%------------------------------------------------------------------------------
% File     : Leo-III---1.7.15
% Problem  : SWW237+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d THM

% Computer : n022.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon Jun 24 18:21:30 EDT 2024

% Result   : Timeout 288.63s 87.88s
% Output   : None 
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   29
%            Number of leaves      : 1263
% Syntax   : Number of formulae    : 3667 (1023 unt;   0 typ;   0 def)
%            Number of atoms       : 9869 (3319 equ;   0 cnn)
%            Maximal formula atoms :   17 (   2 avg)
%            Number of connectives : 46978 (2211   ~;1436   |; 648   &;39017   @)
%                                         ( 251 <=>;3415  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  119 ( 116 usr;  14 con; 0-4 aty)
%            Number of variables   : 7042 (   0   ^6970   !;  72   ?;7042   :)

% 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(v_da_____type,type,
    v_da____: $i ).

thf(v_mazh_type,type,
    v_mazh: $i ).

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

thf(c_Polynomial_Osynthetic__div_type,type,
    c_Polynomial_Osynthetic__div: $i > $i > $i > $i ).

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

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

thf(c_Polynomial_OpCons_type,type,
    c_Polynomial_OpCons: $i > $i > $i > $i ).

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

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

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

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

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

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

thf(v_c_____type,type,
    v_c____: $i ).

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

thf(c_Rings_Odvd__class_Odvd_type,type,
    c_Rings_Odvd__class_Odvd: $i > $i > $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(class_Rings_Odvd_type,type,
    class_Rings_Odvd: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(class_Rings_Osemiring__0_type,type,
    class_Rings_Osemiring__0: $i > $o ).

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

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

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

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

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

thf(v_aa_____type,type,
    v_aa____: $i ).

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

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

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

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

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

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

thf(c_Complex_Orcis_type,type,
    c_Complex_Orcis: $i > $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(v_mzh_type,type,
    v_mzh: $i ).

thf(v_ma_type,type,
    v_ma: $i ).

thf(sk2_type,type,
    sk2: $i > $i > $i > $i > $i ).

thf(sk3_type,type,
    sk3: $i > $i > $i ).

thf(sk8_type,type,
    sk8: $i > $i ).

thf(sk16_type,type,
    sk16: $i > $i ).

thf(sk26_type,type,
    sk26: $i > $i > $i ).

thf(1234,axiom,
    class_Rings_Oring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).

thf(5116,plain,
    class_Rings_Oring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).

thf(418,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( hAPP @ ( hAPP @ ( 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(2778,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(442,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).

thf(2876,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(1115,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(4852,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)],[1115]) ).

thf(76,axiom,
    ! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Obot__least) ).

thf(1526,plain,
    ! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(1527,plain,
    ! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A ),
    inference(cnf,[status(esa)],[1526]) ).

thf(28,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
        & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
    <=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
        & ( B != A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__le) ).

thf(1353,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
       => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
          & ( B != A ) ) )
      & ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
          & ( B != A ) )
       => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(1354,plain,
    ( ! [A: $i,B: $i] :
        ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
       => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
          & ( B != A ) ) )
    & ! [A: $i,B: $i] :
        ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
          & ( B != A ) )
       => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ) ) ),
    inference(miniscope,[status(thm)],[1353]) ).

thf(1356,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
      | ( B = A )
      | ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ),
    inference(cnf,[status(esa)],[1354]) ).

thf(1361,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
      | ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ),
    inference(lifteq,[status(thm)],[1356]) ).

thf(1362,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
      | ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ),
    inference(simp,[status(thm)],[1361]) ).

thf(1,conjecture,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_da____ @ v_mazh,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).

thf(2,negated_conjecture,
    ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_da____ @ v_mazh ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(1263,plain,
    ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_da____ @ v_mazh ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(10147,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
      | ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ v_mazh )
      | ( B != v_da____ ) ),
    inference(paramod_ordered,[status(thm)],[1362,1263]) ).

thf(10148,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ A )
      | ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ v_da____ )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ v_mazh ) ),
    inference(pattern_uni,[status(thm)],[10147:[bind(A,$thf( A )),bind(B,$thf( v_da____ ))]]) ).

thf(15054,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ B )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ v_mazh )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ v_da____ ) ) ),
    inference(paramod_ordered,[status(thm)],[1527,10148]) ).

thf(15055,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
    | ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ v_mazh ) ),
    inference(pattern_uni,[status(thm)],[15054:[bind(A,$thf( v_da____ )),bind(B,$thf( c_Groups_Oone__class_Oone @ tc_Nat_Onat ))]]) ).

thf(630,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(3449,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)],[630]) ).

thf(1057,axiom,
    class_Rings_Osemiring @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).

thf(4682,plain,
    class_Rings_Osemiring @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).

thf(1131,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(4904,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).

thf(247,axiom,
    ! [A: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ A )
     => ? [B: $i] :
        ! [C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ A @ C ) ) @ ( c_RealVector_Onorm__class_Onorm @ A @ D ) ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Obounded) ).

thf(2163,plain,
    ! [A: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ A )
     => ? [B: $i] :
        ! [C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ A @ C ) ) @ ( c_RealVector_Onorm__class_Onorm @ A @ D ) ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(252,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(2177,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)],[252]) ).

thf(2178,plain,
    ( ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
    = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
    inference(lifteq,[status(thm)],[2177]) ).

thf(204,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(2017,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)],[204]) ).

thf(2018,plain,
    ( ! [A: $i,B: $i] :
        ( ( ( c_Nat_OSuc @ B )
          = ( c_Nat_OSuc @ A ) )
       => ( B = A ) )
    & ! [A: $i,B: $i] :
        ( ( B = A )
       => ( ( c_Nat_OSuc @ B )
          = ( c_Nat_OSuc @ A ) ) ) ),
    inference(miniscope,[status(thm)],[2017]) ).

thf(2020,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Nat_OSuc @ B )
       != ( c_Nat_OSuc @ A ) )
      | ( B = A ) ),
    inference(cnf,[status(esa)],[2018]) ).

thf(2023,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Nat_OSuc @ B )
       != ( c_Nat_OSuc @ A ) )
      | ( B = A ) ),
    inference(lifteq,[status(thm)],[2020]) ).

thf(2024,plain,
    ! [A: $i] :
      ( ( sk8 @ ( c_Nat_OSuc @ A ) )
      = A ),
    introduced(tautology,[new_symbols(inverse(c_Nat_OSuc),[sk8])]) ).

thf(16465,plain,
    ! [A: $i] :
      ( ( ( sk8 @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
        = A )
      | ( ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       != ( c_Nat_OSuc @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2178,2024]) ).

thf(16466,plain,
    ( ( sk8 @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
    = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(pattern_uni,[status(thm)],[16465:[bind(A,$thf( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ))]]) ).

thf(83,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(1542,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)],[83]) ).

thf(1543,plain,
    ! [B: $i,A: $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(cnf,[status(esa)],[1542]) ).

thf(608,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(3377,plain,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(3378,plain,
    ~ ? [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
    inference(miniscope,[status(thm)],[3377]) ).

thf(3379,plain,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
    inference(cnf,[status(esa)],[3378]) ).

thf(81403,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
      | ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
       != ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[1543,3379]) ).

thf(81404,plain,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ A ),
    inference(pattern_uni,[status(thm)],[81403:[bind(A,$thf( D )),bind(B,$thf( c_Nat_OSuc @ D )),bind(C,$thf( c_Nat_OSuc @ D ))]]) ).

thf(81500,plain,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ A ),
    inference(simp,[status(thm)],[81404]) ).

thf(81550,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
      | ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) )
       != ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ C ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[1543,81500]) ).

thf(81551,plain,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) @ A ),
    inference(pattern_uni,[status(thm)],[81550:[bind(A,$thf( E )),bind(B,$thf( c_Nat_OSuc @ ( c_Nat_OSuc @ E ) )),bind(C,$thf( c_Nat_OSuc @ E ))]]) ).

thf(81608,plain,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) @ A ),
    inference(simp,[status(thm)],[81551]) ).

thf(261,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ A ) @ B ) )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__pow__int) ).

thf(2199,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ A ) @ B ) )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(19,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__ring__1 @ C )
     => ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ ( c_Polynomial_Osynthetic__div @ C @ A @ B ) ) @ ( c_Polynomial_OpCons @ C @ ( hAPP @ ( c_Polynomial_Opoly @ C @ A ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__correct_H) ).

thf(1322,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__ring__1 @ C )
     => ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ ( c_Polynomial_Osynthetic__div @ C @ A @ B ) ) @ ( c_Polynomial_OpCons @ C @ ( hAPP @ ( c_Polynomial_Opoly @ C @ A ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(1063,axiom,
    class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).

thf(4691,plain,
    class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).

thf(63,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( c_Rings_Odvd__class_Odvd @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__dvd) ).

thf(1490,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( c_Rings_Odvd__class_Odvd @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(1491,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Rings_Ocomm__semiring__1 @ B )
      | ( c_Rings_Odvd__class_Odvd @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A ) ),
    inference(cnf,[status(esa)],[1490]) ).

thf(54351,plain,
    ! [B: $i,A: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
      | ( ( class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex )
       != ( class_Rings_Ocomm__semiring__1 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[4691,1491]) ).

thf(54352,plain,
    ! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_Complex_Ocomplex @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) @ A ),
    inference(pattern_uni,[status(thm)],[54351:[bind(A,$thf( A )),bind(B,$thf( tc_Complex_Ocomplex ))]]) ).

thf(532,axiom,
    ! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Otop__greatest) ).

thf(3169,plain,
    ! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(3170,plain,
    ! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(cnf,[status(esa)],[3169]) ).

thf(1132,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(4905,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)],[1132]) ).

thf(4906,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(cnf,[status(esa)],[4905]) ).

thf(4907,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(lifteq,[status(thm)],[4906]) ).

thf(1119,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(4864,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)],[1119]) ).

thf(4865,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 ) ) )
    & ! [A: $i,B: $i] :
        ( ( ( 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(miniscope,[status(thm)],[4864]) ).

thf(4867,plain,
    ! [B: $i,A: $i] :
      ( ( 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(cnf,[status(esa)],[4865]) ).

thf(4870,plain,
    ! [B: $i,A: $i] :
      ( ( 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(lifteq,[status(thm)],[4867]) ).

thf(4871,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
    inference(simp,[status(thm)],[4870]) ).

thf(46646,plain,
    ! [B: $i,A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
      | ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) @ A )
       != ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4907,4871]) ).

thf(46647,plain,
    c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ),
    inference(pattern_uni,[status(thm)],[46646:[bind(A,$thf( c_Groups_Oone__class_Oone @ tc_Int_Oint )),bind(B,$thf( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ))]]) ).

thf(559,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(3254,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)],[559]) ).

thf(3255,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(miniscope,[status(thm)],[3254]) ).

thf(3256,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
      | ( A
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(cnf,[status(esa)],[3255]) ).

thf(3257,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      | ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
    inference(lifteq,[status(thm)],[3256]) ).

thf(3258,plain,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[3257]) ).

thf(46899,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
     != ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[46647,3258]) ).

thf(46960,plain,
    ! [A: $i] :
      ( ( tc_Int_Oint != tc_Nat_Onat )
      | ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
       != A )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(simp,[status(thm)],[46899]) ).

thf(46989,plain,
    ( ( tc_Int_Oint != tc_Nat_Onat )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(simp,[status(thm)],[46960]) ).

thf(46999,plain,
    ( ( tc_Int_Oint != tc_Nat_Onat )
    | ( tc_Int_Oint != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[46989]) ).

thf(47044,plain,
    tc_Int_Oint != tc_Nat_Onat,
    inference(simp,[status(thm)],[46999]) ).

thf(47056,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
      | ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
      | ( B != tc_Nat_Onat )
      | ( A != tc_Int_Oint ) ),
    inference(paramod_ordered,[status(thm)],[1362,47044]) ).

thf(47057,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ tc_Int_Oint )
      | ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Int_Oint @ A )
      | ( A != tc_Nat_Onat ) ),
    inference(pattern_uni,[status(thm)],[47056:[bind(A,$thf( tc_Int_Oint ))]]) ).

thf(47061,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Int_Oint )
    | ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Int_Oint @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[47057]) ).

thf(54207,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Int_Oint )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Int_Oint @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[3170,47061]) ).

thf(54234,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Int_Oint )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( A != tc_Int_Oint )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[54207]) ).

thf(54260,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Int_Oint )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[54234]) ).

thf(56026,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != tc_Nat_Onat )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Complex_Ocomplex @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Int_Oint ) ) ),
    inference(paramod_ordered,[status(thm)],[54352,54260]) ).

thf(56062,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != tc_Nat_Onat )
      | ( tc_Nat_Onat != tc_Complex_Ocomplex )
      | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
       != tc_Nat_Onat )
      | ( A != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[56026]) ).

thf(56093,plain,
    ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != tc_Nat_Onat )
    | ( tc_Nat_Onat != tc_Complex_Ocomplex )
    | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[56062]) ).

thf(376,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(2630,plain,
    ! [A: $i] :
      ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != ( c_Nat_OSuc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(399,axiom,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).

thf(2726,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(2727,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
      = A ),
    inference(cnf,[status(esa)],[2726]) ).

thf(2728,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
      = A ),
    inference(lifteq,[status(thm)],[2727]) ).

thf(304,axiom,
    ! [A: $i,B: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
    <=> ( ( B
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
        | ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__is__0) ).

thf(2350,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( ( B
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
          | ( A
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
      & ( ( ( B
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
          | ( A
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
       => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(2351,plain,
    ( ! [A: $i,B: $i] :
        ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( ( B
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
          | ( A
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
    & ! [A: $i,B: $i] :
        ( ( ( B
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
          | ( A
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
       => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    inference(miniscope,[status(thm)],[2350]) ).

thf(2353,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(cnf,[status(esa)],[2351]) ).

thf(2357,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(lifteq,[status(thm)],[2353]) ).

thf(2358,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[2357]) ).

thf(51,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
    <=> ( ( 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 ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).

thf(1442,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
       => ( ( 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 ) @ B ) ) )
      & ( ( ( 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 ) @ B ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(1443,plain,
    ( ! [A: $i,B: $i] :
        ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
       => ( ( 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 ) @ B ) ) )
    & ! [A: $i,B: $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 ) @ B ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
    inference(miniscope,[status(thm)],[1442]) ).

thf(1444,plain,
    ! [B: $i,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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ),
    inference(cnf,[status(esa)],[1443]) ).

thf(1447,plain,
    ! [B: $i,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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ),
    inference(lifteq,[status(thm)],[1444]) ).

thf(1448,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(simp,[status(thm)],[1447]) ).

thf(28535,plain,
    ! [B: $i,A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
     != ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[1448,3258]) ).

thf(28601,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != B )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(simp,[status(thm)],[28535]) ).

thf(28636,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[28601]) ).

thf(36989,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
     != ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[2358,28636]) ).

thf(37021,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A )
       != ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(simp,[status(thm)],[36989]) ).

thf(37077,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A )
     != ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) ),
    inference(simp,[status(thm)],[37021]) ).

thf(47852,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
       != ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2728,37077]) ).

thf(47893,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
       != ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) )
      | ( ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B )
       != A ) ),
    inference(simp,[status(thm)],[47852]) ).

thf(47949,plain,
    ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
   != ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[47893]) ).

thf(94,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(1584,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)],[94]) ).

thf(1585,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(cnf,[status(esa)],[1584]) ).

thf(1586,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A )
      = ( c_Nat_OSuc @ A ) ),
    inference(lifteq,[status(thm)],[1585]) ).

thf(889,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(4198,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)],[889]) ).

thf(4199,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(miniscope,[status(thm)],[4198]) ).

thf(4200,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(cnf,[status(esa)],[4199]) ).

thf(4201,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(lifteq,[status(thm)],[4200]) ).

thf(330,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) )
        = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    <=> ( ( B
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
        & ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__two__squares__add__zero__iff) ).

thf(2452,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) )
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ( ( B
            = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
          & ( A
            = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) )
      & ( ( ( B
            = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
          & ( A
            = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
       => ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) )
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(169,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oantisym) ).

thf(1879,plain,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(23,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) @ B )
      <=> ( A
          = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel2) ).

thf(1334,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
     => ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) @ B )
         => ( A
            = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
        & ( ( A
            = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
         => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(1335,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
      | ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) @ B )
      | ( A
        = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
    inference(cnf,[status(esa)],[1334]) ).

thf(1337,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      | ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
      | ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) @ B ) ),
    inference(lifteq,[status(thm)],[1335]) ).

thf(859,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(4115,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)],[859]) ).

thf(4116,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 ) )
    & ! [A: $i] :
        ( ( 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(miniscope,[status(thm)],[4115]) ).

thf(4118,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(cnf,[status(esa)],[4116]) ).

thf(4121,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(lifteq,[status(thm)],[4118]) ).

thf(1161,axiom,
    class_Rings_Olinordered__idom @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).

thf(4968,plain,
    class_Rings_Olinordered__idom @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).

thf(79,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(1533,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Orderings_Olinorder @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(1534,plain,
    ! [A: $i] :
      ( ~ ( class_Rings_Olinordered__idom @ A )
      | ( class_Orderings_Olinorder @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(cnf,[status(esa)],[1533]) ).

thf(76384,plain,
    ! [A: $i] :
      ( ( class_Orderings_Olinorder @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Olinordered__idom @ tc_RealDef_Oreal )
       != ( class_Rings_Olinordered__idom @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4968,1534]) ).

thf(76385,plain,
    class_Orderings_Olinorder @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ),
    inference(pattern_uni,[status(thm)],[76384:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(76448,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( class_Orderings_Olinorder @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      | ( A
       != ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ),
    inference(paramod_ordered,[status(thm)],[4121,76385]) ).

thf(76449,plain,
    ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) )
    | ( class_Orderings_Olinorder @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(pattern_uni,[status(thm)],[76448:[bind(A,$thf( tc_Polynomial_Opoly @ tc_RealDef_Oreal ))]]) ).

thf(126,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(1718,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ouminus @ B )
     => ( class_Groups_Ouminus @ ( tc_fun @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(227,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ A )
        = ( hAPP @ ( hAPP @ ( 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(2094,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ A )
        = ( hAPP @ ( hAPP @ ( 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)],[227]) ).

thf(40,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono) ).

thf(1410,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(1411,plain,
    ! [D: $i,C: $i,B: $i,A: $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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ),
    inference(cnf,[status(esa)],[1410]) ).

thf(853,axiom,
    class_Groups_Ogroup__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).

thf(4094,plain,
    class_Groups_Ogroup__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).

thf(56,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(1463,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)],[56]) ).

thf(1465,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Groups_Osgn__if @ 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_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ),
    inference(cnf,[status(esa)],[1463]) ).

thf(1469,plain,
    ! [B: $i,A: $i] :
      ( ( 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 ) ) )
      | ~ ( class_Groups_Osgn__if @ B )
      | ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ),
    inference(lifteq,[status(thm)],[1465]) ).

thf(405,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__antisym) ).

thf(2744,plain,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(446,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 @ ( hAPP @ ( hAPP @ ( 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(2889,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(291,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(2306,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)],[291]) ).

thf(600,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ 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 @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__imp__le) ).

thf(3345,plain,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ 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 @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(233,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oidom @ C )
     => ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ B @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) @ A )
      <=> ( ( hAPP @ ( c_Polynomial_Opoly @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) )
          = ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__iff__poly__eq__0) ).

thf(2109,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oidom @ C )
     => ( ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ B @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) @ A )
         => ( ( hAPP @ ( c_Polynomial_Opoly @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) )
            = ( c_Groups_Ozero__class_Ozero @ C ) ) )
        & ( ( ( hAPP @ ( c_Polynomial_Opoly @ C @ A ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) )
            = ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ B @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(207,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ E @ D )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ E @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) )
      <=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ E @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__period) ).

thf(2031,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ E @ D )
     => ( ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ E @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) )
         => ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ E @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) @ B ) ) )
        & ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ E @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ D ) ) @ B ) )
         => ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ E @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(1196,axiom,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_mzh @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ v_mazh @ v_ma ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(5032,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_mzh @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ v_mazh @ v_ma ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).

thf(438,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(2861,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)],[438]) ).

thf(2862,plain,
    ~ ? [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ A ),
    inference(miniscope,[status(thm)],[2861]) ).

thf(2863,plain,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ A ),
    inference(cnf,[status(esa)],[2862]) ).

thf(14751,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_mzh @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ v_mazh @ v_ma ) )
     != ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ A ) ),
    inference(paramod_ordered,[status(thm)],[5032,2863]) ).

thf(14772,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( ( c_Nat_OSuc @ A )
       != v_mzh )
      | ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ v_mazh @ v_ma )
       != A ) ),
    inference(simp,[status(thm)],[14751]) ).

thf(14801,plain,
    ( ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ v_mazh @ v_ma ) )
     != v_mzh ) ),
    inference(simp,[status(thm)],[14772]) ).

thf(700,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(3661,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)],[700]) ).

thf(781,axiom,
    class_Groups_Oab__group__add @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).

thf(3912,plain,
    class_Groups_Oab__group__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).

thf(42,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(1416,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)],[42]) ).

thf(1417,plain,
    ! [A: $i] :
      ( ~ ( class_Groups_Oab__group__add @ A )
      | ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(cnf,[status(esa)],[1416]) ).

thf(21006,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ tc_Int_Oint )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3912,1417]) ).

thf(21007,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ tc_Int_Oint ),
    inference(pattern_uni,[status(thm)],[21006:[bind(A,$thf( tc_Int_Oint ))]]) ).

thf(21054,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[21007,1417]) ).

thf(21055,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ),
    inference(pattern_uni,[status(thm)],[21054:[bind(A,$thf( tc_Polynomial_Opoly @ tc_Int_Oint ))]]) ).

thf(21141,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[21055,1417]) ).

thf(21142,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ),
    inference(pattern_uni,[status(thm)],[21141:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ))]]) ).

thf(21397,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[21142,1417]) ).

thf(21398,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ),
    inference(pattern_uni,[status(thm)],[21397:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ))]]) ).

thf(21691,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[21398,1417]) ).

thf(21692,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[21691:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ))]]) ).

thf(22100,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[21692,1417]) ).

thf(22101,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[22100:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ))]]) ).

thf(22656,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[22101,1417]) ).

thf(22657,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[22656:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ))]]) ).

thf(22923,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[22657,1417]) ).

thf(22924,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[22923:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ))]]) ).

thf(23727,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[22924,1417]) ).

thf(23728,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[23727:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ) ))]]) ).

thf(24157,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[23728,1417]) ).

thf(24158,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[24157:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ) ) ))]]) ).

thf(28374,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[24158,1417]) ).

thf(28375,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[28374:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ) ) ) ))]]) ).

thf(37627,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ) ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[28375,1417]) ).

thf(37628,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[37627:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(45272,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[37628,1417]) ).

thf(45273,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[45272:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(616,axiom,
    class_Rings_Ocomm__semiring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).

thf(3399,plain,
    class_Rings_Ocomm__semiring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(792,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(3930,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)],[792]) ).

thf(744,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(3798,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ A )
     => ( class_Groups_Ouminus @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).

thf(87,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ C )
     => ( ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( 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(1552,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ C )
     => ( ( ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) )
            = ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(1555,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Olinordered__ring__strict @ C )
      | ( B
       != ( c_Groups_Ozero__class_Ozero @ C ) )
      | ( A
       != ( c_Groups_Ozero__class_Ozero @ C ) )
      | ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) )
        = ( c_Groups_Ozero__class_Ozero @ C ) ) ),
    inference(cnf,[status(esa)],[1552]) ).

thf(1558,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
       != ( c_Groups_Ozero__class_Ozero @ C ) )
      | ( A
       != ( c_Groups_Ozero__class_Ozero @ C ) )
      | ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) )
        = ( c_Groups_Ozero__class_Ozero @ C ) )
      | ~ ( class_Rings_Olinordered__ring__strict @ C ) ),
    inference(lifteq,[status(thm)],[1555]) ).

thf(1559,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ A ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ A ) ) )
        = ( c_Groups_Ozero__class_Ozero @ A ) )
      | ~ ( class_Rings_Olinordered__ring__strict @ A ) ),
    inference(simp,[status(thm)],[1558]) ).

thf(702,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(3666,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)],[702]) ).

thf(848,axiom,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_c____ ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__0960_A_060_Acmod_Ac_096) ).

thf(4081,plain,
    c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_c____ ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).

thf(1217,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(5070,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)],[1217]) ).

thf(5071,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 ) ) )
    & ! [A: $i,B: $i] :
        ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
          & ( B != A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ) ),
    inference(miniscope,[status(thm)],[5070]) ).

thf(5074,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
      | ( B != A ) ),
    inference(cnf,[status(esa)],[5071]) ).

thf(5077,plain,
    ! [B: $i,A: $i] :
      ( ( B != A )
      | ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ),
    inference(lifteq,[status(thm)],[5074]) ).

thf(5078,plain,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ A ),
    inference(simp,[status(thm)],[5077]) ).

thf(14528,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 @ v_c____ ) )
     != ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ A @ A ) ),
    inference(paramod_ordered,[status(thm)],[4081,5078]) ).

thf(14556,plain,
    ! [A: $i] :
      ( ( tc_RealDef_Oreal != tc_RealDef_Oreal )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal )
       != A )
      | ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_c____ )
       != A ) ),
    inference(simp,[status(thm)],[14528]) ).

thf(14574,plain,
    ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_c____ )
   != ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[14556]) ).

thf(130,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(1729,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)],[130]) ).

thf(639,axiom,
    class_Rings_Olinordered__semiring__1 @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).

thf(3477,plain,
    class_Rings_Olinordered__semiring__1 @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(711,axiom,
    ! [A: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ A )
     => ? [B: $i] :
          ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
          & ! [C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ A @ C ) ) @ ( c_RealVector_Onorm__class_Onorm @ A @ D ) ) ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Opos__bounded) ).

thf(3698,plain,
    ! [A: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ A )
     => ? [B: $i] :
          ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
          & ! [C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ A @ C ) ) @ ( c_RealVector_Onorm__class_Onorm @ A @ D ) ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).

thf(615,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(3397,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)],[615]) ).

thf(8,axiom,
    ( v_cs____
    = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cs0_H) ).

thf(1279,plain,
    ( v_cs____
    = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(1280,plain,
    ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
    = v_cs____ ),
    inference(lifteq,[status(thm)],[1279]) ).

