eq, arity_Int__Oint__Rings_Oordered__comm__semiring, fact_le0, fact_add__Pls__right, fact_Suc__pred, arity_Int__Oint__Groups_Oab__semigroup__add, arity_fun__Groups_Ominus, arity_Int__Oint__Groups_Oone, arity_Nat__Onat__Rings_Olinordered__semidom, fact_add__le__cancel__right, arity_Complex__Ocomplex__Groups_Omonoid__mult, arity_Int__Oint__Groups_Ocomm__monoid__mult, fact_add__left__mono, fact_real__add__eq__0__iff, fact_mult__right_Ominus, fact_less__not__refl, fact_double__add__le__zero__iff__single__add__le__zero, fact_mult__less__cancel__left__neg, fact_zabs__def, fact_ord__eq__less__trans, fact_sgn__if, fact_less__1__mult, fact_right__inverse, fact_compl__le__compl__iff, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_poly__diff, arity_Int__Oint__Orderings_Oorder, fact_le__diff__conv2, fact_mult__pos__pos, 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, fact_sgn__real__def, fact_minus__mult__minus, fact_crossproduct__eq, 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_le__trans, arity_Int__Oint__Groups_Oabs__if, fact_diff__Suc__diff__eq1, fact_comm__mult__left__mono, fact_ge__natfloor__plus__one__imp__gt, fact_plus__numeral__code_I9_J, fact_gr__implies__not0, fact_mult__strict__right__mono__neg, fact_zdiv__zminus__zminus, fact_abs__triangle__ineq, fact_zsgn__def, 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_less__add__one, fact_zero__neq__one, fact_less__Suc__eq, fact_norm__mult__ineq, fact_add__leE, fact_th31, fact_natceiling__subtract, fact_right__minus__eq, fact_mult_Odiff__left, arity_Polynomial__Opoly__Groups_Ogroup__add, fact_diff__Suc__1, fact_add__less__le__mono, arity_Polynomial__Opoly__Orderings_Opreorder, fact_real__of__nat__Suc__gt__zero, fact_wr, arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add, arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero, arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors, fact_int__one__le__iff__zero__less, fact_zdiv__mono2, arity_Nat__Onat__Int_Onumber, arity_Nat__Onat__Rings_Olinordered__semiring__strict, fact_natfloor__add__one, fact_nat__add__commute, arity_Int__Oint__Rings_Ono__zero__divisors, fact_add__poly__code_I1_J, fact_diff__eq__diff__less__eq, fact_less__int__code_I15_J, arity_RealDef__Oreal__Rings_Ocomm__semiring__0, fact_Suc__less__eq, fact_mult__neg__neg, arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add, fact_neg__0__le__iff__le, fact_sgn__one, arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add, fact_complex__i__not__number__of, fact_zdiv__zminus2, fact_zero__less__Suc, fact_rel__simps_I2_J, fact_div__self, arity_Complex__Ocomplex__Rings_Ocomm__ring, fact_mult_Ocomm__neutral, fact_real__add__left__mono, 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, arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_add__nonpos__neg, fact_number__of__Bit1, fact_zdiv__self, arity_RealDef__Oreal__Rings_Oordered__semiring, fact_le__SucE, fact_pos__imp__zdiv__nonneg__iff, fact_divide_Odiff, 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, fact_plus__nat_Oadd__0, fact_subseq__Suc__iff, arity_RealDef__Oreal__Int_Onumber, fact_minus__le__self__iff, fact_diff__eq__diff__eq, fact_order__le__imp__less__or__eq, fact_less__int__code_I16_J, fact_add__strict__increasing, fact_le__less__Suc__eq, fact_real__norm__def, fact_minus__equation__iff, fact_mult__left__mono__neg, fact_add__divide__distrib, arity_Int__Oint__Rings_Olinordered__comm__semiring__strict, fact_diff__le__mono, arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring, fact_le__special_I4_J, fact_nonzero__abs__divide, fact_d_I2_J, fact_div__le__mono, arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le, arity_Polynomial__Opoly__Rings_Ocomm__ring__1, fact_N2, fact_order__antisym__conv, fact_neq0__conv, fact_add__2__eq__Suc, fact_s1, fact_Suc__n__not__n, fact_nat__numeral__1__eq__1, fact_half, fact_real__of__nat__gt__zero__cancel__iff, fact_divide__strict__right__mono, fact_le__antisym, fact_real__of__nat__div2, fact_real__add__less__0__iff, fact_zless__linear, fact_mult__less__cancel__left__pos, fact_bin__less__0__simps_I1