thf(1166,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(4973,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)],[1166]) ).

thf(4974,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 ) ) )
    & ! [A: $i,B: $i] :
        ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
          | ( B = A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ) ),
    inference(miniscope,[status(thm)],[4973]) ).

thf(4976,plain,
    ! [B: $i,A: $i] :
      ( ( B != A )
      | ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ),
    inference(cnf,[status(esa)],[4974]) ).

thf(4979,plain,
    ! [B: $i,A: $i] :
      ( ( B != A )
      | ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ),
    inference(lifteq,[status(thm)],[4976]) ).

thf(4980,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ A ),
    inference(simp,[status(thm)],[4979]) ).

thf(17348,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ B )
      | ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ v_da____ )
      | ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ A )
       != ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ v_mazh ) ) ),
    inference(paramod_ordered,[status(thm)],[4980,10148]) ).

thf(17349,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh )
    | ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ v_da____ ) ),
    inference(pattern_uni,[status(thm)],[17348:[bind(A,$thf( v_mazh )),bind(B,$thf( v_mazh ))]]) ).

thf(17598,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ v_da____ )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh ) ) ),
    inference(paramod_ordered,[status(thm)],[3170,17349]) ).

thf(17626,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ v_da____ )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( A != v_da____ )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_mazh ) ),
    inference(simp,[status(thm)],[17598]) ).

thf(17640,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ v_da____ )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_mazh ) ),
    inference(simp,[status(thm)],[17626]) ).

thf(20964,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ v_da____ )
    | ( v_cs____ != v_mazh )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,17640]) ).

thf(20973,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ v_da____ )
    | ( v_cs____ != v_mazh )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[20964]) ).

thf(767,axiom,
    class_Groups_Ominus @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).

thf(3863,plain,
    class_Groups_Ominus @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).

thf(756,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(3830,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)],[756]) ).

thf(421,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
         => ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).

thf(2787,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
         => ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(365,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) )
      <=> ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__iff1) ).

thf(2595,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
     => ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) )
         => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A ) )
        & ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(1192,axiom,
    class_Rings_Olinordered__semiring__1 @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).

thf(5028,plain,
    class_Rings_Olinordered__semiring__1 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).

thf(1078,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(4728,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)],[1078]) ).

thf(154,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(1818,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)],[154]) ).

thf(12,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ozero @ C )
     => ( ( ( c_Polynomial_OpCons @ C @ B @ A )
          = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
      <=> ( ( B
            = ( c_Groups_Ozero__class_Ozero @ C ) )
          & ( A
            = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).

thf(1295,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Ozero @ C )
     => ( ( ( ( c_Polynomial_OpCons @ C @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
         => ( ( B
              = ( c_Groups_Ozero__class_Ozero @ C ) )
            & ( A
              = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) )
        & ( ( ( B
              = ( c_Groups_Ozero__class_Ozero @ C ) )
            & ( A
              = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) )
         => ( ( c_Polynomial_OpCons @ C @ B @ A )
            = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(188,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__ring__1 @ C )
     => ( ( c_Rings_Odvd__class_Odvd @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
      <=> ( c_Rings_Odvd__class_Odvd @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__minus__iff) ).

thf(1956,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__ring__1 @ C )
     => ( ( ( c_Rings_Odvd__class_Odvd @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
         => ( c_Rings_Odvd__class_Odvd @ C @ B @ A ) )
        & ( ( c_Rings_Odvd__class_Odvd @ C @ B @ A )
         => ( c_Rings_Odvd__class_Odvd @ C @ B @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(1174,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(4992,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)],[1174]) ).

thf(116,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( ( c_Groups_Oabs__class_Oabs @ C @ B )
          = ( c_Groups_Oabs__class_Oabs @ C @ A ) )
       => ( c_Rings_Odvd__class_Odvd @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__if__abs__eq) ).

thf(1686,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( ( c_Groups_Oabs__class_Oabs @ C @ B )
          = ( c_Groups_Oabs__class_Oabs @ C @ A ) )
       => ( c_Rings_Odvd__class_Odvd @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(877,axiom,
    class_Rings_Ozero__neq__one @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).

thf(4166,plain,
    class_Rings_Ozero__neq__one @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).

thf(274,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__ring__1 @ C )
     => ( ( c_Rings_Odvd__class_Odvd @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
      <=> ( c_Rings_Odvd__class_Odvd @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__dvd__iff) ).

thf(2250,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__ring__1 @ C )
     => ( ( ( c_Rings_Odvd__class_Odvd @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A )
         => ( c_Rings_Odvd__class_Odvd @ C @ B @ A ) )
        & ( ( c_Rings_Odvd__class_Odvd @ C @ B @ A )
         => ( c_Rings_Odvd__class_Odvd @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(137,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Fields_Ofield @ E )
     => ( ( D
         != ( c_Groups_Ozero__class_Ozero @ E ) )
       => ( ( C
           != ( c_Groups_Ozero__class_Ozero @ E ) )
         => ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ D ) @ ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) )
            = ( c_Rings_Oinverse__class_Odivide @ E @ ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__eq) ).

thf(1750,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Fields_Ofield @ E )
     => ( ( D
         != ( c_Groups_Ozero__class_Ozero @ E ) )
       => ( ( C
           != ( c_Groups_Ozero__class_Ozero @ E ) )
         => ( ( c_Groups_Oplus__class_Oplus @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ D ) @ ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) )
            = ( c_Rings_Oinverse__class_Odivide @ E @ ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(266,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Olinordered__semiring__1__strict @ F )
     => ( ( c_Orderings_Oord__class_Oless @ F @ E @ D )
       => ( ( c_Orderings_Oord__class_Oless @ F @ C @ D )
         => ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ B )
           => ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ A )
             => ( ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
                  = ( c_Groups_Oone__class_Oone @ F ) )
               => ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ C ) ) @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__lt) ).

thf(2210,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Olinordered__semiring__1__strict @ F )
     => ( ( c_Orderings_Oord__class_Oless @ F @ E @ D )
       => ( ( c_Orderings_Oord__class_Oless @ F @ C @ D )
         => ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ B )
           => ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ A )
             => ( ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
                  = ( c_Groups_Oone__class_Oone @ F ) )
               => ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ C ) ) @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(373,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
      = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).

thf(2622,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
      = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(1156,axiom,
    class_Groups_Ocomm__monoid__mult @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).

thf(4960,plain,
    class_Groups_Ocomm__monoid__mult @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).

thf(1070,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(4711,plain,
    class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).

thf(610,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(3382,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)],[610]) ).

thf(306,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
        & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
     => ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__eq2) ).

thf(2363,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
        & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(162,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(1855,plain,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ A )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(655,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(3534,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)],[655]) ).

thf(705,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(3681,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)],[705]) ).

thf(773,axiom,
    class_Groups_Oab__group__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).

thf(3881,plain,
    class_Groups_Oab__group__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).

thf(21018,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ tc_Complex_Ocomplex )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3881,1417]) ).

thf(21019,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ),
    inference(pattern_uni,[status(thm)],[21018:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(21106,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[21019,1417]) ).

thf(21107,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ),
    inference(pattern_uni,[status(thm)],[21106:[bind(A,$thf( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ))]]) ).

thf(21350,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[21107,1417]) ).

thf(21351,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
    inference(pattern_uni,[status(thm)],[21350:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ))]]) ).

thf(21497,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[21351,1417]) ).

thf(21498,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ),
    inference(pattern_uni,[status(thm)],[21497:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ))]]) ).

thf(22029,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[21498,1417]) ).

thf(22030,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[22029:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ))]]) ).

thf(22391,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[22030,1417]) ).

thf(22392,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[22391:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ))]]) ).

thf(22828,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[22392,1417]) ).

thf(22829,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[22828:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ))]]) ).

thf(23620,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[22829,1417]) ).

thf(23621,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[23620:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) ))]]) ).

thf(23947,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[23621,1417]) ).

thf(23948,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[23947:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) ) ))]]) ).

thf(25736,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[23948,1417]) ).

thf(25737,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[25736:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) ) ) ))]]) ).

thf(473,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(2976,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)],[473]) ).

thf(954,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(4376,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)],[954]) ).

thf(235,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(2117,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)],[235]) ).

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

thf(5141,plain,
    class_Orderings_Opreorder @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).

thf(38,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__sgn__abs) ).

thf(1404,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(1405,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Rings_Olinordered__idom @ B )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
        = A ) ),
    inference(cnf,[status(esa)],[1404]) ).

thf(1406,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
        = A )
      | ~ ( class_Rings_Olinordered__idom @ B ) ),
    inference(lifteq,[status(thm)],[1405]) ).

thf(587,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(3317,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)],[587]) ).

thf(900,axiom,
    class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

thf(4226,plain,
    class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).

thf(1137,axiom,
    class_Rings_Ocomm__ring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).

thf(4920,plain,
    class_Rings_Ocomm__ring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).

thf(90,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(1574,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ A )
     => ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(1575,plain,
    ! [A: $i] :
      ( ~ ( class_Rings_Ocomm__ring @ A )
      | ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(cnf,[status(esa)],[1574]) ).

thf(87098,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__ring @ tc_Complex_Ocomplex )
       != ( class_Rings_Ocomm__ring @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4920,1575]) ).

thf(87099,plain,
    class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ),
    inference(pattern_uni,[status(thm)],[87098:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(87184,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
       != ( class_Rings_Ocomm__ring @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[87099,1575]) ).

thf(87185,plain,
    class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ),
    inference(pattern_uni,[status(thm)],[87184:[bind(A,$thf( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ))]]) ).

thf(940,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ 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_dvd__pos__nat) ).

thf(4339,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ 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)],[940]) ).

thf(845,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(4075,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)],[845]) ).

thf(170,axiom,
    ! [A: $i,B: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A )
        = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
    <=> ( ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
        | ( B
          = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).

thf(1882,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A )
          = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
       => ( ( A
            = ( 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_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
       => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A )
          = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(74,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(1520,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)],[74]) ).

thf(1521,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Rings_Odivision__ring @ B )
      | ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
        = A ) ),
    inference(cnf,[status(esa)],[1520]) ).

thf(1522,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
        = A )
      | ~ ( class_Rings_Odivision__ring @ B ) ),
    inference(lifteq,[status(thm)],[1521]) ).

thf(733,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(3762,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)],[733]) ).

thf(550,axiom,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ v_da____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_aa____ ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ v_z____ ) @ v_c____ ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th0) ).

thf(3230,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ v_da____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_aa____ ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ v_z____ ) @ v_c____ ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(825,axiom,
    class_Groups_Ozero @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).

thf(4028,plain,
    class_Groups_Ozero @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( class_Groups_Ozero @ A )
     => ( ( c_Polynomial_OpCons @ A @ ( c_Groups_Ozero__class_Ozero @ 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_pCons__0__0) ).

thf(1270,plain,
    ! [A: $i] :
      ( ( class_Groups_Ozero @ A )
     => ( ( c_Polynomial_OpCons @ A @ ( c_Groups_Ozero__class_Ozero @ 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)],[5]) ).

thf(1271,plain,
    ! [A: $i] :
      ( ~ ( class_Groups_Ozero @ A )
      | ( ( c_Polynomial_OpCons @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ),
    inference(cnf,[status(esa)],[1270]) ).

thf(1272,plain,
    ! [A: $i] :
      ( ( ( c_Polynomial_OpCons @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
      | ~ ( class_Groups_Ozero @ A ) ),
    inference(lifteq,[status(thm)],[1271]) ).

thf(5291,plain,
    ! [A: $i] :
      ( ( ( c_Polynomial_OpCons @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
      | ( ( class_Groups_Ozero @ tc_Int_Oint )
       != ( class_Groups_Ozero @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4028,1272]) ).

thf(5292,plain,
    ( ( c_Polynomial_OpCons @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) )
    = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ),
    inference(pattern_uni,[status(thm)],[5291:[bind(A,$thf( tc_Int_Oint ))]]) ).

thf(1216,axiom,
    class_Rings_Ocomm__ring__1 @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).

thf(5069,plain,
    class_Rings_Ocomm__ring__1 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).

thf(316,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Odivision__ring @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( B
            = ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
        <=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C )
            = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__eq__divide__eq) ).

thf(2395,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Odivision__ring @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( ( B
              = ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
           => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C )
              = A ) )
          & ( ( ( hAPP @ ( hAPP @ ( 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)],[316]) ).

thf(659,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(3549,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)],[659]) ).

thf(1178,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(5000,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)],[1178]) ).

thf(150,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( hAPP @ ( hAPP @ ( 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(1808,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( hAPP @ ( hAPP @ ( 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)],[150]) ).

thf(619,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(3412,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)],[619]) ).

thf(3413,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 ) ) )
    & ! [A: $i] :
        ( ? [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(miniscope,[status(thm)],[3412]) ).

thf(3414,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( c_Nat_OSuc @ B ) )
      | ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ),
    inference(cnf,[status(esa)],[3413]) ).

thf(3416,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( c_Nat_OSuc @ B ) )
      | ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ),
    inference(lifteq,[status(thm)],[3414]) ).

thf(3417,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ A ) ),
    inference(simp,[status(thm)],[3416]) ).

thf(1098,axiom,
    class_Rings_Ocomm__ring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).

thf(4787,plain,
    class_Rings_Ocomm__ring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).

thf(87108,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__ring @ tc_Int_Oint )
       != ( class_Rings_Ocomm__ring @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4787,1575]) ).

thf(87109,plain,
    class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ tc_Int_Oint ),
    inference(pattern_uni,[status(thm)],[87108:[bind(A,$thf( tc_Int_Oint ))]]) ).

thf(87223,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) )
       != ( class_Rings_Ocomm__ring @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[87109,1575]) ).

thf(87224,plain,
    class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ),
    inference(pattern_uni,[status(thm)],[87223:[bind(A,$thf( tc_Polynomial_Opoly @ tc_Int_Oint ))]]) ).

thf(88883,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) )
       != ( class_Rings_Ocomm__ring @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[87224,1575]) ).

thf(88884,plain,
    class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ),
    inference(pattern_uni,[status(thm)],[88883:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ))]]) ).

thf(574,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(3285,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)],[574]) ).

thf(957,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(4391,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)],[957]) ).

thf(528,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__power) ).

thf(3153,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(803,axiom,
    ( v_c____
   != ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_c0) ).

thf(3961,plain,
    ( v_c____
   != ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).

thf(3962,plain,
    ( v_c____
   != ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
    inference(polarity_switch,[status(thm)],[3961]) ).

thf(3963,plain,
    ( ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex )
   != v_c____ ),
    inference(lifteq,[status(thm)],[3962]) ).

thf(10077,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
      | ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
      | ( A != v_c____ )
      | ( B
       != ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
    inference(paramod_ordered,[status(thm)],[1362,3963]) ).

thf(10078,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) @ A )
      | ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
      | ( A != v_c____ ) ),
    inference(pattern_uni,[status(thm)],[10077:[bind(A,$thf( A )),bind(B,$thf( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ))]]) ).

thf(12089,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) @ v_c____ )
    | ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_c____ @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
    inference(simp,[status(thm)],[10078]) ).

thf(37,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 @ ( hAPP @ ( hAPP @ ( 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(1401,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(44,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ono__zero__divisors @ C )
     => ( ( ( hAPP @ ( hAPP @ ( 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(1422,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ono__zero__divisors @ C )
     => ( ( ( hAPP @ ( hAPP @ ( 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)],[44]) ).

thf(463,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ A ) )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ C )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__dvd__imp__le) ).

thf(2947,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ A ) )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ C )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(183,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oring__1__no__zero__divisors @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A )
         != ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__power__not__zero) ).

thf(1939,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oring__1__no__zero__divisors @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ C ) )
       => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A )
         != ( c_Groups_Ozero__class_Ozero @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(273,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).

thf(2248,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(1185,axiom,
    class_Rings_Ocomm__semiring__0 @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__0) ).

thf(5020,plain,
    class_Rings_Ocomm__semiring__0 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ B )
     => ( ( c_Polynomial_Osynthetic__div @ 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_synthetic__div__0) ).

thf(1264,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ B )
     => ( ( c_Polynomial_Osynthetic__div @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(1265,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Rings_Ocomm__semiring__0 @ B )
      | ( ( c_Polynomial_Osynthetic__div @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
    inference(cnf,[status(esa)],[1264]) ).

thf(1266,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Polynomial_Osynthetic__div @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
      | ~ ( class_Rings_Ocomm__semiring__0 @ B ) ),
    inference(lifteq,[status(thm)],[1265]) ).

thf(8117,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Polynomial_Osynthetic__div @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
      | ( ( class_Rings_Ocomm__semiring__0 @ tc_RealDef_Oreal )
       != ( class_Rings_Ocomm__semiring__0 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[5020,1266]) ).

thf(8118,plain,
    ! [A: $i] :
      ( ( c_Polynomial_Osynthetic__div @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) @ A )
      = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ),
    inference(pattern_uni,[status(thm)],[8117:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal ))]]) ).

thf(386,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Nat_OSuc @ B ) )
          = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Nat_OSuc @ B ) ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
         => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
           => ( C = A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__base) ).

thf(2671,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Nat_OSuc @ B ) )
          = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Nat_OSuc @ B ) ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
         => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
           => ( C = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(84,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
        & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
     => ( B != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__eq) ).

thf(1544,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
        & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(203,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__div__algebra @ C )
     => ( ( c_Groups_Osgn__class_Osgn @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( 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(2014,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__div__algebra @ C )
     => ( ( c_Groups_Osgn__class_Osgn @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( 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)],[203]) ).

thf(229,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(2099,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)],[229]) ).

thf(285,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
          | ( A
            = ( c_Groups_Oone__class_Oone @ C ) ) )
       => ( c_Rings_Odvd__class_Odvd @ C @ A @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power) ).

thf(2282,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
          | ( A
            = ( c_Groups_Oone__class_Oone @ C ) ) )
       => ( c_Rings_Odvd__class_Odvd @ C @ A @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(96,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(1590,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)],[96]) ).

thf(1591,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $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(cnf,[status(esa)],[1590]) ).

thf(234,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Omonoid__mult @ B )
     => ( ( hAPP @ ( hAPP @ ( 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(2114,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Omonoid__mult @ B )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(54219,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Int_Oint )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Int_Oint @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[1527,47061]) ).

thf(54245,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Int_Oint )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != tc_Int_Oint )
      | ( A != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[54219]) ).

thf(54272,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Int_Oint )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[54245]) ).

thf(59904,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != tc_Int_Oint )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Int_Oint ) ) ),
    inference(paramod_ordered,[status(thm)],[1527,54272]) ).

thf(59921,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != tc_Int_Oint )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != tc_Nat_Onat )
      | ( A != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[59904]) ).

thf(59940,plain,
    ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != tc_Int_Oint )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[59921]) ).

thf(4,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ D )
     => ( ( c_Polynomial_Osynthetic__div @ D @ ( c_Polynomial_OpCons @ D @ C @ B ) @ A )
        = ( c_Polynomial_OpCons @ D @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) @ ( c_Polynomial_Osynthetic__div @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__pCons) ).

thf(1267,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ D )
     => ( ( c_Polynomial_Osynthetic__div @ D @ ( c_Polynomial_OpCons @ D @ C @ B ) @ A )
        = ( c_Polynomial_OpCons @ D @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) @ ( c_Polynomial_Osynthetic__div @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(1268,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Ocomm__semiring__0 @ D )
      | ( ( c_Polynomial_Osynthetic__div @ D @ ( c_Polynomial_OpCons @ D @ C @ B ) @ A )
        = ( c_Polynomial_OpCons @ D @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) @ ( c_Polynomial_Osynthetic__div @ D @ B @ A ) ) ) ),
    inference(cnf,[status(esa)],[1267]) ).

thf(1269,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Polynomial_Osynthetic__div @ D @ ( c_Polynomial_OpCons @ D @ C @ B ) @ A )
        = ( c_Polynomial_OpCons @ D @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) @ ( c_Polynomial_Osynthetic__div @ D @ B @ A ) ) )
      | ~ ( class_Rings_Ocomm__semiring__0 @ D ) ),
    inference(lifteq,[status(thm)],[1268]) ).

thf(936,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(4326,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)],[936]) ).

thf(895,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(4215,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Oordered__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).

thf(312,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
        <=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).

thf(2380,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
       => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ 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 @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(436,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Odivision__ring @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( B
            = ( hAPP @ ( hAPP @ ( 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(2854,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Odivision__ring @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( B
            = ( hAPP @ ( hAPP @ ( 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)],[436]) ).

thf(118,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(1692,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)],[118]) ).

thf(61,axiom,
    ! [A: $i,B: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ B ) ) @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc) ).

thf(1484,plain,
    ! [A: $i,B: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ B ) ) @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(1485,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ B ) ) @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
    inference(cnf,[status(esa)],[1484]) ).

thf(1486,plain,
    ! [B: $i,A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
      = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ B ) ) @ A ) ),
    inference(lifteq,[status(thm)],[1485]) ).

thf(1007,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(4532,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)],[1007]) ).

thf(856,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
        <=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__divide__eq) ).

thf(4105,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) ) )
          & ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).

thf(65,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Olinordered__semiring__1 @ F )
     => ( ( c_Orderings_Oord__class_Oless__eq @ F @ E @ D )
       => ( ( c_Orderings_Oord__class_Oless__eq @ F @ C @ D )
         => ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ B )
           => ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ A )
             => ( ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
                  = ( c_Groups_Oone__class_Oone @ F ) )
               => ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ C ) ) @ D ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__le) ).

thf(1495,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Olinordered__semiring__1 @ F )
     => ( ( c_Orderings_Oord__class_Oless__eq @ F @ E @ D )
       => ( ( c_Orderings_Oord__class_Oless__eq @ F @ C @ D )
         => ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ B )
           => ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ A )
             => ( ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
                  = ( c_Groups_Oone__class_Oone @ F ) )
               => ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ C ) ) @ D ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(1496,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Olinordered__semiring__1 @ F )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ F @ E @ D )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ F @ C @ D )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ B )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ A )
      | ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
       != ( c_Groups_Oone__class_Oone @ F ) )
      | ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ C ) ) @ D ) ),
    inference(cnf,[status(esa)],[1495]) ).

thf(1497,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ F @ B @ A )
       != ( c_Groups_Oone__class_Oone @ F ) )
      | ~ ( class_Rings_Olinordered__semiring__1 @ F )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ F @ E @ D )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ F @ C @ D )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ B )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Ozero__class_Ozero @ F ) @ A )
      | ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ A ) @ C ) ) @ D ) ),
    inference(lifteq,[status(thm)],[1496]) ).

thf(851,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(4090,plain,
    ! [A: $i] :
      ( ( class_Rings_Oidom @ A )
     => ( class_Rings_Ono__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).

thf(434,axiom,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1__right) ).

thf(2849,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(2850,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
      = A ),
    inference(cnf,[status(esa)],[2849]) ).

thf(2851,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
      = A ),
    inference(lifteq,[status(thm)],[2850]) ).

thf(47843,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
       != ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[2851,37077]) ).

thf(47889,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) )
       != ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) )
      | ( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
       != B ) ),
    inference(simp,[status(thm)],[47843]) ).

thf(47945,plain,
    ! [A: $i] :
      ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) )
     != ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[47889]) ).

thf(521,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 @ ( hAPP @ ( hAPP @ ( 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(3135,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(460,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power__abs) ).

thf(2933,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(6,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oab__group__add @ C )
     => ( ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ B @ A ) )
        = ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__pCons) ).

thf(1273,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oab__group__add @ C )
     => ( ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ B @ A ) )
        = ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(1274,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Groups_Oab__group__add @ C )
      | ( ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ B @ A ) )
        = ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ A ) ) ) ),
    inference(cnf,[status(esa)],[1273]) ).

thf(1275,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ A ) )
        = ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ B @ A ) ) )
      | ~ ( class_Groups_Oab__group__add @ C ) ),
    inference(lifteq,[status(thm)],[1274]) ).

thf(918,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(4279,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)],[918]) ).

thf(1016,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(4564,plain,
    class_Groups_Ocancel__comm__monoid__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).

thf(1148,axiom,
    class_Rings_Ocomm__semiring__1 @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).

thf(4950,plain,
    class_Rings_Ocomm__semiring__1 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).

thf(69,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(1509,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)],[69]) ).

thf(1510,plain,
    ! [A: $i] :
      ( ~ ( class_Rings_Ocomm__semiring__1 @ A )
      | ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(cnf,[status(esa)],[1509]) ).

thf(63978,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ tc_RealDef_Oreal )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4950,1510]) ).

thf(63979,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ),
    inference(pattern_uni,[status(thm)],[63978:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(64100,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[63979,1510]) ).

thf(64101,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ),
    inference(pattern_uni,[status(thm)],[64100:[bind(A,$thf( tc_Polynomial_Opoly @ tc_RealDef_Oreal ))]]) ).

thf(64676,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[64101,1510]) ).

thf(64677,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ),
    inference(pattern_uni,[status(thm)],[64676:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ))]]) ).

thf(65816,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[64677,1510]) ).

thf(65817,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ),
    inference(pattern_uni,[status(thm)],[65816:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ))]]) ).

thf(55,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Rings_Ocomm__ring @ D )
        & ( class_Rings_Odvd @ D ) )
     => ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
       => ! [E: $i,F: $i] :
            ( ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ E @ A ) )
          <=> ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Ominus__class_Ominus @ D @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ F ) @ B ) ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__period_I4_J) ).

thf(1458,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Rings_Ocomm__ring @ D )
        & ( class_Rings_Odvd @ D ) )
     => ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
       => ! [E: $i,F: $i] :
            ( ( ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ E @ A ) )
             => ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Ominus__class_Ominus @ D @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ F ) @ B ) ) @ A ) ) )
            & ( ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Ominus__class_Ominus @ D @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ F ) @ B ) ) @ A ) )
             => ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ E @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(1237,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(5120,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)],[1237]) ).

thf(902,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(4234,plain,
    class_Rings_Olinordered__comm__semiring__strict @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).

thf(1201,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(5037,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)],[1201]) ).

thf(54338,plain,
    ! [B: $i,A: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
      | ( ( class_Rings_Ocomm__semiring__1 @ tc_RealDef_Oreal )
       != ( class_Rings_Ocomm__semiring__1 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[4950,1491]) ).

thf(54339,plain,
    ! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A ),
    inference(pattern_uni,[status(thm)],[54338:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal ))]]) ).

thf(59894,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != tc_Int_Oint )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Int_Oint ) ) ),
    inference(paramod_ordered,[status(thm)],[54339,54272]) ).

thf(59917,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != tc_Int_Oint )
      | ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
       != tc_Nat_Onat )
      | ( A != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[59894]) ).

thf(59936,plain,
    ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != tc_Int_Oint )
    | ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[59917]) ).

thf(625,axiom,
    class_Rings_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).

thf(3439,plain,
    class_Rings_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(1249,axiom,
    class_Groups_Oab__group__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).

thf(5142,plain,
    class_Groups_Oab__group__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).

thf(21016,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ tc_RealDef_Oreal )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5142,1417]) ).

thf(21017,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ),
    inference(pattern_uni,[status(thm)],[21016:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(21080,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[21017,1417]) ).

thf(21081,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ),
    inference(pattern_uni,[status(thm)],[21080:[bind(A,$thf( tc_Polynomial_Opoly @ tc_RealDef_Oreal ))]]) ).

thf(21180,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[21081,1417]) ).

thf(21181,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ),
    inference(pattern_uni,[status(thm)],[21180:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ))]]) ).

thf(21447,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[21181,1417]) ).

thf(21448,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ),
    inference(pattern_uni,[status(thm)],[21447:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ))]]) ).

thf(21967,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[21448,1417]) ).

thf(21968,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[21967:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ))]]) ).

thf(22174,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[21968,1417]) ).

thf(22175,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[22174:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ))]]) ).

thf(22742,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[22175,1417]) ).

thf(22743,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[22742:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ))]]) ).

thf(23073,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[22743,1417]) ).

thf(23074,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[23073:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ))]]) ).

thf(23837,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[23074,1417]) ).

thf(23838,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[23837:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ) ))]]) ).

thf(24860,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[23838,1417]) ).

thf(24861,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[24860:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ) ) ))]]) ).

thf(967,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(4418,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)],[967]) ).

thf(15,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oidom @ C )
     => ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ ( c_Polynomial_Oorder @ C @ B @ A ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__1) ).

thf(1309,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oidom @ C )
     => ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ ( c_Polynomial_Oorder @ C @ B @ A ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(1310,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Oidom @ C )
      | ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ ( c_Polynomial_Oorder @ C @ B @ A ) ) @ A ) ),
    inference(cnf,[status(esa)],[1309]) ).

thf(139,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
          = ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) ) )
      <=> ( ( D = B )
          | ( C = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__eq) ).

thf(1756,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
            = ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) ) )
         => ( ( D = B )
            | ( C = A ) ) )
        & ( ( ( D = B )
            | ( C = A ) )
         => ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
            = ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(1021,axiom,
    c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).

thf(4575,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).

thf(1110,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(4839,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)],[1110]) ).

thf(593,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(3332,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)],[593]) ).

thf(1046,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(4647,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)],[1046]) ).

thf(697,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(3648,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)],[697]) ).

thf(496,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Fields_Ofield @ E )
     => ( ( D
         != ( c_Groups_Ozero__class_Ozero @ E ) )
       => ( ( C
           != ( c_Groups_Ozero__class_Ozero @ E ) )
         => ( ( c_Groups_Ominus__class_Ominus @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ D ) @ ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) )
            = ( c_Rings_Oinverse__class_Odivide @ E @ ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__frac__eq) ).

thf(3044,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Fields_Ofield @ E )
     => ( ( D
         != ( c_Groups_Ozero__class_Ozero @ E ) )
       => ( ( C
           != ( c_Groups_Ozero__class_Ozero @ E ) )
         => ( ( c_Groups_Ominus__class_Ominus @ E @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ D ) @ ( c_Rings_Oinverse__class_Odivide @ E @ A @ C ) )
            = ( c_Rings_Oinverse__class_Odivide @ E @ ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(1215,axiom,
    class_Rings_Omult__zero @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).

thf(5068,plain,
    class_Rings_Omult__zero @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).

thf(27,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Omult__zero @ B )
     => ( ( hAPP @ ( hAPP @ ( 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(1350,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Omult__zero @ B )
     => ( ( hAPP @ ( hAPP @ ( 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)],[27]) ).

thf(1351,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Rings_Omult__zero @ B )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(cnf,[status(esa)],[1350]) ).

thf(1352,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) )
      | ~ ( class_Rings_Omult__zero @ B ) ),
    inference(lifteq,[status(thm)],[1351]) ).

thf(8980,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) )
      | ( ( class_Rings_Omult__zero @ tc_RealDef_Oreal )
       != ( class_Rings_Omult__zero @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[5068,1352]) ).

thf(8981,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ A )
      = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(pattern_uni,[status(thm)],[8980:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal ))]]) ).

thf(736,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(3772,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)],[736]) ).

thf(3773,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: $i] :
        ( ( 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(miniscope,[status(thm)],[3772]) ).

thf(3774,plain,
    ! [A: $i] :
      ( ( 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(cnf,[status(esa)],[3773]) ).

thf(3776,plain,
    ! [A: $i] :
      ( ( 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(lifteq,[status(thm)],[3774]) ).

thf(3777,plain,
    c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ),
    inference(simp,[status(thm)],[3776]) ).

thf(1015,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(4555,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)],[1015]) ).

thf(4556,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 ) ) )
    & ! [A: $i,B: $i] :
        ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ A )
          & ( B != A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ) ),
    inference(miniscope,[status(thm)],[4555]) ).

thf(4559,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A )
      | ( B != A ) ),
    inference(cnf,[status(esa)],[4556]) ).

thf(4562,plain,
    ! [B: $i,A: $i] :
      ( ( B != A )
      | ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ A ) ),
    inference(lifteq,[status(thm)],[4559]) ).

thf(4563,plain,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ A ),
    inference(simp,[status(thm)],[4562]) ).

thf(15531,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
     != ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ A ) ),
    inference(paramod_ordered,[status(thm)],[3777,4563]) ).

thf(15601,plain,
    ! [A: $i] :
      ( ( tc_Int_Oint != tc_Int_Oint )
      | ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       != A )
      | ( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
       != A ) ),
    inference(simp,[status(thm)],[15531]) ).

thf(15632,plain,
    ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
   != ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
    inference(simp,[status(thm)],[15601]) ).

thf(30509,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[25737,1417]) ).

thf(30510,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[30509:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) ) ) ) ))]]) ).

thf(255,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__mult) ).

thf(2184,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(294,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff2) ).

thf(2316,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(629,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(3446,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)],[629]) ).

thf(1047,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(4650,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)],[1047]) ).

thf(374,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(2625,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)],[374]) ).

thf(2626,plain,
    ( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
   != ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
    inference(polarity_switch,[status(thm)],[2625]) ).

thf(2627,plain,
    ( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
   != ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
    inference(lifteq,[status(thm)],[2626]) ).

thf(107,axiom,
    ! [A: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
    <=> ( A
        = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__1__iff__1) ).

thf(1647,plain,
    ! [A: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
       => ( A
          = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
      & ( ( A
          = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
       => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(1648,plain,
    ( ! [A: $i] :
        ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
       => ( A
          = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
    & ! [A: $i] :
        ( ( A
          = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
       => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
    inference(miniscope,[status(thm)],[1647]) ).

thf(1649,plain,
    ! [A: $i] :
      ( ( A
       != ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      | ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
    inference(cnf,[status(esa)],[1648]) ).

thf(1651,plain,
    ! [A: $i] :
      ( ( A
       != ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      | ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
    inference(lifteq,[status(thm)],[1649]) ).

thf(1652,plain,
    c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ),
    inference(simp,[status(thm)],[1651]) ).

thf(13281,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ v_da____ )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ v_mazh )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[1652,10148]) ).

thf(13302,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ v_da____ )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ v_mazh )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_da____ )
      | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != A ) ),
    inference(simp,[status(thm)],[13281]) ).

thf(13321,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ v_da____ )
    | ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ v_mazh )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_da____ ) ),
    inference(simp,[status(thm)],[13302]) ).

thf(13641,plain,
    ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ v_mazh )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_da____ )
    | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
     != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ v_da____ ) ) ),
    inference(paramod_ordered,[status(thm)],[1652,13321]) ).

thf(13671,plain,
    ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ v_mazh )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_da____ )
    | ( tc_Nat_Onat != tc_Nat_Onat )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_da____ ) ),
    inference(simp,[status(thm)],[13641]) ).

thf(13692,plain,
    ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ v_mazh )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_da____ ) ),
    inference(simp,[status(thm)],[13671]) ).

thf(197,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Omonoid__mult @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc2) ).

thf(1988,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Omonoid__mult @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(755,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(3826,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)],[755]) ).

thf(66162,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[65817,1510]) ).

thf(66163,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[66162:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ))]]) ).

thf(67345,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[66163,1510]) ).

thf(67346,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[67345:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ))]]) ).

thf(24,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(1340,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)],[24]) ).

thf(1342,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ D )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ ( sk2 @ D @ C @ B @ A ) ) @ ( hAPP @ A @ ( sk2 @ D @ C @ B @ A ) ) )
      | ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A ) ),
    inference(cnf,[status(esa)],[1340]) ).

thf(519,axiom,
    ! [A: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
    <=> ( A
        = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__1__iff__1) ).

thf(3121,plain,
    ! [A: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
       => ( A
          = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
      & ( ( A
          = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
       => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(1261,axiom,
    class_Rings_Osemiring__0 @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__0) ).

thf(5161,plain,
    class_Rings_Osemiring__0 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1261]) ).

thf(924,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(4294,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)],[924]) ).

thf(17599,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ v_da____ ) ) ),
    inference(paramod_ordered,[status(thm)],[3170,17349]) ).

thf(17621,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( A != v_mazh )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_da____ ) ),
    inference(simp,[status(thm)],[17599]) ).

thf(17635,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_da____ ) ),
    inference(simp,[status(thm)],[17621]) ).

thf(18819,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_da____ )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh ) ) ),
    inference(paramod_ordered,[status(thm)],[1527,17635]) ).

thf(18829,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_da____ )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_da____ )
      | ( A != v_mazh ) ),
    inference(simp,[status(thm)],[18819]) ).

thf(18841,plain,
    ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_da____ )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_da____ ) ),
    inference(simp,[status(thm)],[18829]) ).

thf(19908,plain,
    ( ( v_cs____ != v_da____ )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_da____ )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,18841]) ).

thf(19919,plain,
    ( ( v_cs____ != v_da____ )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_da____ )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[19908]) ).

thf(665,axiom,
    class_Rings_Olinordered__ring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).

thf(3562,plain,
    class_Rings_Olinordered__ring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(672,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(3577,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)],[672]) ).

thf(759,axiom,
    class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).

thf(3838,plain,
    class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(63976,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3838,1510]) ).

thf(63977,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ),
    inference(pattern_uni,[status(thm)],[63976:[bind(A,$thf( tc_Nat_Onat ))]]) ).

thf(64061,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[63977,1510]) ).

thf(64062,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ),
    inference(pattern_uni,[status(thm)],[64061:[bind(A,$thf( tc_Polynomial_Opoly @ tc_Nat_Onat ))]]) ).

thf(64619,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[64062,1510]) ).

thf(64620,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) ),
    inference(pattern_uni,[status(thm)],[64619:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ))]]) ).

thf(64989,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[64620,1510]) ).

thf(64990,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) ) ),
    inference(pattern_uni,[status(thm)],[64989:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) ))]]) ).

thf(66067,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[64990,1510]) ).

thf(66068,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[66067:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) ) ))]]) ).

thf(17609,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ v_da____ ) ) ),
    inference(paramod_ordered,[status(thm)],[1527,17349]) ).

thf(17624,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_mazh )
      | ( A != v_da____ ) ),
    inference(simp,[status(thm)],[17609]) ).

thf(17638,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_mazh ) ),
    inference(simp,[status(thm)],[17624]) ).

thf(54603,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_mazh )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh ) ) ),
    inference(paramod_ordered,[status(thm)],[54339,17638]) ).

thf(54662,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_mazh )
      | ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
       != v_da____ )
      | ( A != v_mazh ) ),
    inference(simp,[status(thm)],[54603]) ).

thf(54674,plain,
    ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_mazh )
    | ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
     != v_da____ ) ),
    inference(simp,[status(thm)],[54662]) ).

thf(68,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__less__div__pos) ).

thf(1507,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(305,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
        = ( c_Groups_Oone__class_Oone @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).

thf(2360,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
        = ( c_Groups_Oone__class_Oone @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(1145,axiom,
    class_Rings_Ocomm__semiring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).

thf(4941,plain,
    class_Rings_Ocomm__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).

thf(268,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
     => ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
        | ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__imp__less__or__eq) ).

thf(2216,plain,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
     => ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
        | ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(324,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
      <=> ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oantisym__conv) ).

thf(2432,plain,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
     => ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
         => ( A = B ) )
        & ( ( A = B )
         => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(583,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(3308,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ A )
     => ( class_Groups_Ominus @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(723,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(3730,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)],[723]) ).

thf(445,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).

thf(2886,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(34,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(1381,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)],[34]) ).

thf(1383,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Rings_Olinordered__idom @ B )
      | ( A
       != ( c_Groups_Ozero__class_Ozero @ B ) )
      | ( ( c_Groups_Osgn__class_Osgn @ B @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(cnf,[status(esa)],[1381]) ).

thf(1385,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( c_Groups_Ozero__class_Ozero @ B ) )
      | ( ( c_Groups_Osgn__class_Osgn @ B @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) )
      | ~ ( class_Rings_Olinordered__idom @ B ) ),
    inference(lifteq,[status(thm)],[1383]) ).

thf(1386,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
        = ( c_Groups_Ozero__class_Ozero @ A ) )
      | ~ ( class_Rings_Olinordered__idom @ A ) ),
    inference(simp,[status(thm)],[1385]) ).

thf(523,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
       => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel) ).

thf(3140,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
       => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(1086,axiom,
    class_Rings_Ocomm__semiring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).

thf(4760,plain,
    class_Rings_Ocomm__semiring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).

thf(466,axiom,
    ! [A: $i,B: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) ) @ A )
      = ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zminus) ).

thf(2957,plain,
    ! [A: $i,B: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) ) @ A )
      = ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(595,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(3335,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)],[595]) ).

thf(1090,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(4769,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)],[1090]) ).

thf(4770,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(cnf,[status(esa)],[4769]) ).

thf(1085,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(4757,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)],[1085]) ).

thf(4758,plain,
    ! [A: $i] :
      ( ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ A )
      = ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ),
    inference(cnf,[status(esa)],[4757]) ).

thf(4759,plain,
    ! [A: $i] :
      ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A )
      = ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ A ) ),
    inference(lifteq,[status(thm)],[4758]) ).

thf(54858,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_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ A ) ) ),
    inference(rewrite,[status(thm)],[4770,4759]) ).

thf(514,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ B ) )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__pow__nat) ).

thf(3103,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ B ) )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(602,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(3350,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)],[602]) ).

thf(337,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(2489,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)],[337]) ).

thf(2490,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 ) ) )
    & ! [A: $i,B: $i] :
        ( ( ( 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(miniscope,[status(thm)],[2489]) ).

thf(2492,plain,
    ! [B: $i,A: $i] :
      ( ( B != A )
      | ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
    inference(cnf,[status(esa)],[2490]) ).

thf(2495,plain,
    ! [B: $i,A: $i] :
      ( ( B != A )
      | ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( c_Nat_OSuc @ A ) ) ),
    inference(lifteq,[status(thm)],[2492]) ).

thf(2496,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ A ) ),
    inference(simp,[status(thm)],[2495]) ).

thf(81334,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ ( c_Nat_OSuc @ B ) )
      | ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ A ) )
       != ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2496,1543]) ).

thf(81335,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) ),
    inference(pattern_uni,[status(thm)],[81334:[bind(A,$thf( D )),bind(B,$thf( c_Nat_OSuc @ D )),bind(C,$thf( D ))]]) ).

thf(81483,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) ),
    inference(simp,[status(thm)],[81335]) ).

thf(85960,plain,
    ! [B: $i,A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) )
     != ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ B ) ) @ B ) ),
    inference(paramod_ordered,[status(thm)],[81483,81608]) ).

thf(86029,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Nat_Onat != tc_Nat_Onat )
      | ( A
       != ( c_Nat_OSuc @ ( c_Nat_OSuc @ B ) ) )
      | ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) )
       != B ) ),
    inference(simp,[status(thm)],[85960]) ).

thf(86058,plain,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) ) )
     != A ),
    inference(simp,[status(thm)],[86029]) ).

thf(690,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(3634,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)],[690]) ).

thf(212,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).

thf(2046,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(413,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(2763,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(354,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Omult__zero @ B )
     => ( ( hAPP @ ( hAPP @ ( 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(2548,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Omult__zero @ B )
     => ( ( hAPP @ ( hAPP @ ( 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)],[354]) ).

thf(91,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( ( c_Groups_Oplus__class_Oplus @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) )
        = ( hAPP @ ( hAPP @ ( 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(1576,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( ( c_Groups_Oplus__class_Oplus @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) )
        = ( hAPP @ ( hAPP @ ( 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)],[91]) ).

thf(1238,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(5122,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238]) ).

thf(5123,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ A ),
    inference(cnf,[status(esa)],[5122]) ).

thf(557,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(3249,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)],[557]) ).

thf(847,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(4079,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)],[847]) ).

thf(50,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(1439,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)],[50]) ).

thf(1440,plain,
    ! [B: $i,A: $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(cnf,[status(esa)],[1439]) ).

thf(1441,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( c_Nat_OSuc @ A ) )
      | ~ ( 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 ) ),
    inference(lifteq,[status(thm)],[1440]) ).

thf(18810,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_da____ )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh ) ) ),
    inference(paramod_ordered,[status(thm)],[3170,17635]) ).

thf(18827,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_da____ )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( A != v_da____ )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_mazh ) ),
    inference(simp,[status(thm)],[18810]) ).

thf(18838,plain,
    ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_da____ )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_mazh ) ),
    inference(simp,[status(thm)],[18827]) ).

thf(19847,plain,
    ( ( v_cs____ != v_da____ )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_mazh )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,18838]) ).

thf(19859,plain,
    ( ( v_cs____ != v_da____ )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_mazh )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[19847]) ).

thf(22441,plain,
    ( ( v_cs____ != v_da____ )
    | ( v_cs____ != v_mazh )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,19859]) ).

thf(22451,plain,
    ( ( v_cs____ != v_da____ )
    | ( v_cs____ != v_mazh )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[22441]) ).

thf(22461,plain,
    ( ( v_cs____ != v_da____ )
    | ( v_cs____ != v_mazh )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[22451]) ).

thf(1056,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(4679,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)],[1056]) ).

thf(509,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).

thf(3088,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(1036,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(4624,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)],[1036]) ).

thf(4625,plain,
    ! [A: $i] :
      ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
      = A ),
    inference(cnf,[status(esa)],[4624]) ).

thf(4626,plain,
    ! [A: $i] :
      ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
      = A ),
    inference(lifteq,[status(thm)],[4625]) ).

thf(651,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(3510,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)],[651]) ).

thf(3511,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: $i,B: $i] :
        ( ( 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(miniscope,[status(thm)],[3510]) ).

thf(3512,plain,
    ! [B: $i,A: $i] :
      ( ( 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(cnf,[status(esa)],[3511]) ).

thf(3514,plain,
    ! [B: $i,A: $i] :
      ( ( 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(lifteq,[status(thm)],[3512]) ).

thf(3515,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
      = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[3514]) ).

thf(45626,plain,
    ! [B: $i,A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ ( 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 @ B ) ),
    inference(paramod_ordered,[status(thm)],[4871,4563]) ).

thf(45713,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Int_Oint != tc_Int_Oint )
      | ( A != B )
      | ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
       != B ) ),
    inference(simp,[status(thm)],[45626]) ).

thf(45743,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
     != A ),
    inference(simp,[status(thm)],[45713]) ).

thf(45806,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal )
       != B )
      | ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
       != ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3515,45743]) ).

thf(45843,plain,
    ! [A: $i] :
      ( ( tc_Int_Oint != tc_RealDef_Oreal )
      | ( A
       != ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A )
       != ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
    inference(simp,[status(thm)],[45806]) ).

thf(45856,plain,
    ( ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
     != ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
    inference(simp,[status(thm)],[45843]) ).

thf(45980,plain,
    ! [A: $i] :
      ( ( tc_Int_Oint != tc_RealDef_Oreal )
      | ( A
       != ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
      | ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
       != ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4626,45856]) ).

thf(46002,plain,
    ( ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(simp,[status(thm)],[45980]) ).

thf(46014,plain,
    ( ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(simp,[status(thm)],[46002]) ).

thf(223,axiom,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1) ).

thf(2080,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(2081,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
      = A ),
    inference(cnf,[status(esa)],[2080]) ).

thf(2082,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
      = A ),
    inference(lifteq,[status(thm)],[2081]) ).

thf(1052,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(4665,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)],[1052]) ).

thf(31,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( hAPP @ ( hAPP @ ( 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(1374,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( hAPP @ ( hAPP @ ( 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)],[31]) ).

thf(1375,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Rings_Ocomm__semiring__1 @ B )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(cnf,[status(esa)],[1374]) ).

thf(1376,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
        = ( c_Groups_Ozero__class_Ozero @ B ) )
      | ~ ( class_Rings_Ocomm__semiring__1 @ B ) ),
    inference(lifteq,[status(thm)],[1375]) ).

thf(12784,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
        = ( c_Groups_Ozero__class_Ozero @ B ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex )
       != ( class_Rings_Ocomm__semiring__1 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[4691,1376]) ).

thf(12785,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
      = ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
    inference(pattern_uni,[status(thm)],[12784:[bind(A,$thf( A )),bind(B,$thf( tc_Complex_Ocomplex ))]]) ).

thf(874,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(4156,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)],[874]) ).

thf(148,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(1803,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)],[148]) ).

thf(240,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ A @ B )
       => ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ B )
          = ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__antisym__abs) ).

thf(2136,plain,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ A @ B )
       => ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ B )
          = ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(73,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(1518,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Orderings_Oord @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(54621,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_mazh )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ v_da____ ) ) ),
    inference(paramod_ordered,[status(thm)],[54339,17640]) ).

thf(54644,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_mazh )
      | ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
       != v_mazh )
      | ( A != v_da____ ) ),
    inference(simp,[status(thm)],[54621]) ).

thf(54694,plain,
    ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_mazh )
    | ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
     != v_mazh ) ),
    inference(simp,[status(thm)],[54644]) ).

thf(347,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oab__semigroup__mult @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).

thf(2531,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Oab__semigroup__mult @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(598,axiom,
    class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).

thf(3342,plain,
    class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(22,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ B )
     => ( ( hAPP @ ( hAPP @ ( 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(1331,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ B )
     => ( ( hAPP @ ( hAPP @ ( 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)],[22]) ).

thf(1332,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ B )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(cnf,[status(esa)],[1331]) ).

thf(1333,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) )
      | ~ ( class_RealVector_Oreal__normed__algebra @ B ) ),
    inference(lifteq,[status(thm)],[1332]) ).

thf(7177,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) )
      | ( ( class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex )
       != ( class_RealVector_Oreal__normed__algebra @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[3342,1333]) ).

thf(7178,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) @ A )
      = ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
    inference(pattern_uni,[status(thm)],[7177:[bind(A,$thf( A )),bind(B,$thf( tc_Complex_Ocomplex ))]]) ).

thf(60,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
    <=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__reduce) ).

thf(1479,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
       => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) )
      & ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
       => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(1480,plain,
    ( ! [A: $i,B: $i] :
        ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
       => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) )
    & ! [A: $i,B: $i] :
        ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
       => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ) ),
    inference(miniscope,[status(thm)],[1479]) ).

thf(1482,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
      | ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ),
    inference(cnf,[status(esa)],[1480]) ).

thf(681,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(3597,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)],[681]) ).

thf(1093,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(4775,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)],[1093]) ).

thf(441,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
            = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__divide__eq__eq) ).

thf(2869,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
              = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) )
          & ( ( B
              = ( hAPP @ ( hAPP @ ( 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)],[441]) ).

thf(1188,axiom,
    class_Fields_Ofield__inverse__zero @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).

thf(5024,plain,
    class_Fields_Ofield__inverse__zero @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).

thf(15099,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_c____ @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) @ v_c____ ) ) ),
    inference(paramod_ordered,[status(thm)],[3170,12089]) ).

thf(15144,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_c____ @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( A
       != ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_c____ ) ),
    inference(simp,[status(thm)],[15099]) ).

thf(15154,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_c____ @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_c____ ) ),
    inference(simp,[status(thm)],[15144]) ).

thf(24007,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_c____ )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_c____ @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3170,15154]) ).

thf(24045,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_c____ )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( A != v_c____ )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
    inference(simp,[status(thm)],[24007]) ).

thf(24060,plain,
    ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_c____ )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
    inference(simp,[status(thm)],[24045]) ).

thf(210,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
         => ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).

thf(2039,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
         => ( c_Orderings_Oord__class_Oless @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(843,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(4070,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)],[843]) ).

thf(753,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(3821,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)],[753]) ).

thf(1094,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(4778,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)],[1094]) ).

thf(1253,axiom,
    class_Rings_Ocomm__ring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring) ).

thf(5150,plain,
    class_Rings_Ocomm__ring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).

thf(357,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ B )
     => ? [C: $i] :
        ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Obounded) ).

thf(2562,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ B )
     => ? [C: $i] :
        ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(1018,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(4568,plain,
    class_Groups_Ocancel__comm__monoid__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).

thf(905,axiom,
    class_Int_Oring__char__0 @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).

thf(4243,plain,
    class_Int_Oring__char__0 @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).

thf(39,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Power_Opower @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc) ).

thf(1407,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Power_Opower @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(1408,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Opower @ C )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
    inference(cnf,[status(esa)],[1407]) ).

thf(1409,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) )
      | ~ ( class_Power_Opower @ C ) ),
    inference(lifteq,[status(thm)],[1408]) ).

thf(945,axiom,
    class_Rings_Ocomm__semiring__1 @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).

thf(4349,plain,
    class_Rings_Ocomm__semiring__1 @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).

thf(63964,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ tc_Int_Oint )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4349,1510]) ).