_J, fact_trans__le__add1, fact_zadd__0__right, fact_e2, fact_zero__less__mult__pos, arity_Polynomial__Opoly__Rings_Ocomm__semiring, arity_Int__Oint__Groups_Ominus, arity_Complex__Ocomplex__Rings_Omult__zero, arity_Polynomial__Opoly__Rings_Ono__zero__divisors, fact_double__eq__0__iff, fact_le__0__eq, fact_zle__add1__eq__le, fact_mult__1__right, fact_order__less__irrefl, fact_real__of__nat__le__iff, fact_less__Suc0, fact_add__diff__inverse, fact_divide__nonneg__neg, arity_Nat__Onat__Rings_Osemiring, arity_Int__Oint__Groups_Olinordered__ab__group__add, fact_le__diff__iff, arity_Polynomial__Opoly__Groups_Oabs__if, fact_less__iff__Suc__add, fact_order__less__imp__le, fact_termination__basic__simps_I1_J, fact_real__0__le__add__iff, fact_order__less__trans, fact_real__average__minus__first, fact_zero__less__two, fact_diff__is__0__eq, fact_poly__div__minus__right, fact_number__of__Pls, fact_real__of__nat__one, arity_Polynomial__Opoly__Groups_Ozero, fact_rp, fact_add__le__imp__le__right, 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, fact_sum__squares__eq__zero__iff, fact_abs__norm__cancel, fact_le__add__diff__inverse, fact_zabs__less__one__iff, arity_Int__Oint__Rings_Ocomm__ring__1, fact_add__le__mono, fact_order__le__less, fact_rel__simps_I32_J, arity_Nat__Onat__Groups_Oone, fact_diff__Suc__Suc, fact_add__imp__eq, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_inverse__negative__imp__negative, fact_zadd__zminus__inverse2, fact_field__inverse__zero, arity_RealDef__Oreal__Groups_Olinordered__ab__group__add, fact_ab__semigroup__add__class_Oadd__ac_I1_J, arity_Int__Oint__Rings_Ozero__neq__one, arity_RealDef__Oreal__Fields_Ofield, fact_half__gt__zero, arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_minus__poly__code_I1_J, fact_nat__less__le, arity_Complex__Ocomplex__RealVector_Oreal__normed__vector, fact_no__zero__divisors, fact_sgn__1__pos, fact_less__iff__diff__less__0, fact_Deriv_Oinverse__diff__inverse, fact_less__SucE, fact_gt__half__sum, fact_zless__add1__eq, fact_linorder__cases, fact_real__natfloor__le, fact_xt1_I11_J, fact_add__less__mono1, fact_add__le__cancel__left, fact_eq__divide__eq, fact_divisors__zero, arity_Polynomial__Opoly__Rings_Olinordered__ring, fact_nonzero__norm__divide, arity_RealDef__Oreal__Groups_Ogroup__add, arity_Polynomial__Opoly__Groups_Ocomm__monoid__add, fact__096abs_A_Icmod_A_Ipoly_Ap_A_Ig_A_If_A_IN1_A_L_AN2_J_J_J_J_A_N_A_N_As_J_A_060_A1_A_P_Areal_A_ISuc_A_IN1_A_L_AN2_J_J_096, arity_Polynomial__Opoly__Groups_Oone, fact_poly__eq__iff, fact_real__le__linear, fact_ord__eq__le__trans, fact_double__add__less__zero__iff__single__add__less__zero, fact_minus__divide__left, fact_less__diff__iff, fact_real__natfloor__gt__diff__one, fact_odd__less__0, fact_field__inverse, arity_Int__Oint__Groups_Omonoid__add, fact_add__Suc__shift, fact_real__sgn__def, fact_less__special_I1_J, fact_le__special_I2_J, arity_Complex__Ocomplex__Int_Onumber, arity_Int__Oint__Orderings_Opreorder, fact_divide__self, fact_diff__special_I2_J, fact_real__of__nat__inject, fact_INVERSE__ZERO, fact_norm__triangle__ineq2, fact_less__half__sum, arity_Int__Oint__Rings_Ocomm__semiring__0, fact_less__SucI, fact_Suc__not__Zero, fact_real__of__nat__add, fact_xt1_I7_J, fact_order__trans, arity_Complex__Ocomplex__Groups_Ozero, arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add, fact_add__2__eq__Suc_H, fact_not__square__less__zero, fact_Suc__lessI, fact_add__Suc__right, arity_Complex__Ocomplex__Groups_Ominus, fact_mult__1, fact_less__bin__lemma, arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add, arity_Int__Oint__Rings_Olinordered__ring__strict, fact_mult_Odiff__right, fact_natfloor__mono, fact_rel__simps_I22_J, arity_Complex__Ocomplex__Rings_Ocomm__semiring__0, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J
% 23.39/6.10  % No. of inferences in proof: 2498
% 23.39/6.10  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5573 ms resp. 4947 ms w/o parsing
% 24.58/6.42  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 24.58/6.43  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------