thf(63965,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ tc_Int_Oint ),
    inference(pattern_uni,[status(thm)],[63964:[bind(A,$thf( tc_Int_Oint ))]]) ).

thf(64031,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( class_Rings_Ocomm__semiring__1 @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      | ( A
       != ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ),
    inference(paramod_ordered,[status(thm)],[4121,63965]) ).

thf(64032,plain,
    ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) )
    | ( class_Rings_Ocomm__semiring__1 @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(pattern_uni,[status(thm)],[64031:[bind(A,$thf( tc_Polynomial_Opoly @ tc_Int_Oint ))]]) ).

thf(564,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(3263,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)],[564]) ).

thf(11,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Ozero @ E )
     => ( ( ( c_Polynomial_OpCons @ E @ D @ C )
          = ( c_Polynomial_OpCons @ E @ B @ A ) )
      <=> ( ( D = B )
          & ( C = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__iff) ).

thf(1287,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Ozero @ E )
     => ( ( ( ( c_Polynomial_OpCons @ E @ D @ C )
            = ( c_Polynomial_OpCons @ E @ B @ A ) )
         => ( ( D = B )
            & ( C = A ) ) )
        & ( ( ( D = B )
            & ( C = A ) )
         => ( ( c_Polynomial_OpCons @ E @ D @ C )
            = ( c_Polynomial_OpCons @ E @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(862,axiom,
    class_Rings_Ocomm__semiring__0 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).

thf(4126,plain,
    class_Rings_Ocomm__semiring__0 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).

thf(5323,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Polynomial_Osynthetic__div @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
      | ( ( class_Rings_Ocomm__semiring__0 @ tc_Complex_Ocomplex )
       != ( class_Rings_Ocomm__semiring__0 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[4126,1266]) ).

thf(5324,plain,
    ! [A: $i] :
      ( ( c_Polynomial_Osynthetic__div @ tc_Complex_Ocomplex @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) @ A )
      = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
    inference(pattern_uni,[status(thm)],[5323:[bind(A,$thf( A )),bind(B,$thf( tc_Complex_Ocomplex ))]]) ).

thf(29621,plain,
    ! [A: $i] :
      ( ( c_Polynomial_Osynthetic__div @ tc_Complex_Ocomplex @ v_cs____ @ A )
      = v_cs____ ),
    inference(rewrite,[status(thm)],[5324,1280]) ).

thf(1012,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(4546,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)],[1012]) ).

thf(976,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(4439,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)],[976]) ).

thf(15036,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) @ v_c____ )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_c____ @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1527,12089]) ).

thf(15073,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) @ v_c____ )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_c____ )
      | ( A
       != ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
    inference(simp,[status(thm)],[15036]) ).

thf(15079,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) @ v_c____ )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_c____ ) ),
    inference(simp,[status(thm)],[15073]) ).

thf(22228,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_c____ )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) @ v_c____ ) ) ),
    inference(paramod_ordered,[status(thm)],[3170,15079]) ).

thf(22257,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_c____ )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( A
       != ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_c____ ) ),
    inference(simp,[status(thm)],[22228]) ).

thf(22274,plain,
    ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_c____ )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_c____ ) ),
    inference(simp,[status(thm)],[22257]) ).

thf(22309,plain,
    ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_c____ )
    | ( v_cs____ != v_c____ )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,22274]) ).

thf(22320,plain,
    ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_c____ )
    | ( v_cs____ != v_c____ )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[22309]) ).

thf(809,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(3976,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Groups_Osgn__if @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).

thf(368,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A )
      <=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
           => ( c_Orderings_Oord__class_Oless @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
          & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
           => ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ C ) )
              & ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq) ).

thf(2603,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ D )
     => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A )
         => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
             => ( c_Orderings_Oord__class_Oless @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ C ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) )
        & ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
             => ( c_Orderings_Oord__class_Oless @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ C ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

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 @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).

thf(4524,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)],[1005]) ).

thf(541,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__pos__lemma) ).

thf(3195,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(944,axiom,
    class_Fields_Ofield__inverse__zero @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).

thf(4348,plain,
    class_Fields_Ofield__inverse__zero @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).

thf(46,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Groups_Ominus__class_Ominus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
          = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__diff__eq__iff) ).

thf(1428,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Groups_Ominus__class_Ominus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
          = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(1429,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Fields_Ofield @ D )
      | ( C
        = ( c_Groups_Ozero__class_Ozero @ D ) )
      | ( ( c_Groups_Ominus__class_Ominus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
        = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ C ) ) ),
    inference(cnf,[status(esa)],[1428]) ).

thf(1430,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( c_Groups_Ozero__class_Ozero @ D ) )
      | ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ C )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) )
      | ~ ( class_Fields_Ofield @ D ) ),
    inference(lifteq,[status(thm)],[1429]) ).

thf(695,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(3644,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)],[695]) ).

thf(1153,axiom,
    class_Rings_Oordered__ring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).

thf(4956,plain,
    class_Rings_Oordered__ring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).

thf(1064,axiom,
    class_Groups_Ocancel__semigroup__add @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).

thf(4692,plain,
    class_Groups_Ocancel__semigroup__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).

thf(708,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(3689,plain,
    class_Groups_Oordered__comm__monoid__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(899,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(4224,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)],[899]) ).

thf(166,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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(1871,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(1087,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(4761,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)],[1087]) ).

thf(499,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(3061,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)],[499]) ).

thf(174,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ B )
     => ( ( hAPP @ ( hAPP @ ( 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(1907,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ B )
     => ( ( hAPP @ ( hAPP @ ( 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)],[174]) ).

thf(59,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(1477,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Orderings_Opreorder @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(1478,plain,
    ! [A: $i] :
      ( ~ ( class_Rings_Olinordered__idom @ A )
      | ( class_Orderings_Opreorder @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(cnf,[status(esa)],[1477]) ).

thf(48883,plain,
    ! [A: $i] :
      ( ( class_Orderings_Opreorder @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Olinordered__idom @ tc_RealDef_Oreal )
       != ( class_Rings_Olinordered__idom @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4968,1478]) ).

thf(48884,plain,
    class_Orderings_Opreorder @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ),
    inference(pattern_uni,[status(thm)],[48883:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(60994,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( class_Orderings_Opreorder @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      | ( A
       != ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ),
    inference(paramod_ordered,[status(thm)],[4121,48884]) ).

thf(60995,plain,
    ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) )
    | ( class_Orderings_Opreorder @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(pattern_uni,[status(thm)],[60994:[bind(A,$thf( tc_Polynomial_Opoly @ tc_RealDef_Oreal ))]]) ).

thf(1049,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(4654,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)],[1049]) ).

thf(21,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ D )
     => ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Polynomial_OpCons @ D @ C @ B ) ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pCons) ).

thf(1328,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ D )
     => ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Polynomial_OpCons @ D @ C @ B ) ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(1329,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Ocomm__semiring__0 @ D )
      | ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Polynomial_OpCons @ D @ C @ B ) ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ) ),
    inference(cnf,[status(esa)],[1328]) ).

thf(1330,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) )
        = ( hAPP @ ( c_Polynomial_Opoly @ D @ ( c_Polynomial_OpCons @ D @ C @ B ) ) @ A ) )
      | ~ ( class_Rings_Ocomm__semiring__0 @ D ) ),
    inference(lifteq,[status(thm)],[1329]) ).

thf(70,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
          = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__num__frac) ).

thf(1511,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
          = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(282,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
        <=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__divide__less__eq) ).

thf(2274,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
           => ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ B ) )
          & ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ B )
           => ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(865,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(4130,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)],[865]) ).

thf(16,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Ocomm__monoid__add @ E )
     => ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) @ ( c_Polynomial_OpCons @ E @ D @ C ) @ ( c_Polynomial_OpCons @ E @ B @ A ) )
        = ( c_Polynomial_OpCons @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pCons) ).

thf(1311,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Ocomm__monoid__add @ E )
     => ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) @ ( c_Polynomial_OpCons @ E @ D @ C ) @ ( c_Polynomial_OpCons @ E @ B @ A ) )
        = ( c_Polynomial_OpCons @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(1312,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Groups_Ocomm__monoid__add @ E )
      | ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) @ ( c_Polynomial_OpCons @ E @ D @ C ) @ ( c_Polynomial_OpCons @ E @ B @ A ) )
        = ( c_Polynomial_OpCons @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) @ C @ A ) ) ) ),
    inference(cnf,[status(esa)],[1311]) ).

thf(1313,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) @ ( c_Polynomial_OpCons @ E @ D @ C ) @ ( c_Polynomial_OpCons @ E @ B @ A ) )
        = ( c_Polynomial_OpCons @ E @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ E ) @ C @ A ) ) )
      | ~ ( class_Groups_Ocomm__monoid__add @ E ) ),
    inference(lifteq,[status(thm)],[1312]) ).

thf(917,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(4275,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)],[917]) ).

thf(53,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__add__left) ).

thf(1453,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(1454,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Ocomm__semiring__0 @ D )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ B ) @ A ) ) ) ),
    inference(cnf,[status(esa)],[1453]) ).

thf(1455,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ D ) @ C @ B ) ) @ A ) )
      | ~ ( class_Rings_Ocomm__semiring__0 @ D ) ),
    inference(lifteq,[status(thm)],[1454]) ).

thf(572,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(3280,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)],[572]) ).

thf(333,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).

thf(2466,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B ) @ A ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(1229,axiom,
    class_Fields_Olinordered__field @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).

thf(5108,plain,
    class_Fields_Olinordered__field @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).

thf(1459,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Rings_Ocomm__ring @ D )
        & ( class_Rings_Odvd @ D ) )
     => ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
       => ( ! [E: $i] :
              ( ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ E @ A ) )
             => ! [F: $i] : ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Ominus__class_Ominus @ D @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ F ) @ B ) ) @ A ) ) )
          & ! [E: $i] :
              ( ? [F: $i] : ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Ominus__class_Ominus @ D @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ F ) @ B ) ) @ A ) )
             => ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ E @ A ) ) ) ) ) ),
    inference(miniscope,[status(thm)],[1458]) ).

thf(1460,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Ocomm__ring @ D )
      | ~ ( class_Rings_Odvd @ D )
      | ~ ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
      | ~ ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Ominus__class_Ominus @ D @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ F ) @ B ) ) @ A ) )
      | ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ E @ A ) ) ),
    inference(cnf,[status(esa)],[1459]) ).

thf(1462,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Ocomm__ring @ D )
      | ~ ( class_Rings_Odvd @ D )
      | ~ ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
      | ~ ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Ominus__class_Ominus @ D @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ F ) @ B ) ) @ A ) )
      | ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ E @ A ) ) ),
    inference(simp,[status(thm)],[1460]) ).

thf(970,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__imp__le) ).

thf(4428,plain,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).

thf(12692,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
        = ( c_Groups_Ozero__class_Ozero @ B ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ tc_Int_Oint )
       != ( class_Rings_Ocomm__semiring__1 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[4349,1376]) ).

thf(12693,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
      = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
    inference(pattern_uni,[status(thm)],[12692:[bind(A,$thf( A )),bind(B,$thf( tc_Int_Oint ))]]) ).

thf(147,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
     => ( ( A
          = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
        | ( B
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).

thf(1800,plain,
    ! [A: $i,B: $i] :
      ( ( B
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
     => ( ( A
          = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
        | ( B
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(652,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(3517,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)],[652]) ).

thf(887,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(4194,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)],[887]) ).

thf(638,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(3470,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)],[638]) ).

thf(585,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(3312,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)],[585]) ).

thf(64,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ B )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ B ) ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__right) ).

thf(1492,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ B )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ B ) ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(1493,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Rings_Ocomm__semiring__0 @ B )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ B ) ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
    inference(cnf,[status(esa)],[1492]) ).

thf(1494,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ B ) ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
      | ~ ( class_Rings_Ocomm__semiring__0 @ B ) ),
    inference(lifteq,[status(thm)],[1493]) ).

thf(161,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(1847,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)],[161]) ).

thf(171,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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(1892,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(915,axiom,
    class_Groups_Ozero @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).

thf(4273,plain,
    class_Groups_Ozero @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).

thf(5354,plain,
    ! [A: $i] :
      ( ( ( c_Polynomial_OpCons @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
      | ( ( class_Groups_Ozero @ tc_Nat_Onat )
       != ( class_Groups_Ozero @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4273,1272]) ).

thf(5355,plain,
    ( ( c_Polynomial_OpCons @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) )
    = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) ),
    inference(pattern_uni,[status(thm)],[5354:[bind(A,$thf( tc_Nat_Onat ))]]) ).

thf(33,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( c_Rings_Odvd__class_Odvd @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__left) ).

thf(1379,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( c_Rings_Odvd__class_Odvd @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(948,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(4353,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)],[948]) ).

thf(1099,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(4788,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)],[1099]) ).

thf(250,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ A ) @ C ) )
      <=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__eq__int) ).

thf(2169,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
     => ( ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ A ) @ C ) )
         => ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A ) )
        & ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A )
         => ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ A ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(71,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ E )
     => ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
         => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
           => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
             => ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).

thf(1514,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ E )
     => ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
         => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
           => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
             => ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(1033,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(4617,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)],[1033]) ).

thf(87088,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__ring @ tc_RealDef_Oreal )
       != ( class_Rings_Ocomm__ring @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[5150,1575]) ).

thf(87089,plain,
    class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ),
    inference(pattern_uni,[status(thm)],[87088:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(87145,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) )
       != ( class_Rings_Ocomm__ring @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[87089,1575]) ).

thf(87146,plain,
    class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ),
    inference(pattern_uni,[status(thm)],[87145:[bind(A,$thf( tc_Polynomial_Opoly @ tc_RealDef_Oreal ))]]) ).

thf(87270,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) )
       != ( class_Rings_Ocomm__ring @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[87146,1575]) ).

thf(87271,plain,
    class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ),
    inference(pattern_uni,[status(thm)],[87270:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ))]]) ).

thf(88949,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) )
       != ( class_Rings_Ocomm__ring @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[87271,1575]) ).

thf(88950,plain,
    class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ),
    inference(pattern_uni,[status(thm)],[88949:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ))]]) ).

thf(89192,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) )
       != ( class_Rings_Ocomm__ring @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[88950,1575]) ).

thf(89193,plain,
    class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[89192:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ))]]) ).

thf(90445,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) )
       != ( class_Rings_Ocomm__ring @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[89193,1575]) ).

thf(90446,plain,
    class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[90445:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ))]]) ).

thf(56025,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != tc_Nat_Onat )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Int_Oint ) ) ),
    inference(paramod_ordered,[status(thm)],[3170,54260]) ).

thf(56048,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != tc_Nat_Onat )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( A != tc_Nat_Onat )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[56025]) ).

thf(56079,plain,
    ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != tc_Nat_Onat )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[56048]) ).

thf(657,axiom,
    class_Rings_Ocomm__semiring__0 @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).

thf(3537,plain,
    class_Rings_Ocomm__semiring__0 @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(5198,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Polynomial_Osynthetic__div @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
      | ( ( class_Rings_Ocomm__semiring__0 @ tc_Int_Oint )
       != ( class_Rings_Ocomm__semiring__0 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[3537,1266]) ).

thf(5199,plain,
    ! [A: $i] :
      ( ( c_Polynomial_Osynthetic__div @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) @ A )
      = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ),
    inference(pattern_uni,[status(thm)],[5198:[bind(A,$thf( A )),bind(B,$thf( tc_Int_Oint ))]]) ).

thf(1051,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(4662,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)],[1051]) ).

thf(4663,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(cnf,[status(esa)],[4662]) ).

thf(4664,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(lifteq,[status(thm)],[4663]) ).

thf(415,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( c_Rings_Odvd__class_Odvd @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
       => ( A
          = ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__left) ).

thf(2767,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( c_Rings_Odvd__class_Odvd @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A )
       => ( A
          = ( c_Groups_Ozero__class_Ozero @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(647,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(3497,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)],[647]) ).

thf(3498,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      = A ),
    inference(cnf,[status(esa)],[3497]) ).

thf(3499,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      = A ),
    inference(lifteq,[status(thm)],[3498]) ).

thf(14744,plain,
    ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_mzh @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ v_mazh @ v_ma ) )
   != ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_da____ @ v_mazh ) ),
    inference(paramod_ordered,[status(thm)],[5032,1263]) ).

thf(14783,plain,
    ( ( tc_RealDef_Oreal != tc_RealDef_Oreal )
    | ( v_mzh != v_da____ )
    | ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ v_mazh @ v_ma )
     != v_mazh ) ),
    inference(simp,[status(thm)],[14744]) ).

thf(14811,plain,
    ( ( v_mzh != v_da____ )
    | ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ v_mazh @ v_ma )
     != v_mazh ) ),
    inference(simp,[status(thm)],[14783]) ).

thf(20561,plain,
    ! [A: $i] :
      ( ( v_mzh != v_da____ )
      | ( A != v_mazh )
      | ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
       != ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ v_mazh @ v_ma ) ) ),
    inference(paramod_ordered,[status(thm)],[3499,14811]) ).

thf(20573,plain,
    ( ( v_mzh != v_da____ )
    | ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_mazh )
    | ( v_ma != v_mazh ) ),
    inference(simp,[status(thm)],[20561]) ).

thf(1140,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(4928,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)],[1140]) ).

thf(26,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A ) )
        = ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__power__minus) ).

thf(1347,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A ) )
        = ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(36,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
    <=> ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
        | ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__less) ).

thf(1390,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
       => ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
            & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
          | ( B = A ) ) )
      & ( ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
            & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
          | ( B = A ) )
       => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(1391,plain,
    ( ! [A: $i,B: $i] :
        ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
       => ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
            & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
          | ( B = A ) ) )
    & ! [A: $i,B: $i] :
        ( ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
            & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
          | ( B = A ) )
       => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
    inference(miniscope,[status(thm)],[1390]) ).

thf(1393,plain,
    ! [B: $i,A: $i] :
      ( ( B != A )
      | ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ),
    inference(cnf,[status(esa)],[1391]) ).

thf(1397,plain,
    ! [B: $i,A: $i] :
      ( ( B != A )
      | ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ),
    inference(lifteq,[status(thm)],[1393]) ).

thf(1398,plain,
    ! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ A ),
    inference(simp,[status(thm)],[1397]) ).

thf(1108,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(4830,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)],[1108]) ).

thf(507,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(3084,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)],[507]) ).

thf(724,axiom,
    ! [A: $i,B: $i] :
      ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Complex_Orcis @ B @ A ) )
      = ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__rcis) ).

thf(3734,plain,
    ! [A: $i,B: $i] :
      ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Complex_Orcis @ B @ A ) )
      = ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).

thf(54206,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Int_Oint @ tc_Nat_Onat )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Int_Oint ) ) ),
    inference(paramod_ordered,[status(thm)],[3170,47061]) ).

thf(54238,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Int_Oint @ tc_Nat_Onat )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( A != tc_Nat_Onat )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[54206]) ).

thf(54263,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Int_Oint @ tc_Nat_Onat )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[54238]) ).

thf(58211,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != tc_Int_Oint )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Int_Oint @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[1527,54263]) ).

thf(58225,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != tc_Int_Oint )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != tc_Int_Oint )
      | ( A != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[58211]) ).

thf(58251,plain,
    ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != tc_Int_Oint )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[58225]) ).

thf(59211,plain,
    ( ( tc_Int_Oint != v_cs____ )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != tc_Int_Oint )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,58251]) ).

thf(59218,plain,
    ( ( tc_Int_Oint != v_cs____ )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != tc_Int_Oint )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[59211]) ).

thf(344,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(2520,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)],[344]) ).

thf(867,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(4141,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)],[867]) ).

thf(799,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(3951,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)],[799]) ).

thf(246,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
     => ( ( B != A )
       => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__neq__trans) ).

thf(2158,plain,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
     => ( ( B != A )
       => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(1039,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(4632,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)],[1039]) ).

thf(758,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(3835,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)],[758]) ).

thf(63990,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4691,1510]) ).

thf(63991,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ),
    inference(pattern_uni,[status(thm)],[63990:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(64139,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[63991,1510]) ).

thf(64140,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ),
    inference(pattern_uni,[status(thm)],[64139:[bind(A,$thf( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ))]]) ).

thf(64733,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[64140,1510]) ).

thf(64734,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
    inference(pattern_uni,[status(thm)],[64733:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ))]]) ).

thf(65891,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[64734,1510]) ).

thf(65892,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ),
    inference(pattern_uni,[status(thm)],[65891:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ))]]) ).

thf(1101,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(4793,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)],[1101]) ).

thf(663,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(3557,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)],[663]) ).

thf(89,axiom,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
      = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0) ).

thf(1571,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
      = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(1572,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
      = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(cnf,[status(esa)],[1571]) ).

thf(1573,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
      = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(lifteq,[status(thm)],[1572]) ).

thf(36981,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
     != ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[1573,28636]) ).

thf(37018,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       != ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) )
      | ( A
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(simp,[status(thm)],[36981]) ).

thf(37074,plain,
    ! [A: $i] :
      ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
     != ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) ),
    inference(simp,[status(thm)],[37018]) ).

thf(44366,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
       != ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2851,37074]) ).

thf(44545,plain,
    ! [A: $i] :
      ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
       != ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) )
      | ( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
       != A ) ),
    inference(simp,[status(thm)],[44366]) ).

thf(44620,plain,
    ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
   != ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[44545]) ).

thf(435,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono) ).

thf(2852,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(1091,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(4771,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)],[1091]) ).

thf(551,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(3231,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)],[551]) ).

thf(1000,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(4514,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)],[1000]) ).

thf(68153,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[67346,1510]) ).

thf(68154,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[68153:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ))]]) ).

thf(567,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(3268,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)],[567]) ).

thf(818,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Olinordered__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring) ).

thf(4008,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Olinordered__semiring @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).

thf(54304,plain,
    ! [B: $i,A: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
      | ( ( class_Rings_Ocomm__semiring__1 @ tc_Int_Oint )
       != ( class_Rings_Ocomm__semiring__1 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[4349,1491]) ).

thf(54305,plain,
    ! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ),
    inference(pattern_uni,[status(thm)],[54304:[bind(A,$thf( A )),bind(B,$thf( tc_Int_Oint ))]]) ).

thf(428,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(2829,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)],[428]) ).

thf(82823,plain,
    ! [B: $i,A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) )
     != ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ B ) ),
    inference(paramod_ordered,[status(thm)],[81483,81500]) ).

thf(82916,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Nat_Onat != tc_Nat_Onat )
      | ( A
       != ( c_Nat_OSuc @ B ) )
      | ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) )
       != B ) ),
    inference(simp,[status(thm)],[82823]) ).

thf(82959,plain,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) )
     != A ),
    inference(simp,[status(thm)],[82916]) ).

thf(83681,plain,
    ! [A: $i] :
      ( ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
       != A )
      | ( ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       != ( c_Nat_OSuc @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2178,82959]) ).

thf(83682,plain,
    ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
   != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(pattern_uni,[status(thm)],[83681:[bind(A,$thf( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ))]]) ).

thf(64022,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[63965,1510]) ).

thf(64023,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ),
    inference(pattern_uni,[status(thm)],[64022:[bind(A,$thf( tc_Polynomial_Opoly @ tc_Int_Oint ))]]) ).

thf(64256,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[64023,1510]) ).

thf(64257,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ),
    inference(pattern_uni,[status(thm)],[64256:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ))]]) ).

thf(64798,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[64257,1510]) ).

thf(64799,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ),
    inference(pattern_uni,[status(thm)],[64798:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ))]]) ).

thf(65974,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[64799,1510]) ).

thf(65975,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[65974:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ))]]) ).

thf(67036,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[65975,1510]) ).

thf(67037,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[67036:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ))]]) ).

thf(370,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
       => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__trans) ).

thf(2616,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
       => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(623,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(3431,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)],[623]) ).

thf(40862,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
       != ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2082,37074]) ).

thf(41037,plain,
    ! [A: $i] :
      ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
       != ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) )
      | ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       != A ) ),
    inference(simp,[status(thm)],[40862]) ).

thf(41177,plain,
    ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
   != ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[41037]) ).

thf(1105,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(4820,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)],[1105]) ).

thf(43,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(1418,plain,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ A )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(1103,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(4815,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)],[1103]) ).

thf(1258,axiom,
    class_RealVector_Oreal__normed__field @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__field) ).

thf(5156,plain,
    class_RealVector_Oreal__normed__field @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1258]) ).

thf(782,axiom,
    class_Rings_Olinordered__idom @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).

thf(3913,plain,
    class_Rings_Olinordered__idom @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).

thf(1519,plain,
    ! [A: $i] :
      ( ~ ( class_Rings_Olinordered__idom @ A )
      | ( class_Orderings_Oord @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(cnf,[status(esa)],[1518]) ).

thf(67491,plain,
    ! [A: $i] :
      ( ( class_Orderings_Oord @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Olinordered__idom @ tc_Int_Oint )
       != ( class_Rings_Olinordered__idom @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3913,1519]) ).

thf(67492,plain,
    class_Orderings_Oord @ ( tc_Polynomial_Opoly @ tc_Int_Oint ),
    inference(pattern_uni,[status(thm)],[67491:[bind(A,$thf( tc_Int_Oint ))]]) ).

thf(579,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(3300,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)],[579]) ).

thf(763,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(3851,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)],[763]) ).

thf(964,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(4411,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)],[964]) ).

thf(62,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
      = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).

thf(1487,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
      = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(1488,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
      = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ A ) ) ),
    inference(cnf,[status(esa)],[1487]) ).

thf(1489,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
      = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ A ) ) ),
    inference(lifteq,[status(thm)],[1488]) ).

thf(1172,axiom,
    class_Rings_Olinordered__semiring__strict @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).

thf(4988,plain,
    class_Rings_Olinordered__semiring__strict @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).

thf(41,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Odvd @ D )
     => ( ( C
          = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
       => ( c_Rings_Odvd__class_Odvd @ D @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvdI) ).

thf(1412,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Odvd @ D )
     => ( ( C
          = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
       => ( c_Rings_Odvd__class_Odvd @ D @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(1413,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Odvd @ D )
      | ( C
       != ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
      | ( c_Rings_Odvd__class_Odvd @ D @ B @ C ) ),
    inference(cnf,[status(esa)],[1412]) ).

thf(1414,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
       != ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
      | ~ ( class_Rings_Odvd @ D )
      | ( c_Rings_Odvd__class_Odvd @ D @ B @ C ) ),
    inference(lifteq,[status(thm)],[1413]) ).

thf(1415,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Odvd @ C )
      | ( c_Rings_Odvd__class_Odvd @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ),
    inference(simp,[status(thm)],[1414]) ).

thf(111,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(1664,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)],[111]) ).

thf(56038,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != tc_Nat_Onat )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Int_Oint ) ) ),
    inference(paramod_ordered,[status(thm)],[1527,54260]) ).

thf(56058,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != tc_Nat_Onat )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != tc_Nat_Onat )
      | ( A != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[56038]) ).

thf(56089,plain,
    ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != tc_Nat_Onat )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[56058]) ).

thf(423,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 ) )
           => ( ( hAPP @ ( hAPP @ ( 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(2794,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 ) )
             => ( ( hAPP @ ( hAPP @ ( 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 ) )
             => ( ( hAPP @ ( hAPP @ ( 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)],[423]) ).

thf(1130,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(4903,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).

thf(1023,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(4578,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)],[1023]) ).

thf(151,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).

thf(1811,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(1446,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
      | ( 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 ) @ B ) ),
    inference(cnf,[status(esa)],[1443]) ).

thf(1450,plain,
    ! [B: $i,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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
      | ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ),
    inference(lifteq,[status(thm)],[1446]) ).

thf(1191,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(5027,plain,
    class_Rings_Odivision__ring__inverse__zero @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).

thf(613,axiom,
    class_Groups_Ouminus @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).

thf(3393,plain,
    class_Groups_Ouminus @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(1181,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(5013,plain,
    class_Rings_Olinordered__comm__semiring__strict @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).

thf(30,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono2) ).

thf(1372,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(1373,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
      | ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ),
    inference(cnf,[status(esa)],[1372]) ).

thf(721,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(3724,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)],[721]) ).

thf(719,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__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ D ) @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) @ D ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__bound__exists) ).

thf(3716,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__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ D ) @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ A ) @ D ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).

thf(3718,plain,
    ! [B: $i,A: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( sk26 @ B @ A ) ),
    inference(cnf,[status(esa)],[3716]) ).

thf(38670,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( sk26 @ B @ A ) )
     != ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ C @ C ) ),
    inference(paramod_ordered,[status(thm)],[3718,5078]) ).

thf(38687,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal != tc_RealDef_Oreal )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal )
       != C )
      | ( ( sk26 @ B @ A )
       != C ) ),
    inference(simp,[status(thm)],[38670]) ).

thf(38707,plain,
    ! [B: $i,A: $i] :
      ( ( sk26 @ B @ A )
     != ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[38687]) ).

thf(578,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(3295,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)],[578]) ).

thf(739,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(3784,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)],[739]) ).

thf(3785,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ),
    inference(cnf,[status(esa)],[3784]) ).

thf(15178,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
     != ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_da____ @ v_mazh ) ),
    inference(paramod_ordered,[status(thm)],[3785,1263]) ).

thf(15199,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_da____ )
      | ( A != v_mazh ) ),
    inference(simp,[status(thm)],[15178]) ).

thf(15220,plain,
    ( ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_da____ ) ),
    inference(simp,[status(thm)],[15199]) ).

thf(15256,plain,
    ( ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( v_cs____ != v_da____ )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,15220]) ).

thf(15261,plain,
    ( ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( v_cs____ != v_da____ )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[15256]) ).

thf(104,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) ) @ A )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__left) ).

thf(1632,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) ) @ A )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(334,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
       != ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
     => ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B )
          = ( hAPP @ ( hAPP @ ( 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(2469,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
       != ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
     => ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B )
            = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B )
            = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(654,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(3527,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)],[654]) ).

thf(713,axiom,
    class_Rings_Oordered__comm__semiring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).

thf(3702,plain,
    class_Rings_Oordered__comm__semiring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).

thf(444,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) @ B )
      <=> ( A
          = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel1) ).

thf(2880,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
     => ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) @ B )
         => ( A
            = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
        & ( ( A
            = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
         => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(830,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(4042,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)],[830]) ).

thf(4043,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      = A ),
    inference(cnf,[status(esa)],[4042]) ).

thf(4044,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      = A ),
    inference(lifteq,[status(thm)],[4043]) ).

thf(20655,plain,
    ! [A: $i] :
      ( ( v_mzh != v_da____ )
      | ( A != v_mazh )
      | ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       != ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ v_mazh @ v_ma ) ) ),
    inference(paramod_ordered,[status(thm)],[4044,14811]) ).

thf(20661,plain,
    ( ( v_mzh != v_da____ )
    | ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( v_mazh != v_mazh )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_ma ) ),
    inference(simp,[status(thm)],[20655]) ).

thf(20687,plain,
    ( ( v_mzh != v_da____ )
    | ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_ma ) ),
    inference(simp,[status(thm)],[20661]) ).

thf(835,axiom,
    class_Rings_Osemiring__0 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).

thf(4050,plain,
    class_Rings_Osemiring__0 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).

thf(807,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(3973,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)],[807]) ).

thf(194,axiom,
    ! [A: $i,B: $i] :
      ( ( B != A )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
       => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oneq__le__trans) ).

thf(1978,plain,
    ! [A: $i,B: $i] :
      ( ( B != A )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
       => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(64148,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( class_Rings_Ocomm__semiring__1 @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      | ( A
       != ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
    inference(paramod_ordered,[status(thm)],[4121,63991]) ).

thf(64149,plain,
    ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
    | ( class_Rings_Ocomm__semiring__1 @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(pattern_uni,[status(thm)],[64148:[bind(A,$thf( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ))]]) ).

thf(29259,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[24861,1417]) ).

thf(29260,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[29259:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ) ) ) ))]]) ).

thf(351,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(2540,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)],[351]) ).

thf(208,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
        <=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).

thf(2034,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) )
          & ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(93,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).

thf(1581,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(1060,axiom,
    class_Power_Opower @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).

thf(4686,plain,
    class_Power_Opower @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).

thf(1096,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(4783,plain,
    class_Groups_Oordered__ab__semigroup__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).

thf(81534,plain,
    ! [B: $i,A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ A ) )
     != ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ B ) ),
    inference(paramod_ordered,[status(thm)],[2496,81500]) ).

thf(81595,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Nat_Onat != tc_Nat_Onat )
      | ( A
       != ( c_Nat_OSuc @ B ) )
      | ( ( c_Nat_OSuc @ A )
       != B ) ),
    inference(simp,[status(thm)],[81534]) ).

thf(81639,plain,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) )
     != A ),
    inference(simp,[status(thm)],[81595]) ).

thf(9,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Oab__group__add @ E )
     => ( ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ E ) @ ( c_Polynomial_OpCons @ E @ D @ C ) @ ( c_Polynomial_OpCons @ E @ B @ A ) )
        = ( c_Polynomial_OpCons @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ E ) @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__pCons) ).

thf(1281,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Groups_Oab__group__add @ E )
     => ( ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ E ) @ ( c_Polynomial_OpCons @ E @ D @ C ) @ ( c_Polynomial_OpCons @ E @ B @ A ) )
        = ( c_Polynomial_OpCons @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ E ) @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(1282,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Groups_Oab__group__add @ E )
      | ( ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ E ) @ ( c_Polynomial_OpCons @ E @ D @ C ) @ ( c_Polynomial_OpCons @ E @ B @ A ) )
        = ( c_Polynomial_OpCons @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ E ) @ C @ A ) ) ) ),
    inference(cnf,[status(esa)],[1281]) ).

thf(1283,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ E ) @ ( c_Polynomial_OpCons @ E @ D @ C ) @ ( c_Polynomial_OpCons @ E @ B @ A ) )
        = ( c_Polynomial_OpCons @ E @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_Polynomial_Opoly @ E ) @ C @ A ) ) )
      | ~ ( class_Groups_Oab__group__add @ E ) ),
    inference(lifteq,[status(thm)],[1282]) ).

thf(221,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(2073,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)],[221]) ).

thf(814,axiom,
    class_Groups_Ocomm__monoid__mult @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).

thf(3986,plain,
    class_Groups_Ocomm__monoid__mult @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).

thf(1227,axiom,
    class_Rings_Olinordered__semiring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).

thf(5101,plain,
    class_Rings_Olinordered__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).

thf(67493,plain,
    ! [A: $i] :
      ( ( class_Orderings_Oord @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Olinordered__idom @ tc_RealDef_Oreal )
       != ( class_Rings_Olinordered__idom @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4968,1519]) ).

thf(67494,plain,
    class_Orderings_Oord @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ),
    inference(pattern_uni,[status(thm)],[67493:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(67549,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( class_Orderings_Oord @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      | ( A
       != ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ),
    inference(paramod_ordered,[status(thm)],[4121,67494]) ).

thf(67550,plain,
    ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) )
    | ( class_Orderings_Oord @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(pattern_uni,[status(thm)],[67549:[bind(A,$thf( tc_Polynomial_Opoly @ tc_RealDef_Oreal ))]]) ).

thf(829,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(4040,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)],[829]) ).

thf(469,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
        <=> ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__divide__less__eq) ).

thf(2965,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
           => ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) )
          & ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
           => ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(1245,axiom,
    class_Rings_Olinordered__semiring__1__strict @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).

thf(5137,plain,
    class_Rings_Olinordered__semiring__1__strict @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).

thf(396,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(2718,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)],[396]) ).

thf(1206,axiom,
    class_Fields_Ofield @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield) ).

thf(5045,plain,
    class_Fields_Ofield @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).

thf(341,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(2508,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)],[341]) ).

thf(1075,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(4718,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)],[1075]) ).

thf(1082,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(4751,plain,
    class_Groups_Oordered__ab__group__add__abs @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).

thf(307,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(2367,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Orderings_Oorder @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(86702,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != A )
      | ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) ) )
       != ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2178,86058]) ).

thf(86753,plain,
    ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) )
   != ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(simp,[status(thm)],[86702]) ).

thf(92643,plain,
    ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) )
   != ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
    inference(rewrite,[status(thm)],[86753,2178]) ).

thf(520,axiom,
    ! [A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) )
    <=> ( A
        = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__real__square__gt__zero) ).

thf(3128,plain,
    ! [A: $i] :
      ( ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) )
       => ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
      & ( ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(3129,plain,
    ( ! [A: $i] :
        ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) )
       => ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
    & ! [A: $i] :
        ( ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) ) ) ),
    inference(miniscope,[status(thm)],[3128]) ).

thf(3130,plain,
    ! [A: $i] :
      ( ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) ) ),
    inference(cnf,[status(esa)],[3129]) ).

thf(3132,plain,
    ! [A: $i] :
      ( ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) ) ),
    inference(lifteq,[status(thm)],[3130]) ).

thf(3133,plain,
    ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(simp,[status(thm)],[3132]) ).

thf(5358,plain,
    ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ v_cs____ @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,3133]) ).

thf(5361,plain,
    ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ v_cs____ @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[5358]) ).

thf(6569,plain,
    ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ v_cs____ @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ v_cs____ ) )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_RealDef_Oreal )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,5361]) ).

thf(6593,plain,
    ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ v_cs____ @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ v_cs____ ) )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_RealDef_Oreal )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[6569]) ).

thf(6594,plain,
    ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ v_cs____ @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ v_cs____ ) )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[6593]) ).

thf(6620,plain,
    ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ v_cs____ @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ v_cs____ ) @ v_cs____ ) )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_RealDef_Oreal )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,6594]) ).

thf(6639,plain,
    ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ v_cs____ @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ v_cs____ ) @ v_cs____ ) )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_RealDef_Oreal )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[6620]) ).

thf(6648,plain,
    ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ v_cs____ @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ v_cs____ ) @ v_cs____ ) )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[6639]) ).

thf(838,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(4055,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)],[838]) ).

thf(32,axiom,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ B ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__zpower__abs) ).

thf(1377,plain,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ B ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(1141,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(4935,plain,
    class_Rings_Odivision__ring__inverse__zero @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).

thf(371,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
       => ( ( c_Rings_Odvd__class_Odvd @ D @ B @ A )
         => ( c_Rings_Odvd__class_Odvd @ D @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__trans) ).

thf(2618,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
       => ( ( c_Rings_Odvd__class_Odvd @ D @ B @ A )
         => ( c_Rings_Odvd__class_Odvd @ D @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(430,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ F ) @ E ) @ D )
        = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ D @ F )
         => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
           => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
             => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ F )
               => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ E ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).

thf(2833,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ F ) @ E ) @ D )
        = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ D @ F )
         => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
           => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
             => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ F )
               => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ E ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(824,axiom,
    c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).

thf(4027,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).

thf(13915,plain,
    ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
   != ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_da____ @ v_mazh ) ),
    inference(paramod_ordered,[status(thm)],[4027,1263]) ).

thf(13945,plain,
    ( ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
     != v_da____ )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
     != v_mazh ) ),
    inference(simp,[status(thm)],[13915]) ).

thf(14348,plain,
    ( ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( v_cs____ != v_da____ )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
     != v_mazh )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,13945]) ).

thf(14361,plain,
    ( ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( v_cs____ != v_da____ )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
     != v_mazh )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[14348]) ).

thf(1222,axiom,
    class_Groups_Omonoid__mult @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).

thf(5096,plain,
    class_Groups_Omonoid__mult @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).

thf(258,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).

thf(2190,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(995,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(4504,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)],[995]) ).

thf(145,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).

thf(1796,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(493,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Complex_Orcis @ D @ C ) ) @ ( c_Complex_Orcis @ B @ A ) )
      = ( c_Complex_Orcis @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ D ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rcis__mult) ).

thf(3036,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Complex_Orcis @ D @ C ) ) @ ( c_Complex_Orcis @ B @ A ) )
      = ( c_Complex_Orcis @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ D ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(103,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(1622,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)],[103]) ).

thf(322,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).

thf(2424,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(474,axiom,
    ! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__refl) ).

thf(2979,plain,
    ! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(927,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(4307,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)],[927]) ).

thf(22240,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_c____ )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) @ v_c____ ) ) ),
    inference(paramod_ordered,[status(thm)],[1527,15079]) ).

thf(22251,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_c____ )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
      | ( A != v_c____ ) ),
    inference(simp,[status(thm)],[22240]) ).

thf(22271,plain,
    ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_c____ )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
    inference(simp,[status(thm)],[22251]) ).

thf(1107,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(4825,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)],[1107]) ).

thf(48,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).

thf(1433,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(231,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
     => ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
       => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__less__trans) ).

thf(2103,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
     => ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
       => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(407,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(2750,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)],[407]) ).

thf(676,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(3588,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)],[676]) ).

thf(1125,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(4892,plain,
    ! [A: $i] :
      ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).

thf(120,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Oone__class_Oone @ D ) )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__decreasing) ).

thf(1697,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Oone__class_Oone @ D ) )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(893,axiom,
    class_Rings_Ono__zero__divisors @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).

thf(4211,plain,
    class_Rings_Ono__zero__divisors @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).

thf(538,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( c_Rings_Odvd__class_Odvd @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__right) ).

thf(3184,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( c_Rings_Odvd__class_Odvd @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(984,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(4475,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)],[984]) ).

thf(363,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ E )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).

thf(2586,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ E )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(193,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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(1975,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(849,axiom,
    class_Rings_Oordered__comm__semiring @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).

thf(4082,plain,
    class_Rings_Oordered__comm__semiring @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).

thf(987,axiom,
    class_Rings_Oidom @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).

thf(4483,plain,
    class_Rings_Oidom @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).

thf(5297,plain,
    ! [A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ v_cs____ )
      | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,3258]) ).

thf(5298,plain,
    ! [A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ v_cs____ )
      | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
       != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[5297]) ).

thf(455,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(2922,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)],[455]) ).

thf(484,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).

thf(3011,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(668,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(3567,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)],[668]) ).

thf(49,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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(1436,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
          = ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(1437,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Fields_Ofield__inverse__zero @ D )
      | ( C
        = ( c_Groups_Ozero__class_Ozero @ D ) )
      | ( ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
        = ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ),
    inference(cnf,[status(esa)],[1436]) ).

thf(1438,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( c_Groups_Ozero__class_Ozero @ D ) )
      | ( ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
        = ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
      | ~ ( class_Fields_Ofield__inverse__zero @ D ) ),
    inference(lifteq,[status(thm)],[1437]) ).

thf(539,axiom,
    ! [A: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
    <=> ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A )
        = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd1__eq) ).

thf(3186,plain,
    ! [A: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
       => ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A )
          = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
      & ( ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A )
          = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
       => ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(1198,axiom,
    class_RealVector_Oreal__normed__vector @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).

thf(5034,plain,
    class_RealVector_Oreal__normed__vector @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).

thf(1134,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(4910,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)],[1134]) ).

thf(25262,plain,
    ! [A: $i] :
      ( ( ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ A )
       != ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
      | ( ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A )
       != ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4759,15632]) ).

thf(25284,plain,
    ! [A: $i] :
      ( ( ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ A )
       != ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
      | ( tc_Int_Oint != tc_RealDef_Oreal )
      | ( A
       != ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
    inference(simp,[status(thm)],[25262]) ).

thf(25288,plain,
    ( ( ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
     != ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
    | ( tc_Int_Oint != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[25284]) ).

thf(202,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(2011,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)],[202]) ).

thf(512,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(3097,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)],[512]) ).

thf(765,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(3857,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)],[765]) ).

thf(1259,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(5157,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)],[1259]) ).

thf(649,axiom,
    class_Rings_Olinordered__semiring__1__strict @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).

thf(3503,plain,
    class_Rings_Olinordered__semiring__1__strict @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(633,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(3459,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)],[633]) ).

thf(431,axiom,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).

thf(2836,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(2837,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      = A ),
    inference(cnf,[status(esa)],[2836]) ).

thf(2838,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      = A ),
    inference(lifteq,[status(thm)],[2837]) ).

thf(47850,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
       != ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2838,37077]) ).

thf(47918,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) )
       != ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) )
      | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != A ) ),
    inference(simp,[status(thm)],[47850]) ).

thf(47981,plain,
    ! [A: $i] :
      ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) )
     != ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[47918]) ).

thf(934,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(4323,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)],[934]) ).

thf(677,axiom,
    class_Groups_Ocomm__monoid__add @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).

thf(3591,plain,
    class_Groups_Ocomm__monoid__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(263,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).

thf(2204,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(1158,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(4962,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)],[1158]) ).

thf(1025,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(4589,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)],[1025]) ).

thf(962,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(4407,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)],[962]) ).

thf(813,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(3984,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)],[813]) ).

thf(565,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(3265,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)],[565]) ).

thf(1336,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
      | ( A
       != ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      | ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) @ B ) ),
    inference(cnf,[status(esa)],[1334]) ).

thf(1338,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      | ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
      | ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) @ B ) ),
    inference(lifteq,[status(thm)],[1336]) ).

thf(1339,plain,
    ! [A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) @ A ) ),
    inference(simp,[status(thm)],[1338]) ).

thf(18405,plain,
    ! [B: $i,A: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ B ) @ B )
      | ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Nat_OSuc @ A ) )
       != ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2496,1339]) ).

thf(18406,plain,
    c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(pattern_uni,[status(thm)],[18405:[bind(A,$thf( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )),bind(B,$thf( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ))]]) ).

thf(43716,plain,
    c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ),
    inference(rewrite,[status(thm)],[18406,2178,2728]) ).

thf(1235,axiom,
    class_Rings_Osemiring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).

thf(5117,plain,
    class_Rings_Osemiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).

thf(1466,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Groups_Osgn__if @ 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 ) ) ),
    inference(cnf,[status(esa)],[1463]) ).

thf(1470,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( c_Groups_Ozero__class_Ozero @ B ) )
      | ( ( c_Groups_Osgn__class_Osgn @ B @ A )
        = ( c_Groups_Oone__class_Oone @ B ) )
      | ~ ( class_Groups_Osgn__if @ B )
      | ~ ( c_Orderings_Oord__class_Oless @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ A ) ),
    inference(lifteq,[status(thm)],[1466]) ).

thf(143,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(1783,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)],[143]) ).

thf(54218,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Int_Oint @ tc_Nat_Onat )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Int_Oint ) ) ),
    inference(paramod_ordered,[status(thm)],[1527,47061]) ).

thf(54247,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Int_Oint @ tc_Nat_Onat )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != tc_Nat_Onat )
      | ( A != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[54218]) ).

thf(54275,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Int_Oint @ tc_Nat_Onat )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[54247]) ).

thf(64890,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != tc_Nat_Onat )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Complex_Ocomplex @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Int_Oint @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[54352,54275]) ).

thf(64926,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != tc_Nat_Onat )
      | ( tc_Nat_Onat != tc_Complex_Ocomplex )
      | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
       != tc_Int_Oint )
      | ( A != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[64890]) ).

thf(64946,plain,
    ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != tc_Nat_Onat )
    | ( tc_Nat_Onat != tc_Complex_Ocomplex )
    | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
     != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[64926]) ).

thf(953,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(4370,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)],[953]) ).

thf(403,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(2737,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)],[403]) ).

thf(289,axiom,
    ! [A: $i,B: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
      = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).

thf(2296,plain,
    ! [A: $i,B: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
      = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(1022,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(4576,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)],[1022]) ).

thf(224,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
     => ( ( B = A )
       => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__le__eq__trans) ).

thf(2083,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
     => ( ( B = A )
       => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(827,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(4031,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)],[827]) ).

thf(24699,plain,
    ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_c____ )
    | ( tc_Nat_Onat != tc_Complex_Ocomplex ) ),
    inference(simp,[status(thm)],[24060]) ).

thf(165,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( c_Groups_Oabs__class_Oabs @ B @ A )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__sgn) ).

thf(1868,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( c_Groups_Oabs__class_Oabs @ B @ A )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Osgn__class_Osgn @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(417,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(2773,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)],[417]) ).

thf(1177,axiom,
    class_Rings_Ozero__neq__one @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).

thf(4999,plain,
    class_Rings_Ozero__neq__one @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).

thf(367,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(2601,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ominus @ B )
     => ( class_Groups_Ominus @ ( tc_fun @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(973,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(4434,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)],[973]) ).

thf(46680,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ B )
        = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
      | ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
       != ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[4626,4907]) ).

thf(46681,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
      = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
    inference(pattern_uni,[status(thm)],[46680:[bind(A,$thf( D )),bind(B,$thf( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ D ))]]) ).

thf(46754,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
      = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
    inference(simp,[status(thm)],[46681]) ).

thf(993,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(4499,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)],[993]) ).

thf(990,axiom,
    class_Groups_Oab__semigroup__mult @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).

thf(4493,plain,
    class_Groups_Oab__semigroup__mult @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).

thf(86700,plain,
    ! [A: $i] :
      ( ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
       != A )
      | ( ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       != ( c_Nat_OSuc @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2178,86058]) ).

thf(86701,plain,
    ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
   != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(pattern_uni,[status(thm)],[86700:[bind(A,$thf( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ))]]) ).

thf(1209,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(5049,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)],[1209]) ).

thf(364,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) )
    <=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
        & ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).

thf(2589,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
          & ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) ) )
      & ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
          & ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(35,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oring @ C )
     => ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( 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(1387,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oring @ C )
     => ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(173,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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(1900,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ D )
     => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(128,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(1723,plain,
    ! [A: $i] :
      ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != ( c_Nat_OSuc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(562,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(3261,plain,
    class_Rings_Olinordered__comm__semiring__strict @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(1071,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(4712,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)],[1071]) ).

thf(25,axiom,
    ! [A: $i] :
      ( A
     != ( c_Nat_OSuc @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).

thf(1343,plain,
    ! [A: $i] :
      ( A
     != ( c_Nat_OSuc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(821,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(4016,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)],[821]) ).

thf(356,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono1) ).

thf(2560,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(959,axiom,
    class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).

thf(4397,plain,
    class_Groups_Ocomm__monoid__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).

thf(92,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
     => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incr__lemma) ).

thf(1579,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
     => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(1580,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
      | ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ A @ B ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ C ) ) ) ),
    inference(cnf,[status(esa)],[1579]) ).

thf(283,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(2277,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)],[283]) ).

thf(1173,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(4989,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)],[1173]) ).

thf(114,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
     => ( ! [D: $i] :
            ( ( hBOOL @ ( hAPP @ B @ D ) )
           => ( hBOOL @ ( hAPP @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ D @ C ) ) ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
         => ! [D: $i] :
              ( ( hBOOL @ ( hAPP @ B @ D ) )
             => ( hBOOL @ ( hAPP @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incr__mult__lemma) ).

thf(1676,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
     => ( ! [D: $i] :
            ( ( hBOOL @ ( hAPP @ B @ D ) )
           => ( hBOOL @ ( hAPP @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ D @ C ) ) ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
         => ! [D: $i] :
              ( ( hBOOL @ ( hAPP @ B @ D ) )
             => ( hBOOL @ ( hAPP @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(488,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Odivision__ring @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
        = ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__eq__right) ).

thf(3022,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Odivision__ring @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
        = ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(66934,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[65892,1510]) ).

thf(66935,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[66934:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ))]]) ).

thf(67610,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[66935,1510]) ).

thf(67611,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[67610:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ))]]) ).

thf(1004,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(4521,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)],[1004]) ).

thf(864,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(4128,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)],[864]) ).

thf(501,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( 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(3069,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( 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)],[501]) ).

thf(605,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(3371,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)],[605]) ).

thf(891,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(4204,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)],[891]) ).

thf(155,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_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
      <=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel1) ).

thf(1824,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_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
         => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) )
        & ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
         => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(919,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Olinordered__semiring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).

thf(4284,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Olinordered__semiring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).

thf(751,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(3816,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)],[751]) ).

thf(102,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__ring__1 @ B )
     => ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).

thf(1619,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__ring__1 @ B )
     => ( ( c_Groups_Ouminus__class_Ouminus @ B @ A )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(1228,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(5102,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)],[1228]) ).

thf(67729,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[67037,1510]) ).

thf(67730,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[67729:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ))]]) ).

thf(68419,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[67730,1510]) ).

thf(68420,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[68419:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ))]]) ).

thf(750,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(3814,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)],[750]) ).

thf(54748,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Complex_Ocomplex @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ v_da____ ) ) ),
    inference(paramod_ordered,[status(thm)],[54352,17349]) ).

thf(54800,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh )
      | ( tc_Nat_Onat != tc_Complex_Ocomplex )
      | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
       != v_mazh )
      | ( A != v_da____ ) ),
    inference(simp,[status(thm)],[54748]) ).

thf(54833,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh )
    | ( tc_Nat_Onat != tc_Complex_Ocomplex )
    | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
     != v_mazh ) ),
    inference(simp,[status(thm)],[54800]) ).

thf(319,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 @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__power) ).

thf(2414,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 @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(88,axiom,
    ! [A: $i,B: $i] :
      ( ( B = A )
    <=> ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
        & ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oeq__iff) ).

thf(1560,plain,
    ! [A: $i,B: $i] :
      ( ( ( B = A )
       => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
          & ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ) )
      & ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
          & ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(332,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(2464,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)],[332]) ).

thf(92300,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) )
       != ( class_Rings_Ocomm__ring @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[90446,1575]) ).

thf(92301,plain,
    class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[92300:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ))]]) ).

thf(219,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 ) @ ( hAPP @ ( hAPP @ ( 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(2068,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 ) @ ( hAPP @ ( hAPP @ ( 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)],[219]) ).

thf(790,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(3926,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)],[790]) ).

thf(1288,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Groups_Ozero @ E )
      | ( ( c_Polynomial_OpCons @ E @ D @ C )
       != ( c_Polynomial_OpCons @ E @ B @ A ) )
      | ( C = A ) ),
    inference(cnf,[status(esa)],[1287]) ).

thf(1291,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Polynomial_OpCons @ E @ D @ C )
       != ( c_Polynomial_OpCons @ E @ B @ A ) )
      | ( C = A )
      | ~ ( class_Groups_Ozero @ E ) ),
    inference(lifteq,[status(thm)],[1288]) ).

thf(77,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).

thf(1528,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(1529,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
      | ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
      | ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
    inference(cnf,[status(esa)],[1528]) ).

thf(70256,plain,
    ! [B: $i,A: $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_Oone__class_Oone @ tc_Nat_Onat ) @ A )
      | ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
    inference(rewrite,[status(thm)],[1529,2178]) ).

thf(582,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(3307,plain,
    class_Groups_Oordered__ab__semigroup__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(569,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(3271,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)],[569]) ).

thf(328,axiom,
    ! [A: $i,B: $i] :
      ( ( B = A )
     => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oeq__refl) ).

thf(2445,plain,
    ! [A: $i,B: $i] :
      ( ( B = A )
     => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(61142,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( A != v_da____ )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_mazh )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[4121,18838]) ).

thf(61143,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( A != v_da____ )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_mazh ) ),
    inference(pattern_uni,[status(thm)],[61142:[]]) ).

thf(63777,plain,
    ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ v_da____ )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_mazh ) ),
    inference(simp,[status(thm)],[61143]) ).

thf(811,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(3980,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)],[811]) ).

thf(159,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(1837,plain,
    ! [A: $i] :
      ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != ( c_Nat_OSuc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(97,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(1592,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)],[97]) ).

thf(1593,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: $i] :
        ( ( 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(miniscope,[status(thm)],[1592]) ).

thf(1596,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 ) ) ),
    inference(cnf,[status(esa)],[1593]) ).

thf(1601,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 ) ) ),
    inference(lifteq,[status(thm)],[1596]) ).

thf(1602,plain,
    ( ( c_Groups_Osgn__class_Osgn @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[1601]) ).

thf(1113,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(4849,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).

thf(29,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C = B )
     => ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
       => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__eq__less__trans) ).

thf(1365,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C = B )
     => ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
       => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(375,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) )
           => ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).

thf(2628,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) )
           => ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(618,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(3403,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)],[618]) ).

thf(21602,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( ( c_Nat_OSuc @ A )
       != v_mzh )
      | ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       != ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ v_mazh @ v_ma ) ) ),
    inference(paramod_ordered,[status(thm)],[4044,14801]) ).

thf(21622,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( ( c_Nat_OSuc @ A )
       != v_mzh )
      | ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( A != v_mazh )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_ma ) ),
    inference(simp,[status(thm)],[21602]) ).

thf(21641,plain,
    ( ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( ( c_Nat_OSuc @ v_mazh )
     != v_mzh )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_ma ) ),
    inference(simp,[status(thm)],[21622]) ).

thf(300,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__order) ).

thf(2332,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(427,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Osemiring @ E )
     => ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( 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(2826,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Osemiring @ E )
     => ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C ) @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Oplus__class_Oplus @ E @ D @ B ) ) @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(424,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(2813,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Nat_OSuc @ B )
        = ( c_Nat_OSuc @ A ) )
     => ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(2814,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Nat_OSuc @ B )
       != ( c_Nat_OSuc @ A ) )
      | ( B = A ) ),
    inference(cnf,[status(esa)],[2813]) ).

thf(2815,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Nat_OSuc @ B )
       != ( c_Nat_OSuc @ A ) )
      | ( B = A ) ),
    inference(lifteq,[status(thm)],[2814]) ).

thf(2816,plain,
    ! [A: $i] :
      ( ( sk16 @ ( c_Nat_OSuc @ A ) )
      = A ),
    introduced(tautology,[new_symbols(inverse(c_Nat_OSuc),[sk16])]) ).

thf(16789,plain,
    ! [A: $i] :
      ( ( ( sk16 @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
        = A )
      | ( ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       != ( c_Nat_OSuc @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2178,2816]) ).

thf(16790,plain,
    ( ( sk16 @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
    = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(pattern_uni,[status(thm)],[16789:[bind(A,$thf( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ))]]) ).

thf(873,axiom,
    class_Rings_Olinordered__semidom @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).

thf(4155,plain,
    class_Rings_Olinordered__semidom @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).

thf(426,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
    <=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
        & ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).

thf(2820,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
          & ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) )
      & ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
          & ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(522,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ) )
       => ( B
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rabs__ratiotest__lemma) ).

thf(3137,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ A ) ) )
       => ( B
          = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(729,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
        <=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__le__divide__eq) ).

thf(3750,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A ) )
          & ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).

thf(20728,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_mazh )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh ) ) ),
    inference(paramod_ordered,[status(thm)],[3170,17638]) ).

thf(20746,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_mazh )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( A != v_da____ )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_mazh ) ),
    inference(simp,[status(thm)],[20728]) ).

thf(20756,plain,
    ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_mazh )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_mazh ) ),
    inference(simp,[status(thm)],[20746]) ).

thf(20901,plain,
    ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_mazh )
    | ( v_cs____ != v_mazh )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,20756]) ).

thf(20912,plain,
    ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_mazh )
    | ( v_cs____ != v_mazh )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[20901]) ).

thf(956,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(4385,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)],[956]) ).

thf(1186,axiom,
    class_Rings_Olinordered__ring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).

thf(5021,plain,
    class_Rings_Olinordered__ring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).

thf(1013,axiom,
    class_Orderings_Olinorder @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).

thf(4553,plain,
    class_Orderings_Olinorder @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).

thf(682,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(3600,plain,
    class_Groups_Olinordered__ab__group__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

thf(54,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono) ).

thf(1456,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(1457,plain,
    ! [D: $i,C: $i,B: $i,A: $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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ),
    inference(cnf,[status(esa)],[1456]) ).

thf(883,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(4187,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)],[883]) ).

thf(253,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__div__algebra @ C )
     => ( ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__power) ).

thf(2179,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__div__algebra @ C )
     => ( ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(525,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ B )
     => ( ( hAPP @ ( hAPP @ ( 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(3144,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ B )
     => ( ( hAPP @ ( hAPP @ ( 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)],[525]) ).

thf(1080,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(4746,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)],[1080]) ).

thf(158,axiom,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( 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(1834,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( 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)],[158]) ).

thf(1835,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A )
      = A ),
    inference(cnf,[status(esa)],[1834]) ).

thf(1836,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A )
      = A ),
    inference(lifteq,[status(thm)],[1835]) ).

thf(1225,axiom,
    class_Orderings_Oord @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oord) ).

thf(5099,plain,
    class_Orderings_Oord @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).

thf(80,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(1535,plain,
    ! [A: $i,B: $i] :
      ( ( class_Orderings_Oord @ B )
     => ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(1536,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ B )
      | ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
    inference(cnf,[status(esa)],[1535]) ).

thf(77422,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Oord @ ( tc_fun @ A @ B ) )
      | ( ( class_Orderings_Oord @ tc_RealDef_Oreal )
       != ( class_Orderings_Oord @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[5099,1536]) ).

thf(77423,plain,
    ! [A: $i] : ( class_Orderings_Oord @ ( tc_fun @ A @ tc_RealDef_Oreal ) ),
    inference(pattern_uni,[status(thm)],[77422:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal ))]]) ).

thf(1146,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(4942,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)],[1146]) ).

thf(298,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ C ) @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) ) @ C ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).

thf(2327,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ C ) @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ D @ B ) ) @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(267,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__ring__1 @ C )
     => ( ( c_Groups_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__diff) ).

thf(2213,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__ring__1 @ C )
     => ( ( c_Groups_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ominus__class_Ominus @ C @ B @ A ) ) @ ( c_Groups_Oplus__class_Oplus @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(87328,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
       != ( class_Rings_Ocomm__ring @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[87185,1575]) ).

thf(87329,plain,
    class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
    inference(pattern_uni,[status(thm)],[87328:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ))]]) ).

thf(89026,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) )
       != ( class_Rings_Ocomm__ring @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[87329,1575]) ).

thf(89027,plain,
    class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ),
    inference(pattern_uni,[status(thm)],[89026:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ))]]) ).

thf(90245,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) )
       != ( class_Rings_Ocomm__ring @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[89027,1575]) ).

thf(90246,plain,
    class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[90245:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ))]]) ).

thf(14509,plain,
    ! [A: $i] :
      ( ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
       != tc_Nat_Onat )
      | ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ v_cs____ )
       != ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_c____ ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4081,5298]) ).

thf(14545,plain,
    ! [A: $i] :
      ( ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
       != tc_Nat_Onat )
      | ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( A
       != ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_c____ )
       != v_cs____ ) ),
    inference(simp,[status(thm)],[14509]) ).

thf(14565,plain,
    ( ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat )
    | ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_c____ )
     != v_cs____ ) ),
    inference(simp,[status(thm)],[14545]) ).

thf(293,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(2313,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)],[293]) ).

thf(48077,plain,
    ! [A: $i] :
      ( ( A
       != ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
       != ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2838,47949]) ).

thf(48113,plain,
    ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) )
     != ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
    inference(simp,[status(thm)],[48077]) ).

thf(48145,plain,
    ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) )
   != ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[48113]) ).

thf(855,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(4102,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)],[855]) ).

thf(4103,plain,
    ! [A: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ A )
      = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(cnf,[status(esa)],[4102]) ).

thf(4104,plain,
    ! [A: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ A )
      = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(lifteq,[status(thm)],[4103]) ).

thf(722,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(3727,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)],[722]) ).

thf(134,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Omonoid__mult @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__commutes) ).

thf(1740,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Omonoid__mult @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(175,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
       => ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B )
            = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
        <=> ( B = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__exp) ).

thf(1910,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
       => ( ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B )
              = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
           => ( B = A ) )
          & ( ( B = A )
           => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B )
              = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(680,axiom,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ A )
     => ( class_Groups_Oab__semigroup__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).

thf(3595,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ A )
     => ( class_Groups_Oab__semigroup__mult @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(931,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(4316,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)],[931]) ).

thf(1402,plain,
    ! [C: $i,B: $i,A: $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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ),
    inference(cnf,[status(esa)],[1401]) ).

thf(311,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(2377,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)],[311]) ).

thf(62231,plain,
    ! [B: $i,A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != B )
      | ( A
       != ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4121,45743]) ).

thf(62232,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != A ) ),
    inference(pattern_uni,[status(thm)],[62231:[bind(A,$thf( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ D @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )),bind(B,$thf( D ))]]) ).

thf(63419,plain,
    c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ),
    inference(simp,[status(thm)],[62232]) ).

thf(81560,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ A )
     != ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ),
    inference(paramod_ordered,[status(thm)],[63419,81500]) ).

thf(81579,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( c_Nat_OSuc @ A )
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      | ( A
       != ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ),
    inference(simp,[status(thm)],[81560]) ).

thf(81619,plain,
    ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
   != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[81579]) ).

thf(16081,plain,
    ( ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( v_cs____ != v_da____ )
    | ( v_cs____ != v_mazh )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Int_Oint )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,14361]) ).

thf(16092,plain,
    ( ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( v_cs____ != v_da____ )
    | ( v_cs____ != v_mazh )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Int_Oint )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[16081]) ).

thf(16108,plain,
    ( ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( v_cs____ != v_da____ )
    | ( v_cs____ != v_mazh )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[16092]) ).

thf(715,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(3704,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)],[715]) ).

thf(1220,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(5081,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)],[1220]) ).

thf(698,axiom,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring__1 @ A )
     => ( class_Rings_Oring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).

thf(3650,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring__1 @ A )
     => ( class_Rings_Oring__1 @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(69313,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[68154,1510]) ).

thf(69314,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[69313:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ))]]) ).

thf(808,axiom,
    class_Orderings_Oord @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).

thf(3975,plain,
    class_Orderings_Oord @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).

thf(77424,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Oord @ ( tc_fun @ A @ B ) )
      | ( ( class_Orderings_Oord @ tc_Int_Oint )
       != ( class_Orderings_Oord @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[3975,1536]) ).

thf(77425,plain,
    ! [A: $i] : ( class_Orderings_Oord @ ( tc_fun @ A @ tc_Int_Oint ) ),
    inference(pattern_uni,[status(thm)],[77424:[bind(A,$thf( A )),bind(B,$thf( tc_Int_Oint ))]]) ).

thf(17335,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_da____ )
      | ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ A )
       != ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ v_mazh ) ) ),
    inference(paramod_ordered,[status(thm)],[4980,13692]) ).

thf(17373,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_da____ )
      | ( tc_RealDef_Oreal != tc_RealDef_Oreal )
      | ( A
       != ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      | ( A != v_mazh ) ),
    inference(simp,[status(thm)],[17335]) ).

thf(17395,plain,
    ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_da____ )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_mazh ) ),
    inference(simp,[status(thm)],[17373]) ).

thf(338,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semidom @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__Suc__le__self) ).

thf(2498,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semidom @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(780,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(3909,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)],[780]) ).

thf(82,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono) ).

thf(1540,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(1541,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ),
    inference(cnf,[status(esa)],[1540]) ).

thf(195,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Oring @ E )
     => ( ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( 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(1983,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Oring @ E )
     => ( ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(1154,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(4957,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).

thf(1210,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(5053,plain,
    class_Groups_Oordered__ab__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).

thf(1224,axiom,
    class_Rings_Olinordered__ring__strict @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).

thf(5098,plain,
    class_Rings_Olinordered__ring__strict @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).

thf(187,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) ) @ A )
        = ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__divide) ).

thf(1953,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) ) @ A )
        = ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(85923,plain,
    ! [B: $i,A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ A ) )
     != ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ B ) ) @ B ) ),
    inference(paramod_ordered,[status(thm)],[3417,81608]) ).

thf(86022,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ B ) )
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      | ( ( c_Nat_OSuc @ A )
       != B ) ),
    inference(simp,[status(thm)],[85923]) ).

thf(86053,plain,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[86022]) ).

thf(998,axiom,
    class_Rings_Ono__zero__divisors @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).

thf(4512,plain,
    class_Rings_Ono__zero__divisors @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).

thf(857,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(4108,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)],[857]) ).

thf(472,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
        <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing__iff) ).

thf(2973,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
       => ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ 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 @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(1883,plain,
    ( ! [A: $i,B: $i] :
        ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A )
          = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
       => ( ( A
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
          | ( B
            = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
    & ! [A: $i,B: $i] :
        ( ( ( A
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
          | ( B
            = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
       => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A )
          = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
    inference(miniscope,[status(thm)],[1882]) ).

thf(1885,plain,
    ! [B: $i,A: $i] :
      ( ( B
       != ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A )
        = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    inference(cnf,[status(esa)],[1883]) ).

thf(1889,plain,
    ! [B: $i,A: $i] :
      ( ( B
       != ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A )
        = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    inference(lifteq,[status(thm)],[1885]) ).

thf(1890,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A )
      = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(simp,[status(thm)],[1889]) ).

thf(49386,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
      = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
    inference(rewrite,[status(thm)],[1890,2178]) ).

thf(395,axiom,
    ! [A: $i,B: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
        = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
    <=> ( ( B
          = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
        & ( A
          = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).

thf(2709,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
          = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
       => ( ( B
            = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
          & ( A
            = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
      & ( ( ( B
            = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
          & ( A
            = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
       => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
          = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(191,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Ocomm__monoid__mult @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult__distrib) ).

thf(1970,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Ocomm__monoid__mult @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(547,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(3218,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)],[547]) ).

thf(833,axiom,
    class_Groups_Omonoid__add @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).

thf(4048,plain,
    class_Groups_Omonoid__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).

thf(75453,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[68420,1510]) ).

thf(75454,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[75453:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ) ))]]) ).

thf(1041,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ B )
     => ? [C: $i] :
          ( ( c_Orderings_Oord__class_Oless__eq @ 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 @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ononneg__bounded) ).

thf(4636,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ B )
     => ? [C: $i] :
          ( ( c_Orderings_Oord__class_Oless__eq @ 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 @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).

thf(66,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semidom @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less) ).

thf(1498,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semidom @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(95,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ E )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).

thf(1587,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ E )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(10145,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
      | ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ A @ v_da____ @ v_mazh )
      | ( B != tc_RealDef_Oreal ) ),
    inference(paramod_ordered,[status(thm)],[1362,1263]) ).

thf(10146,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_RealDef_Oreal @ A )
      | ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ tc_RealDef_Oreal )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ A @ v_da____ @ v_mazh ) ),
    inference(pattern_uni,[status(thm)],[10145:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal ))]]) ).

thf(15064,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_RealDef_Oreal @ B )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ B @ v_da____ @ v_mazh )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ tc_RealDef_Oreal ) ) ),
    inference(paramod_ordered,[status(thm)],[1527,10146]) ).

thf(15065,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
    | ~ ( c_Orderings_Oord__class_Oless__eq @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ v_da____ @ v_mazh ) ),
    inference(pattern_uni,[status(thm)],[15064:[bind(A,$thf( tc_RealDef_Oreal )),bind(B,$thf( c_Groups_Oone__class_Oone @ tc_Nat_Onat ))]]) ).

thf(45,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) ) @ A )
      = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).

thf(1425,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) ) @ A )
      = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(1065,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(4693,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)],[1065]) ).

thf(398,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__neg__lemma) ).

thf(2724,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(901,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(4227,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)],[901]) ).

thf(437,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(2858,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)],[437]) ).

thf(689,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(3632,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)],[689]) ).

thf(854,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(4095,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)],[854]) ).

thf(518,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semidom @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).

thf(3119,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semidom @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) @ ( c_Groups_Oone__class_Oone @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(505,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(3078,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)],[505]) ).

thf(1123,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(4883,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)],[1123]) ).

thf(784,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(3916,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)],[784]) ).

thf(553,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(3237,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)],[553]) ).

thf(798,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(3941,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)],[798]) ).

thf(543,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(3205,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( hAPP @ B @ C )
          = ( hAPP @ A @ C ) )
     => ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(897,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(4219,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)],[897]) ).

thf(280,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__left) ).

thf(2268,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(626,axiom,
    class_Groups_Oab__semigroup__add @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).

thf(3440,plain,
    class_Groups_Oab__semigroup__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(1128,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__field @ B )
     => ? [C: $i] :
        ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Rings_Oinverse__class_Odivide @ B @ D @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Obounded) ).

thf(4898,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__field @ B )
     => ? [C: $i] :
        ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( c_Rings_Oinverse__class_Odivide @ B @ D @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).

thf(913,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(4263,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)],[913]) ).

thf(933,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(4320,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)],[933]) ).

thf(1149,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(4951,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)],[1149]) ).

thf(184,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) ) @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).

thf(1942,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ C @ B ) ) @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(545,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).

thf(3210,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(77418,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Oord @ ( tc_fun @ A @ B ) )
      | ( ( class_Orderings_Oord @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) )
       != ( class_Orderings_Oord @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[67492,1536]) ).

thf(77419,plain,
    ! [A: $i] : ( class_Orderings_Oord @ ( tc_fun @ A @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ),
    inference(pattern_uni,[status(thm)],[77418:[bind(A,$thf( A )),bind(B,$thf( tc_Polynomial_Opoly @ tc_Int_Oint ))]]) ).

thf(260,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(2196,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)],[260]) ).

thf(42441,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A )
       != ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2728,37074]) ).

thf(42548,plain,
    ! [A: $i] :
      ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
       != ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) )
      | ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       != A ) ),
    inference(simp,[status(thm)],[42441]) ).

thf(42687,plain,
    ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
   != ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[42548]) ).

thf(355,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) )
         != ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).

thf(2551,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) )
           != ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ B ) ) ) )
        & ( ( ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) )
           != ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ B ) ) )
         => ( ( D != C )
            & ( B != A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(694,axiom,
    class_Groups_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).

thf(3643,plain,
    class_Groups_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).

thf(662,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(3555,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)],[662]) ).

thf(923,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(4291,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)],[923]) ).

thf(800,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(3954,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)],[800]) ).

thf(834,axiom,
    class_Rings_Ocomm__ring__1 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).

thf(4049,plain,
    class_Rings_Ocomm__ring__1 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).

thf(1048,axiom,
    class_Rings_Ocomm__semiring @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).

thf(4653,plain,
    class_Rings_Ocomm__semiring @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).

thf(1002,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(4518,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)],[1002]) ).

thf(591,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(3326,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)],[591]) ).

thf(1195,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(5031,plain,
    class_Groups_Ocancel__ab__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).

thf(4929,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: $i] :
        ( ( 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(miniscope,[status(thm)],[4928]) ).

thf(4930,plain,
    ! [A: $i] :
      ( ( 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(cnf,[status(esa)],[4929]) ).

thf(4932,plain,
    ! [A: $i] :
      ( ( 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(lifteq,[status(thm)],[4930]) ).

thf(4933,plain,
    c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[4932]) ).

thf(14613,plain,
    c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ),
    inference(rewrite,[status(thm)],[4933,2178]) ).

thf(1117,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(4858,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)],[1117]) ).

thf(4859,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
      = A ),
    inference(cnf,[status(esa)],[4858]) ).

thf(4860,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
      = A ),
    inference(lifteq,[status(thm)],[4859]) ).

thf(480,axiom,
    ! [A: $i,B: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( c_Nat_OSuc @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc__right) ).

thf(3000,plain,
    ! [A: $i,B: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ ( c_Nat_OSuc @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(536,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).

thf(3179,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(1168,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(4983,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)],[1168]) ).

thf(761,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(3846,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)],[761]) ).

thf(1219,axiom,
    class_Rings_Oring__1__no__zero__divisors @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).

thf(5080,plain,
    class_Rings_Oring__1__no__zero__divisors @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).

thf(1289,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Groups_Ozero @ E )
      | ( ( c_Polynomial_OpCons @ E @ D @ C )
       != ( c_Polynomial_OpCons @ E @ B @ A ) )
      | ( D = B ) ),
    inference(cnf,[status(esa)],[1287]) ).

thf(1292,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Polynomial_OpCons @ E @ D @ C )
       != ( c_Polynomial_OpCons @ E @ B @ A ) )
      | ( D = B )
      | ~ ( class_Groups_Ozero @ E ) ),
    inference(lifteq,[status(thm)],[1289]) ).

thf(511,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ocomm__monoid__mult @ B )
     => ( ( hAPP @ ( hAPP @ ( 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(3094,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ocomm__monoid__mult @ B )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(1077,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(4721,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)],[1077]) ).

thf(878,axiom,
    class_Groups_Omonoid__add @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).

thf(4167,plain,
    class_Groups_Omonoid__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).

thf(1461,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Ocomm__ring @ D )
      | ~ ( class_Rings_Odvd @ D )
      | ~ ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
      | ~ ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ E @ A ) )
      | ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Ominus__class_Ominus @ D @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ F ) @ B ) ) @ A ) ) ),
    inference(cnf,[status(esa)],[1459]) ).

thf(968,axiom,
    class_Groups_Omonoid__mult @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).

thf(4425,plain,
    class_Groups_Omonoid__mult @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).

thf(1423,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Ono__zero__divisors @ C )
      | ( ( hAPP @ ( hAPP @ ( 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(cnf,[status(esa)],[1422]) ).

thf(1424,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( 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 ) )
      | ~ ( class_Rings_Ono__zero__divisors @ C ) ),
    inference(lifteq,[status(thm)],[1423]) ).

thf(627,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(3441,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)],[627]) ).

thf(1011,axiom,
    class_Rings_Oring__1 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).

thf(4545,plain,
    class_Rings_Oring__1 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).

thf(61144,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_da____ )
      | ( A != v_mazh )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[4121,18838]) ).

thf(61145,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_da____ )
      | ( A != v_mazh ) ),
    inference(pattern_uni,[status(thm)],[61144:[]]) ).

thf(63778,plain,
    ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ v_mazh )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_da____ ) ),
    inference(simp,[status(thm)],[61145]) ).

thf(885,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(4191,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)],[885]) ).

thf(999,axiom,
    class_Groups_Ouminus @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ouminus) ).

thf(4513,plain,
    class_Groups_Ouminus @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).

thf(491,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(3032,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)],[491]) ).

thf(182,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring @ C )
     => ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).

thf(1937,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring @ C )
     => ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(1118,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(4861,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)],[1118]) ).

thf(837,axiom,
    class_Rings_Oring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).

thf(4054,plain,
    class_Rings_Oring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).

thf(99,axiom,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ A )
     => ( class_Power_Opower @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).

thf(1612,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ A )
     => ( class_Power_Opower @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(1035,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(4621,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)],[1035]) ).

thf(880,axiom,
    class_Rings_Oordered__ring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).

thf(4180,plain,
    class_Rings_Oordered__ring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).

thf(577,axiom,
    class_Rings_Odvd @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odvd) ).

thf(3294,plain,
    class_Rings_Odvd @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(656,axiom,
    class_Rings_Omult__zero @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).

thf(3536,plain,
    class_Rings_Omult__zero @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(8951,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) )
      | ( ( class_Rings_Omult__zero @ tc_Int_Oint )
       != ( class_Rings_Omult__zero @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[3536,1352]) ).

thf(8952,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) @ A )
      = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
    inference(pattern_uni,[status(thm)],[8951:[bind(A,$thf( A )),bind(B,$thf( tc_Int_Oint ))]]) ).

thf(419,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( 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(2781,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
          = ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(794,axiom,
    class_Rings_Odvd @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).

thf(3935,plain,
    class_Rings_Odvd @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).

thf(45520,plain,
    ! [A: $i] :
      ( ( v_mzh != v_da____ )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal )
       != v_mazh )
      | ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
       != ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ v_mazh @ v_ma ) ) ),
    inference(paramod_ordered,[status(thm)],[3515,14811]) ).

thf(45535,plain,
    ! [A: $i] :
      ( ( v_mzh != v_da____ )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal )
       != v_mazh )
      | ( tc_RealDef_Oreal != tc_RealDef_Oreal )
      | ( A != v_mazh )
      | ( ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A )
       != v_ma ) ),
    inference(simp,[status(thm)],[45520]) ).

thf(45588,plain,
    ( ( v_mzh != v_da____ )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal )
     != v_mazh )
    | ( ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ v_mazh )
     != v_ma ) ),
    inference(simp,[status(thm)],[45535]) ).

thf(52,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 ) @ ( hAPP @ ( hAPP @ ( 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(1451,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 ) @ ( hAPP @ ( hAPP @ ( 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)],[52]) ).

thf(366,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).

thf(2598,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(361,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(2579,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)],[361]) ).

thf(2580,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(cnf,[status(esa)],[2579]) ).

thf(2581,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      = ( c_Nat_OSuc @ A ) ),
    inference(lifteq,[status(thm)],[2580]) ).

thf(410,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(2756,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)],[410]) ).

thf(75,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
        = ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__left) ).

thf(1523,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
        = ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(1524,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ C )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
        = ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
    inference(cnf,[status(esa)],[1523]) ).

thf(1525,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A ) )
      | ~ ( class_RealVector_Oreal__normed__algebra @ C ) ),
    inference(lifteq,[status(thm)],[1524]) ).

thf(12755,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) )
        = ( c_Groups_Ozero__class_Ozero @ B ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ tc_RealDef_Oreal )
       != ( class_Rings_Ocomm__semiring__1 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[4950,1376]) ).

thf(12756,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      = ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(pattern_uni,[status(thm)],[12755:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal ))]]) ).

thf(555,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(3242,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)],[555]) ).

thf(714,axiom,
    class_Orderings_Oorder @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).

thf(3703,plain,
    class_Orderings_Oorder @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

thf(470,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Groups_Osgn__class_Osgn @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( 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(2968,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Groups_Osgn__class_Osgn @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( 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)],[470]) ).

thf(1323,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Ocomm__ring__1 @ C )
      | ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ ( c_Polynomial_Osynthetic__div @ C @ A @ B ) ) @ ( c_Polynomial_OpCons @ C @ ( hAPP @ ( c_Polynomial_Opoly @ C @ A ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) )
        = A ) ),
    inference(cnf,[status(esa)],[1322]) ).

thf(1324,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ ( c_Polynomial_Osynthetic__div @ C @ A @ B ) ) @ ( c_Polynomial_OpCons @ C @ ( hAPP @ ( c_Polynomial_Opoly @ C @ A ) @ B ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) )
        = A )
      | ~ ( class_Rings_Ocomm__ring__1 @ C ) ),
    inference(lifteq,[status(thm)],[1323]) ).

thf(141,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) )
    <=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).

thf(1776,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(1111,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(4846,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)],[1111]) ).

thf(643,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(3486,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)],[643]) ).

thf(238,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semidom @ 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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power) ).

thf(2125,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semidom @ 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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(60574,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( class_Groups_Oab__group__add @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      | ( A
       != ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ),
    inference(paramod_ordered,[status(thm)],[4121,21017]) ).

thf(60575,plain,
    ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) )
    | ( class_Groups_Oab__group__add @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(pattern_uni,[status(thm)],[60574:[bind(A,$thf( tc_Polynomial_Opoly @ tc_RealDef_Oreal ))]]) ).

thf(349,axiom,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ A )
     => ( class_Rings_Odvd @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Odvd) ).

thf(2536,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ A )
     => ( class_Rings_Odvd @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(388,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) ) @ A )
      = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__assoc) ).

thf(2681,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) ) @ A )
      = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(741,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(3787,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)],[741]) ).

thf(78,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(1530,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)],[78]) ).

thf(81,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(1537,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)],[81]) ).

thf(1538,plain,
    ! [D: $i,C: $i,B: $i,A: $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(cnf,[status(esa)],[1537]) ).

thf(1539,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_fun @ C @ D ) @ B ) @ A )
        = ( c_Groups_Ouminus__class_Ouminus @ D @ ( hAPP @ B @ A ) ) )
      | ~ ( class_Groups_Ouminus @ D ) ),
    inference(lifteq,[status(thm)],[1538]) ).

thf(842,axiom,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ A )
     => ( class_Rings_Osemiring__0 @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__0) ).

thf(4068,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ A )
     => ( class_Rings_Osemiring__0 @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).

thf(1163,axiom,
    class_Rings_Odvd @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odvd) ).

thf(4970,plain,
    class_Rings_Odvd @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).

thf(1244,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(5134,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)],[1244]) ).

thf(180,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
        & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
     => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__le) ).

thf(1932,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
        & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
     => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(906,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(4244,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)],[906]) ).

thf(89103,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) )
       != ( class_Rings_Ocomm__ring @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[88884,1575]) ).

thf(89104,plain,
    class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ),
    inference(pattern_uni,[status(thm)],[89103:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ))]]) ).

thf(340,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mult__cancel) ).

thf(2505,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(612,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(3390,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)],[612]) ).

thf(752,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(3819,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)],[752]) ).

thf(904,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(4237,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)],[904]) ).

thf(1010,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(4540,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)],[1010]) ).

thf(200,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).

thf(2006,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(59893,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != tc_Int_Oint )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Complex_Ocomplex @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Int_Oint ) ) ),
    inference(paramod_ordered,[status(thm)],[54352,54272]) ).

thf(59913,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != tc_Int_Oint )
      | ( tc_Nat_Onat != tc_Complex_Ocomplex )
      | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
       != tc_Nat_Onat )
      | ( A != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[59893]) ).

thf(59931,plain,
    ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != tc_Int_Oint )
    | ( tc_Nat_Onat != tc_Complex_Ocomplex )
    | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[59913]) ).

thf(796,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(3937,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)],[796]) ).

thf(1074,axiom,
    class_Rings_Oring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).

thf(4717,plain,
    class_Rings_Oring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).

thf(943,axiom,
    class_Rings_Oring__1__no__zero__divisors @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).

thf(4347,plain,
    class_Rings_Oring__1__no__zero__divisors @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).

thf(687,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(3628,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)],[687]) ).

thf(167,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Omonoid__mult @ B )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__right) ).

thf(1874,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Omonoid__mult @ B )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(67515,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( class_Orderings_Oord @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      | ( A
       != ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ),
    inference(paramod_ordered,[status(thm)],[4121,67492]) ).

thf(67516,plain,
    ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) )
    | ( class_Orderings_Oord @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(pattern_uni,[status(thm)],[67515:[bind(A,$thf( tc_Polynomial_Opoly @ tc_Int_Oint ))]]) ).

thf(516,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
        & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
     => ~ ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__asym) ).

thf(3115,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
        & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
     => ~ ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(732,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(3760,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)],[732]) ).

thf(805,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(3967,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)],[805]) ).

thf(556,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(3247,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)],[556]) ).

thf(710,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(3692,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)],[710]) ).

thf(215,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
       => ( ( c_Rings_Odvd__class_Odvd @ D @ C @ A )
         => ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__add) ).

thf(2052,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
       => ( ( c_Rings_Odvd__class_Odvd @ D @ C @ A )
         => ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(391,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
     => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ C ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_decr__lemma) ).

thf(2697,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
     => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) @ C ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(125,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
        <=> ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__less__divide__eq) ).

thf(1715,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
           => ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A ) )
          & ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A )
           => ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(1150,axiom,
    class_Groups_Oabs__if @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oabs__if) ).

thf(4953,plain,
    class_Groups_Oabs__if @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).

thf(872,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(4152,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)],[872]) ).

thf(127,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
        = ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ominus) ).

thf(1720,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
        = ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(1190,axiom,
    class_Groups_Omonoid__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).

thf(5026,plain,
    class_Groups_Omonoid__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).

thf(503,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__pos) ).

thf(3074,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(1061,axiom,
    ! [A: $i] :
      ( ( c_Complex_Orcis @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
      = ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rcis__zero__mod) ).

thf(4687,plain,
    ! [A: $i] :
      ( ( c_Complex_Orcis @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
      = ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).

thf(4688,plain,
    ! [A: $i] :
      ( ( c_Complex_Orcis @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
      = ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
    inference(cnf,[status(esa)],[4687]) ).

thf(4689,plain,
    ! [A: $i] :
      ( ( c_Complex_Orcis @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
      = ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
    inference(lifteq,[status(thm)],[4688]) ).

thf(786,axiom,
    class_Rings_Osemiring__0 @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).

thf(3920,plain,
    class_Rings_Osemiring__0 @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).

thf(966,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(4416,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)],[966]) ).

thf(566,axiom,
    class_Orderings_Oord @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).

thf(3267,plain,
    class_Orderings_Oord @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(77436,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Oord @ ( tc_fun @ A @ B ) )
      | ( ( class_Orderings_Oord @ tc_Nat_Onat )
       != ( class_Orderings_Oord @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[3267,1536]) ).

thf(77437,plain,
    ! [A: $i] : ( class_Orderings_Oord @ ( tc_fun @ A @ tc_Nat_Onat ) ),
    inference(pattern_uni,[status(thm)],[77436:[bind(A,$thf( A )),bind(B,$thf( tc_Nat_Onat ))]]) ).

thf(77571,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( class_Orderings_Oord @ ( tc_fun @ B @ C ) )
      | ( ( class_Orderings_Oord @ ( tc_fun @ A @ tc_Nat_Onat ) )
       != ( class_Orderings_Oord @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[77437,1536]) ).

thf(77572,plain,
    ! [B: $i,A: $i] : ( class_Orderings_Oord @ ( tc_fun @ A @ ( tc_fun @ B @ tc_Nat_Onat ) ) ),
    inference(pattern_uni,[status(thm)],[77571:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( tc_fun @ D @ tc_Nat_Onat ))]]) ).

thf(77588,plain,
    ! [B: $i,A: $i] : ( class_Orderings_Oord @ ( tc_fun @ A @ ( tc_fun @ B @ tc_Nat_Onat ) ) ),
    inference(simp,[status(thm)],[77572]) ).

thf(531,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 ) @ ( hAPP @ ( hAPP @ ( 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(3162,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 ) @ ( hAPP @ ( hAPP @ ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(898,axiom,
    class_Rings_Osemiring__0 @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).

thf(4223,plain,
    class_Rings_Osemiring__0 @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).

thf(1044,axiom,
    class_Groups_Oab__semigroup__mult @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).

thf(4644,plain,
    class_Groups_Oab__semigroup__mult @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).

thf(1160,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(4966,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)],[1160]) ).

thf(534,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
     => ( ( hBOOL @ ( hAPP @ B @ A ) )
       => ? [C: $i] :
            ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A )
            & ! [D: $i] :
                ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D @ C )
               => ~ ( hBOOL @ ( hAPP @ B @ D ) ) )
            & ( hBOOL @ ( hAPP @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).

thf(3173,plain,
    ! [A: $i,B: $i] :
      ( ~ ( hBOOL @ ( hAPP @ B @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
     => ( ( hBOOL @ ( hAPP @ B @ A ) )
       => ? [C: $i] :
            ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ A )
            & ! [D: $i] :
                ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ D @ C )
               => ~ ( hBOOL @ ( hAPP @ B @ D ) ) )
            & ( hBOOL @ ( hAPP @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(222,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ C )
     => ( ! [D: $i] :
            ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ D )
           => ( ( c_Orderings_Oord__class_Oless @ C @ D @ ( c_Groups_Oone__class_Oone @ C ) )
             => ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ D ) @ B ) @ A ) ) )
       => ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__le__mult__one__interval) ).

thf(2076,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ C )
     => ( ! [D: $i] :
            ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ D )
           => ( ( c_Orderings_Oord__class_Oless @ C @ D @ ( c_Groups_Oone__class_Oone @ C ) )
             => ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ D ) @ B ) @ A ) ) )
       => ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(17,axiom,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ A )
     => ( ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ A ) )
        = ( c_Polynomial_OpCons @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__poly__def) ).

thf(1314,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ A )
     => ( ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ A ) )
        = ( c_Polynomial_OpCons @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(1315,plain,
    ! [A: $i] :
      ( ~ ( class_Rings_Ocomm__semiring__1 @ A )
      | ( ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ A ) )
        = ( c_Polynomial_OpCons @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ) ) ),
    inference(cnf,[status(esa)],[1314]) ).

thf(1316,plain,
    ! [A: $i] :
      ( ( ( c_Polynomial_OpCons @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
        = ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ A ) ) )
      | ~ ( class_Rings_Ocomm__semiring__1 @ A ) ),
    inference(lifteq,[status(thm)],[1315]) ).

thf(5433,plain,
    ! [A: $i] :
      ( ( ( c_Polynomial_OpCons @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
        = ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ A ) ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ tc_Int_Oint )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4349,1316]) ).

thf(5434,plain,
    ( ( c_Polynomial_OpCons @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) )
    = ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ),
    inference(pattern_uni,[status(thm)],[5433:[bind(A,$thf( tc_Int_Oint ))]]) ).

thf(317,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
    <=> ( ( C
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
        | ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).

thf(2402,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
       => ( ( C
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
          | ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) )
      & ( ( ( C
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
          | ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) )
       => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(1240,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(5126,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)],[1240]) ).

thf(704,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(3675,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)],[704]) ).

thf(1341,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ D )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A )
      | ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) @ ( hAPP @ A @ E ) ) ),
    inference(cnf,[status(esa)],[1340]) ).

thf(8215,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ D )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A )
      | ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) @ ( hAPP @ A @ E ) )
       != ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_da____ @ v_mazh ) ) ),
    inference(paramod_ordered,[status(thm)],[1341,1263]) ).

thf(8239,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ D )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A )
      | ( D != tc_RealDef_Oreal )
      | ( ( hAPP @ B @ E )
       != v_da____ )
      | ( ( hAPP @ A @ E )
       != v_mazh ) ),
    inference(simp,[status(thm)],[8215]) ).

thf(8249,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ tc_RealDef_Oreal )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_RealDef_Oreal ) @ B @ A )
      | ( ( hAPP @ B @ D )
       != v_da____ )
      | ( ( hAPP @ A @ D )
       != v_mazh ) ),
    inference(simp,[status(thm)],[8239]) ).

thf(8707,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ $true
      | ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_RealDef_Oreal ) @ B @ A )
      | ( ( hAPP @ B @ D )
       != v_da____ )
      | ( ( hAPP @ A @ D )
       != v_mazh ) ),
    inference(rewrite,[status(thm)],[8249,5099]) ).

thf(8708,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_RealDef_Oreal ) @ B @ A )
      | ( ( hAPP @ B @ D )
       != v_da____ )
      | ( ( hAPP @ A @ D )
       != v_mazh ) ),
    inference(simp,[status(thm)],[8707]) ).

thf(1175,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(4995,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)],[1175]) ).

thf(876,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(4163,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)],[876]) ).

thf(526,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__right) ).

thf(3147,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(12930,plain,
    ! [A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A )
      | ( ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       != ( c_Nat_OSuc @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[2178,2863]) ).

thf(12931,plain,
    ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(pattern_uni,[status(thm)],[12930:[bind(A,$thf( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ))]]) ).

thf(1008,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(4535,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)],[1008]) ).

thf(754,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(3824,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)],[754]) ).

thf(377,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
          = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__eq__iff) ).

thf(2634,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
          = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(1233,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(5112,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)],[1233]) ).

thf(882,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(4184,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)],[882]) ).

thf(198,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Oring @ F )
     => ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C )
          = ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
      <=> ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( 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(1991,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Oring @ F )
     => ( ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C )
            = ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
         => ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) @ C )
            = A ) )
        & ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) @ C )
            = A )
         => ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C )
            = ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(746,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(3802,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)],[746]) ).

thf(1256,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(5153,plain,
    class_RealVector_Oreal__normed__div__algebra @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256]) ).

thf(67147,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) ) ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[66068,1510]) ).

thf(67148,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[67147:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) ) ) ))]]) ).

thf(67858,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) ) ) ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[67148,1510]) ).

thf(67859,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[67858:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) ) ) ) ))]]) ).

thf(457,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ E )
     => ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
         => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ C )
           => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
             => ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono) ).

thf(2926,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ E )
     => ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
         => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ C )
           => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
             => ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(947,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(4352,plain,
    class_Rings_Oring__no__zero__divisors @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).

thf(921,axiom,
    class_Groups_Oone @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).

thf(4288,plain,
    class_Groups_Oone @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).

thf(666,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(3563,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)],[666]) ).

thf(412,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 @ ( hAPP @ ( hAPP @ ( 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(2761,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(265,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semidom @ 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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power) ).

thf(2208,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semidom @ 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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(571,axiom,
    class_Groups_Oone @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).

thf(3279,plain,
    class_Groups_Oone @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(894,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(4212,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)],[894]) ).

thf(46613,plain,
    ! [B: $i,A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) @ 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 ) @ B ) @ B ) ),
    inference(paramod_ordered,[status(thm)],[4907,4201]) ).

thf(46717,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Int_Oint != tc_Int_Oint )
      | ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A )
       != ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ B ) )
      | ( A != B ) ),
    inference(simp,[status(thm)],[46613]) ).

thf(46777,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A )
     != ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ),
    inference(simp,[status(thm)],[46717]) ).

thf(1124,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(4889,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)],[1124]) ).

thf(675,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(3587,plain,
    class_Groups_Ocancel__comm__monoid__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).

thf(217,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
    <=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
        | ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).

thf(2057,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
          | ( 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 ) @ B )
          | ( 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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(124,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(1712,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)],[124]) ).

thf(949,axiom,
    class_Rings_Ozero__neq__one @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).

thf(4359,plain,
    class_Rings_Ozero__neq__one @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).

thf(2314,plain,
    ! [A: $i] :
      ( ~ ( class_Rings_Ozero__neq__one @ A )
      | ( ( c_Groups_Ozero__class_Ozero @ A )
       != ( c_Groups_Oone__class_Oone @ A ) ) ),
    inference(cnf,[status(esa)],[2313]) ).

thf(2315,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ A )
       != ( c_Groups_Ozero__class_Ozero @ A ) )
      | ~ ( class_Rings_Ozero__neq__one @ A ) ),
    inference(lifteq,[status(thm)],[2314]) ).

thf(8278,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ A )
       != ( c_Groups_Ozero__class_Ozero @ A ) )
      | ( ( class_Rings_Ozero__neq__one @ tc_Nat_Onat )
       != ( class_Rings_Ozero__neq__one @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4359,2315]) ).

thf(8279,plain,
    ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
   != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(pattern_uni,[status(thm)],[8278:[bind(A,$thf( tc_Nat_Onat ))]]) ).

thf(678,axiom,
    class_Rings_Olinordered__semidom @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).

thf(3592,plain,
    class_Rings_Olinordered__semidom @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(692,axiom,
    class_Orderings_Opreorder @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).

thf(3639,plain,
    class_Orderings_Opreorder @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).

thf(326,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ B ) @ A ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ E )
         => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ E )
           => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ D @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).

thf(2440,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ B ) @ A ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ E )
         => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ E )
           => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ D @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(1515,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Olinordered__semiring__strict @ E )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
      | ~ ( c_Orderings_Oord__class_Oless @ E @ B @ A )
      | ~ ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
      | ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ),
    inference(cnf,[status(esa)],[1514]) ).

thf(269,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Omonoid__mult @ B )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
        = ( c_Groups_Oone__class_Oone @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).

thf(2221,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Omonoid__mult @ B )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
        = ( c_Groups_Oone__class_Oone @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(14349,plain,
    ( ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
     != v_da____ )
    | ( v_cs____ != v_mazh )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,13945]) ).

thf(14362,plain,
    ( ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
     != v_da____ )
    | ( v_cs____ != v_mazh )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[14349]) ).

thf(172,axiom,
    ! [A: $i,B: $i] :
      ( ( B
       != ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) @ B )
      <=> ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A )
          = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mult__cancel1) ).

thf(1895,plain,
    ! [A: $i,B: $i] :
      ( ( B
       != ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
     => ( ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) @ B )
         => ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A )
            = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
        & ( ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A )
            = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
         => ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(621,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(3422,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Olinordered__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(452,axiom,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0__right) ).

thf(2909,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(54975,plain,
    ! [B: $i,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_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ A ) ) )
     != ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ B ) ),
    inference(paramod_ordered,[status(thm)],[54858,5078]) ).

thf(54992,plain,
    ! [B: $i,A: $i] :
      ( ( tc_RealDef_Oreal != tc_RealDef_Oreal )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal )
       != B )
      | ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ A ) )
       != B ) ),
    inference(simp,[status(thm)],[54975]) ).

thf(55044,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ A ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[54992]) ).

thf(748,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(3807,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)],[748]) ).

thf(1138,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(4921,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)],[1138]) ).

thf(400,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) ) @ A )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Odiff) ).

thf(2729,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Ominus__class_Ominus @ D @ C @ B ) ) @ A )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(62113,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( class_Groups_Oab__group__add @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      | ( A
       != ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
    inference(paramod_ordered,[status(thm)],[4121,21019]) ).

thf(62114,plain,
    ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
    | ( class_Groups_Oab__group__add @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(pattern_uni,[status(thm)],[62113:[bind(A,$thf( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ))]]) ).

thf(450,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ E )
     => ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
           => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
             => ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).

thf(2904,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ E )
     => ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
           => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
             => ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(189,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) ) @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib) ).

thf(1959,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ C @ B ) ) @ A )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(777,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A )
      <=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
          & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
           => ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ C ) )
              & ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__eq) ).

thf(3890,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ D )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A )
         => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
             => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ C ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) ) )
        & ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
             => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ C ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A ) ) ) ) )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ C @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).

thf(563,axiom,
    class_Rings_Oordered__cancel__semiring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).

thf(3262,plain,
    class_Rings_Oordered__cancel__semiring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(4195,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
      = A ),
    inference(cnf,[status(esa)],[4194]) ).

thf(4196,plain,
    ! [A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
      = A ),
    inference(lifteq,[status(thm)],[4195]) ).

thf(24647,plain,
    ! [A: $i] :
      ( ( v_mzh != v_da____ )
      | ( A != v_mazh )
      | ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       != ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ v_mazh @ v_ma ) ) ),
    inference(paramod_ordered,[status(thm)],[4196,14811]) ).

thf(24660,plain,
    ( ( v_mzh != v_da____ )
    | ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( v_mazh != v_mazh )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
     != v_ma ) ),
    inference(simp,[status(thm)],[24647]) ).

thf(24681,plain,
    ( ( v_mzh != v_da____ )
    | ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
     != v_ma ) ),
    inference(simp,[status(thm)],[24660]) ).

thf(24915,plain,
    ( ( v_mzh != v_da____ )
    | ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( v_ma != v_cs____ )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,24681]) ).

thf(24925,plain,
    ( ( v_mzh != v_da____ )
    | ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( v_ma != v_cs____ )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[24915]) ).

thf(1481,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
      | ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
    inference(cnf,[status(esa)],[1480]) ).

thf(1483,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
      | ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) ) ),
    inference(simp,[status(thm)],[1481]) ).

thf(51095,plain,
    ! [B: $i,A: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ A @ B ) )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[43716,1483]) ).

thf(51096,plain,
    c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(pattern_uni,[status(thm)],[51095:[bind(A,$thf( c_Groups_Oone__class_Oone @ tc_Nat_Onat )),bind(B,$thf( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ))]]) ).

thf(51250,plain,
    c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(rewrite,[status(thm)],[51096,1586,2178]) ).

thf(1205,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(5043,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)],[1205]) ).

thf(717,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(3707,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)],[717]) ).

thf(129,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
       => ( c_Rings_Odvd__class_Odvd @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power__same) ).

thf(1727,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
       => ( c_Rings_Odvd__class_Odvd @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(1069,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(4708,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)],[1069]) ).

thf(64151,plain,
    ! [B: $i,A: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
       != ( class_Rings_Ocomm__semiring__1 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[63991,1491]) ).

thf(64152,plain,
    ! [A: $i] : ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) @ A ),
    inference(pattern_uni,[status(thm)],[64151:[bind(A,$thf( A )),bind(B,$thf( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ))]]) ).

thf(982,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(4470,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)],[982]) ).

thf(955,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(4380,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)],[955]) ).

thf(1246,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(5138,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)],[1246]) ).

thf(243,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__div__pos__less) ).

thf(2149,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
         => ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(275,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__ring @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__square) ).

thf(2253,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__ring @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Groups_Ozero__class_Ozero @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(770,axiom,
    class_Groups_Oab__semigroup__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).

thf(3871,plain,
    class_Groups_Oab__semigroup__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).

thf(645,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B )
          = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
         => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
           => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
             => ( C = A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).

thf(3491,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B )
          = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
         => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
           => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
             => ( C = A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(81538,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ A ) @ A )
     != ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[14613,81500]) ).

thf(81584,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( c_Nat_OSuc @ A )
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      | ( A
       != ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
    inference(simp,[status(thm)],[81538]) ).

thf(81627,plain,
    ( ( c_Nat_OSuc @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
   != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[81584]) ).

thf(5219,plain,
    ( ( v_cs____ != v_c____ )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,3963]) ).

thf(5230,plain,
    ( ( v_cs____ != v_c____ )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Complex_Ocomplex ) ),
    inference(simp,[status(thm)],[5219]) ).

thf(359,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__ring__1 @ D )
     => ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
       => ( ( c_Rings_Odvd__class_Odvd @ D @ C @ A )
         => ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diff) ).

thf(2570,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__ring__1 @ D )
     => ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
       => ( ( c_Rings_Odvd__class_Odvd @ D @ C @ A )
         => ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(909,axiom,
    class_Rings_Oring__1 @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).

thf(4256,plain,
    class_Rings_Oring__1 @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).

thf(975,axiom,
    class_Rings_Oordered__semiring @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).

thf(4438,plain,
    class_Rings_Oordered__semiring @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).

thf(85,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 @ ( hAPP @ ( hAPP @ ( 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(1548,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(178,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
      <=> ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).

thf(1927,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
     => ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
         => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) )
        & ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
         => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(1050,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(4657,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)],[1050]) ).

thf(7,axiom,
    ( ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ v_c____ @ v_cs____ )
   != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons_Oprems) ).

thf(1276,plain,
    ( ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ v_c____ @ v_cs____ )
   != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(1277,plain,
    ( ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ v_c____ @ v_cs____ )
   != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
    inference(polarity_switch,[status(thm)],[1276]) ).

thf(1278,plain,
    ( ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ v_c____ @ v_cs____ )
   != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
    inference(lifteq,[status(thm)],[1277]) ).

thf(5218,plain,
    ( ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ v_c____ @ v_cs____ )
   != v_cs____ ),
    inference(rewrite,[status(thm)],[1278,1280]) ).

thf(5447,plain,
    ! [A: $i] :
      ( ~ ( class_Rings_Ocomm__semiring__1 @ A )
      | ( ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ A ) )
       != v_cs____ )
      | ( ( c_Polynomial_OpCons @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
       != ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ v_c____ @ v_cs____ ) ) ),
    inference(paramod_ordered,[status(thm)],[1316,5218]) ).

thf(5463,plain,
    ! [A: $i] :
      ( ~ ( class_Rings_Ocomm__semiring__1 @ A )
      | ( ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ A ) )
       != v_cs____ )
      | ( A != tc_Complex_Ocomplex )
      | ( ( c_Groups_Oone__class_Oone @ A )
       != v_c____ )
      | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) )
       != v_cs____ ) ),
    inference(simp,[status(thm)],[5447]) ).

thf(5478,plain,
    ( ~ ( class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex )
    | ( ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != v_cs____ )
    | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
     != v_c____ )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != v_cs____ ) ),
    inference(simp,[status(thm)],[5463]) ).

thf(5959,plain,
    ( ~ $true
    | ( ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != v_cs____ )
    | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
     != v_c____ )
    | ( v_cs____ != v_cs____ ) ),
    inference(rewrite,[status(thm)],[5478,1280,4691]) ).

thf(5960,plain,
    ( ( ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != v_cs____ )
    | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
     != v_c____ ) ),
    inference(simp,[status(thm)],[5959]) ).

thf(1208,axiom,
    class_Power_Opower @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Power_Opower) ).

thf(5048,plain,
    class_Power_Opower @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).

thf(206,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Oring__1 @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ ( c_Groups_Ominus__class_Ominus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__squared__diff__one__factored) ).

thf(2028,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Oring__1 @ B )
     => ( ( c_Groups_Ominus__class_Ominus @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oplus__class_Oplus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) @ ( c_Groups_Ominus__class_Ominus @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(607,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(3375,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)],[607]) ).

thf(776,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(3888,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)],[776]) ).

thf(402,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(2734,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)],[402]) ).

thf(760,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(3839,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)],[760]) ).

thf(1184,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(5016,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)],[1184]) ).

thf(743,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(3792,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)],[743]) ).

thf(1202,axiom,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ v_da____ ) @ v_ma ) @ v_mzh,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

thf(5039,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ v_da____ ) @ v_ma ) @ v_mzh,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).

thf(25256,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ v_da____ ) @ v_ma ) @ v_mzh,
    inference(rewrite,[status(thm)],[5039,4759]) ).

thf(448,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
         => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) )
           => ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__left__mono__neg) ).

thf(2894,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
         => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) )
           => ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(599,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(3343,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)],[599]) ).

thf(278,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A )
    <=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I2_J) ).

thf(2260,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A )
       => ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) ) )
      & ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
       => ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(3372,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(lifteq,[status(thm)],[3371]) ).

thf(941,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(4341,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)],[941]) ).

thf(588,axiom,
    class_Groups_Ominus @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).

thf(3319,plain,
    class_Groups_Ominus @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(176,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).

thf(1916,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(650,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(3504,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)],[650]) ).

thf(422,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(2789,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)],[422]) ).

thf(508,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
         => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).

thf(3086,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) )
         => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(506,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Omonoid__mult @ B )
     => ( ( hAPP @ ( hAPP @ ( 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(3081,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Omonoid__mult @ B )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(860,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(4122,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)],[860]) ).

thf(90560,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) )
       != ( class_Rings_Ocomm__ring @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[90246,1575]) ).

thf(90561,plain,
    class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[90560:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ))]]) ).

thf(980,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(4465,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)],[980]) ).

thf(684,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(3604,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)],[684]) ).

thf(1147,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(4946,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)],[1147]) ).

thf(1187,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(5022,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)],[1187]) ).

thf(546,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Rings_Ocomm__ring @ D )
        & ( class_Rings_Odvd @ D ) )
     => ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
       => ! [E: $i,F: $i] :
            ( ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ E @ A ) )
          <=> ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Ominus__class_Ominus @ D @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ F ) @ B ) ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__period_I3_J) ).

thf(3213,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( class_Rings_Ocomm__ring @ D )
        & ( class_Rings_Odvd @ D ) )
     => ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
       => ! [E: $i,F: $i] :
            ( ( ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ E @ A ) )
             => ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Ominus__class_Ominus @ D @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ F ) @ B ) ) @ A ) ) )
            & ( ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ ( c_Groups_Ominus__class_Ominus @ D @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ F ) @ B ) ) @ A ) )
             => ( c_Rings_Odvd__class_Odvd @ D @ C @ ( c_Groups_Oplus__class_Oplus @ D @ E @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(81805,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != A )
      | ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) )
       != ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2178,81639]) ).

thf(81832,plain,
    ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
   != ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(simp,[status(thm)],[81805]) ).

thf(81856,plain,
    ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
   != ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
    inference(rewrite,[status(thm)],[81832,2178]) ).

thf(552,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(3234,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)],[552]) ).

thf(213,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
        & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
     => ~ ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__not__sym) ).

thf(2048,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
        & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
     => ~ ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(6915,plain,
    ! [A: $i] :
      ( ( ( c_Polynomial_OpCons @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
        = ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ A ) ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ tc_RealDef_Oreal )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4950,1316]) ).

thf(6916,plain,
    ( ( c_Polynomial_OpCons @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) )
    = ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ),
    inference(pattern_uni,[status(thm)],[6915:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(789,axiom,
    class_Power_Opower @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).

thf(3925,plain,
    class_Power_Opower @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).

thf(892,axiom,
    class_Rings_Odivision__ring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).

thf(4210,plain,
    class_Rings_Odivision__ring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).

thf(68067,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
        = A )
      | ( ( class_Rings_Odivision__ring @ tc_Complex_Ocomplex )
       != ( class_Rings_Odivision__ring @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[4210,1522]) ).

thf(68068,plain,
    ! [A: $i] :
      ( ( c_Rings_Oinverse__class_Odivide @ tc_Complex_Ocomplex @ A @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) )
      = A ),
    inference(pattern_uni,[status(thm)],[68067:[bind(A,$thf( A )),bind(B,$thf( tc_Complex_Ocomplex ))]]) ).

thf(991,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(4494,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)],[991]) ).

thf(1388,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Oring @ C )
      | ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
    inference(cnf,[status(esa)],[1387]) ).

thf(1389,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) )
      | ~ ( class_Rings_Oring @ C ) ),
    inference(lifteq,[status(thm)],[1388]) ).

thf(846,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(4077,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)],[846]) ).

thf(554,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(3240,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)],[554]) ).

thf(41602,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) ) ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[30510,1417]) ).

thf(41603,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[41602:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(48705,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[41603,1417]) ).

thf(48706,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[48705:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(346,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
     => ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
          = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).

thf(2525,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
     => ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
            = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
            = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(685,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(3609,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)],[685]) ).

thf(257,axiom,
    ! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__1__left) ).

thf(2188,plain,
    ! [A: $i] : ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(475,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).

thf(2981,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ B )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(1214,axiom,
    class_Rings_Odivision__ring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).

thf(5067,plain,
    class_Rings_Odivision__ring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).

thf(928,axiom,
    class_Rings_Omult__zero @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).

thf(4309,plain,
    class_Rings_Omult__zero @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).

thf(1139,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 @ B @ A )
       => ~ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__not__zless) ).

thf(4926,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 @ B @ A )
       => ~ ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).

thf(573,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(3283,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)],[573]) ).

thf(387,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Oidom @ D )
     => ( ( c_Rings_Odvd__class_Odvd @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
      <=> ( ( B
            = ( c_Groups_Ozero__class_Ozero @ D ) )
          | ( c_Rings_Odvd__class_Odvd @ D @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel__right) ).

thf(2674,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Oidom @ D )
     => ( ( ( c_Rings_Odvd__class_Odvd @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
         => ( ( B
              = ( c_Groups_Ozero__class_Ozero @ D ) )
            | ( c_Rings_Odvd__class_Odvd @ D @ C @ A ) ) )
        & ( ( ( B
              = ( c_Groups_Ozero__class_Ozero @ D ) )
            | ( c_Rings_Odvd__class_Odvd @ D @ C @ A ) )
         => ( c_Rings_Odvd__class_Odvd @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(1030,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(4605,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)],[1030]) ).

thf(1403,plain,
    ! [C: $i,B: $i,A: $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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ),
    inference(cnf,[status(esa)],[1401]) ).

thf(1223,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(5097,plain,
    class_Fields_Olinordered__field__inverse__zero @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).

thf(144,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(1785,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)],[144]) ).

thf(1786,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: $i] :
        ( ( 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(miniscope,[status(thm)],[1785]) ).

thf(1789,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 ) ) ),
    inference(cnf,[status(esa)],[1786]) ).

thf(1794,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 ) ) ),
    inference(lifteq,[status(thm)],[1789]) ).

thf(1795,plain,
    ( ( c_Groups_Osgn__class_Osgn @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
    = ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
    inference(simp,[status(thm)],[1794]) ).

thf(937,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).

thf(4328,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).

thf(1031,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(4612,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)],[1031]) ).

thf(425,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) )
      = ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__divide__square__eq) ).

thf(2817,plain,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) )
      = ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(24726,plain,
    ( ( v_cs____ != v_c____ )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,24060]) ).

thf(24745,plain,
    ( ( v_cs____ != v_c____ )
    | ( tc_Nat_Onat != tc_Complex_Ocomplex )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[24726]) ).

thf(64070,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( class_Rings_Ocomm__semiring__1 @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      | ( A
       != ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[4121,63977]) ).

thf(64071,plain,
    ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) )
    | ( class_Rings_Ocomm__semiring__1 @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(pattern_uni,[status(thm)],[64070:[bind(A,$thf( tc_Polynomial_Opoly @ tc_Nat_Onat ))]]) ).

thf(738,axiom,
    class_Rings_Omult__zero @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).

thf(3783,plain,
    class_Rings_Omult__zero @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).

thf(5448,plain,
    ! [A: $i] :
      ( ( ( c_Polynomial_OpCons @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
        = ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ A ) ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ tc_Nat_Onat )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3838,1316]) ).

thf(5449,plain,
    ( ( c_Polynomial_OpCons @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) )
    = ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) ),
    inference(pattern_uni,[status(thm)],[5448:[bind(A,$thf( tc_Nat_Onat ))]]) ).

thf(140,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
      <=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
           => ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ B ) )
          & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
           => ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
              & ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq) ).

thf(1765,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ D )
     => ( ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
         => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
             => ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ B ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) )
        & ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
             => ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ B ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) )
         => ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(510,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).

thf(3091,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ A ) )
      = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(47790,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) @ A )
       != ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2082,37077]) ).

thf(47922,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
       != ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) )
      | ( ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B )
       != A ) ),
    inference(simp,[status(thm)],[47790]) ).

thf(47985,plain,
    ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
   != ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[47922]) ).

thf(548,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(3223,plain,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ A )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(907,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(4251,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)],[907]) ).

thf(1006,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(4526,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)],[1006]) ).

thf(1009,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(4537,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)],[1009]) ).

thf(54747,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ v_da____ )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Complex_Ocomplex @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh ) ) ),
    inference(paramod_ordered,[status(thm)],[54352,17349]) ).

thf(54810,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ v_da____ )
      | ( tc_Nat_Onat != tc_Complex_Ocomplex )
      | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
       != v_da____ )
      | ( A != v_mazh ) ),
    inference(simp,[status(thm)],[54747]) ).

thf(54847,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ v_da____ )
    | ( tc_Nat_Onat != tc_Complex_Ocomplex )
    | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
     != v_da____ ) ),
    inference(simp,[status(thm)],[54810]) ).

thf(259,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Rings_Odvd__class_Odvd @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A )
      <=> ( c_Rings_Odvd__class_Odvd @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__dvd__iff) ).

thf(2193,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( ( c_Rings_Odvd__class_Odvd @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A )
         => ( c_Rings_Odvd__class_Odvd @ C @ B @ A ) )
        & ( ( c_Rings_Odvd__class_Odvd @ C @ B @ A )
         => ( c_Rings_Odvd__class_Odvd @ C @ ( c_Groups_Oabs__class_Oabs @ C @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

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

thf(5033,plain,
    class_Groups_Ouminus @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).

thf(863,axiom,
    class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).

thf(4127,plain,
    class_Rings_Olinordered__semiring__strict @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).

thf(804,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(3964,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)],[804]) ).

thf(1236,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(5118,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)],[1236]) ).

thf(288,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(2293,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)],[288]) ).

thf(498,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) )
    <=> ( ( C = A )
        | ( B
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel2) ).

thf(3051,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
          = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) )
       => ( ( C = A )
          | ( B
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
      & ( ( ( C = A )
          | ( B
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
       => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
          = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(447,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Oordered__ring @ F )
     => ( ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
      <=> ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff1) ).

thf(2891,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Oordered__ring @ F )
     => ( ( ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
         => ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) @ C ) @ A ) )
        & ( ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(292,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 ) )
          <=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C )
              = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ A ) @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__eq__eq) ).

thf(2308,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 ) )
             => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C )
                = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ A ) @ D ) ) )
            & ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ C )
                = ( hAPP @ ( hAPP @ ( 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)],[292]) ).

thf(1045,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(4645,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)],[1045]) ).

thf(696,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(3646,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ A )
     => ( class_Rings_Oring @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).

thf(15874,plain,
    ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ v_da____ ) @ v_ma ) @ v_mzh )
   != ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_da____ @ v_mazh ) ),
    inference(paramod_ordered,[status(thm)],[5039,1263]) ).

thf(15914,plain,
    ( ( tc_RealDef_Oreal != tc_RealDef_Oreal )
    | ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ v_da____ ) @ v_ma )
     != v_da____ )
    | ( v_mzh != v_mazh ) ),
    inference(simp,[status(thm)],[15874]) ).

thf(15940,plain,
    ( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ v_da____ ) @ v_ma )
     != v_da____ )
    | ( v_mzh != v_mazh ) ),
    inference(simp,[status(thm)],[15914]) ).

thf(25255,plain,
    ( ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ v_da____ ) @ v_ma )
     != v_da____ )
    | ( v_mzh != v_mazh ) ),
    inference(rewrite,[status(thm)],[15940,4759]) ).

thf(871,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ 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 @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Opos__bounded) ).

thf(4149,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ 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 @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ D ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).

thf(544,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__algebra__1 @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__power__ineq) ).

thf(3208,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__algebra__1 @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(701,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(3663,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)],[701]) ).

thf(105,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(1635,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)],[105]) ).

thf(461,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(2935,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)],[461]) ).

thf(1106,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(4822,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)],[1106]) ).

thf(597,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(3340,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)],[597]) ).

thf(1020,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(4573,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)],[1020]) ).

thf(199,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oidom @ C )
     => ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B )
          = ( hAPP @ ( hAPP @ ( 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(1997,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oidom @ C )
     => ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B )
            = ( hAPP @ ( hAPP @ ( 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 ) ) )
         => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B )
            = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(1252,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(5148,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)],[1252]) ).

thf(1088,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(4764,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)],[1088]) ).

thf(327,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Omonoid__mult @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult) ).

thf(2442,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Omonoid__mult @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(411,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono_H) ).

thf(2759,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(1116,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(4854,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)],[1116]) ).

thf(1043,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(4640,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)],[1043]) ).

thf(580,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(3302,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)],[580]) ).

thf(1073,axiom,
    class_Groups_Ozero @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).

thf(4716,plain,
    class_Groups_Ozero @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).

thf(5949,plain,
    ! [A: $i] :
      ( ( ( c_Polynomial_OpCons @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
      | ( ( class_Groups_Ozero @ tc_Complex_Ocomplex )
       != ( class_Groups_Ozero @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4716,1272]) ).

thf(5950,plain,
    ( ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
    = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
    inference(pattern_uni,[status(thm)],[5949:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(19666,plain,
    ( ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) @ v_cs____ )
    = v_cs____ ),
    inference(rewrite,[status(thm)],[5950,1280]) ).

thf(720,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(3719,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)],[720]) ).

thf(295,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Omonoid__mult @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__add) ).

thf(2319,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Groups_Omonoid__mult @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ B @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(68282,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[67611,1510]) ).

thf(68283,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[68282:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ))]]) ).

thf(48879,plain,
    ! [A: $i] :
      ( ( class_Orderings_Opreorder @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Olinordered__idom @ tc_Int_Oint )
       != ( class_Rings_Olinordered__idom @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3913,1478]) ).

thf(48880,plain,
    class_Orderings_Opreorder @ ( tc_Polynomial_Opoly @ tc_Int_Oint ),
    inference(pattern_uni,[status(thm)],[48879:[bind(A,$thf( tc_Int_Oint ))]]) ).

thf(62512,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( class_Orderings_Opreorder @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      | ( A
       != ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ),
    inference(paramod_ordered,[status(thm)],[4121,48880]) ).

thf(62513,plain,
    ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) )
    | ( class_Orderings_Opreorder @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(pattern_uni,[status(thm)],[62512:[bind(A,$thf( tc_Polynomial_Opoly @ tc_Int_Oint ))]]) ).

thf(1100,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(4790,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)],[1100]) ).

thf(397,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Power_Opower @ B )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
        = ( c_Groups_Oone__class_Oone @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0) ).

thf(2721,plain,
    ! [A: $i,B: $i] :
      ( ( class_Power_Opower @ B )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
        = ( c_Groups_Oone__class_Oone @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(85992,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) @ A )
     != ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ),
    inference(paramod_ordered,[status(thm)],[63419,81608]) ).

thf(86031,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) )
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      | ( A
       != ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ),
    inference(simp,[status(thm)],[85992]) ).

thf(86060,plain,
    ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) )
   != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[86031]) ).

thf(313,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult) ).

thf(2383,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(1211,axiom,
    class_Rings_Olinordered__semidom @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).

thf(5054,plain,
    class_Rings_Olinordered__semidom @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).

thf(718,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(3710,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)],[718]) ).

thf(648,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(3500,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)],[648]) ).

thf(14,axiom,
    ( v_cs____
    = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cs0) ).

thf(1307,plain,
    ( v_cs____
    = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(21214,plain,
    ( ( v_mzh != v_da____ )
    | ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( v_ma != v_cs____ )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,20687]) ).

thf(21222,plain,
    ( ( v_mzh != v_da____ )
    | ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( v_ma != v_cs____ )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[21214]) ).

thf(303,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
        & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
     => ( B != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__neq) ).

thf(2346,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
        & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(1250,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(5143,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)],[1250]) ).

thf(816,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(3996,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)],[816]) ).

thf(688,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(3631,plain,
    class_RealVector_Oreal__normed__div__algebra @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(350,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(2538,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)],[350]) ).

thf(336,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(2478,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)],[336]) ).

thf(558,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(3251,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)],[558]) ).

thf(244,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ C ) )
      <=> ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__eq__nat) ).

thf(2151,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
     => ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ C ) )
         => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) )
        & ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
         => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(272,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
              = ( hAPP @ ( hAPP @ ( 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(2229,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
                = ( hAPP @ ( hAPP @ ( 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
                = ( hAPP @ ( hAPP @ ( 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)],[272]) ).

thf(25516,plain,
    ! [A: $i] :
      ( ( v_mzh != v_da____ )
      | ( A != v_mazh )
      | ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
       != ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ v_mazh @ v_ma ) ) ),
    inference(paramod_ordered,[status(thm)],[4860,14811]) ).

thf(25518,plain,
    ( ( v_mzh != v_da____ )
    | ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
     != v_mazh )
    | ( v_ma != v_mazh ) ),
    inference(simp,[status(thm)],[25516]) ).

thf(477,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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(2987,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ D )
     => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(378,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(2637,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)],[378]) ).

thf(660,axiom,
    class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).

thf(3551,plain,
    class_Groups_Oab__semigroup__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(321,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 @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).

thf(2422,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 @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(801,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(3957,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)],[801]) ).

thf(37131,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat )
       != ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != A ) ),
    inference(simp,[status(thm)],[37074]) ).

thf(37304,plain,
    ( ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat )
   != ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[37131]) ).

thf(737,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(3779,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)],[737]) ).

thf(451,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oring @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
        = ( hAPP @ ( hAPP @ ( 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(2906,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oring @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(620,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(3419,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)],[620]) ).

thf(1066,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(4699,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)],[1066]) ).

thf(1348,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Olinordered__idom @ C )
      | ( ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A ) )
        = ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
    inference(cnf,[status(esa)],[1347]) ).

thf(1349,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A ) )
        = ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) )
      | ~ ( class_Rings_Olinordered__idom @ C ) ),
    inference(lifteq,[status(thm)],[1348]) ).

thf(228,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).

thf(2097,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(568,axiom,
    class_RealVector_Oreal__field @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__field) ).

thf(3270,plain,
    class_RealVector_Oreal__field @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(77522,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( class_Orderings_Oord @ ( tc_fun @ B @ C ) )
      | ( ( class_Orderings_Oord @ ( tc_fun @ A @ tc_Int_Oint ) )
       != ( class_Orderings_Oord @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[77425,1536]) ).

thf(77523,plain,
    ! [B: $i,A: $i] : ( class_Orderings_Oord @ ( tc_fun @ A @ ( tc_fun @ B @ tc_Int_Oint ) ) ),
    inference(pattern_uni,[status(thm)],[77522:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( tc_fun @ D @ tc_Int_Oint ))]]) ).

thf(77547,plain,
    ! [B: $i,A: $i] : ( class_Orderings_Oord @ ( tc_fun @ A @ ( tc_fun @ B @ tc_Int_Oint ) ) ),
    inference(simp,[status(thm)],[77523]) ).

thf(277,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
     => ( ( C
          = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).

thf(2257,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
     => ( ( C
          = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(1588,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Ocomm__semiring__1 @ E )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ A ) ) ) ),
    inference(cnf,[status(esa)],[1587]) ).

thf(1589,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ A ) ) )
      | ~ ( class_Rings_Ocomm__semiring__1 @ E ) ),
    inference(lifteq,[status(thm)],[1588]) ).

thf(465,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( c_Rings_Odvd__class_Odvd @ B @ A @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__refl) ).

thf(2955,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( c_Rings_Odvd__class_Odvd @ B @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(98,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Oring__1__no__zero__divisors @ B )
     => ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A )
          = ( c_Groups_Oone__class_Oone @ B ) )
      <=> ( ( A
            = ( c_Groups_Oone__class_Oone @ B ) )
          | ( A
            = ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).

thf(1603,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Oring__1__no__zero__divisors @ B )
     => ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A )
            = ( c_Groups_Oone__class_Oone @ B ) )
         => ( ( A
              = ( c_Groups_Oone__class_Oone @ B ) )
            | ( A
              = ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) ) )
        & ( ( ( A
              = ( c_Groups_Oone__class_Oone @ B ) )
            | ( A
              = ( c_Groups_Ouminus__class_Ouminus @ B @ ( c_Groups_Oone__class_Oone @ B ) ) ) )
         => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A )
            = ( c_Groups_Oone__class_Oone @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(290,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Oidom @ D )
     => ( ( c_Rings_Odvd__class_Odvd @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
      <=> ( ( C
            = ( c_Groups_Ozero__class_Ozero @ D ) )
          | ( c_Rings_Odvd__class_Odvd @ D @ B @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel__left) ).

thf(2299,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Oidom @ D )
     => ( ( ( c_Rings_Odvd__class_Odvd @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
         => ( ( C
              = ( c_Groups_Ozero__class_Ozero @ D ) )
            | ( c_Rings_Odvd__class_Odvd @ D @ B @ A ) ) )
        & ( ( ( C
              = ( c_Groups_Ozero__class_Ozero @ D ) )
            | ( c_Rings_Odvd__class_Odvd @ D @ B @ A ) )
         => ( c_Rings_Odvd__class_Odvd @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(1028,axiom,
    class_Rings_Olinordered__ring__strict @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).

thf(4601,plain,
    class_Rings_Olinordered__ring__strict @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).

thf(515,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oordered__ring__abs @ C )
     => ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
            | ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
          & ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
            | ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
       => ( ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
          = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__eq__mult) ).

thf(3106,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oordered__ring__abs @ C )
     => ( ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
            | ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
          & ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
            | ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
       => ( ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
          = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(637,axiom,
    ! [A: $i] :
      ( ( class_Rings_Oidom @ A )
     => ( class_Rings_Oring__1__no__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).

thf(3468,plain,
    ! [A: $i] :
      ( ( class_Rings_Oidom @ A )
     => ( class_Rings_Oring__1__no__zero__divisors @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(62913,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_mazh )
      | ( A != v_mazh )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[4121,20756]) ).

thf(62914,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_mazh )
      | ( A != v_mazh ) ),
    inference(pattern_uni,[status(thm)],[62913:[]]) ).

thf(63698,plain,
    ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ v_mazh )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_mazh ) ),
    inference(simp,[status(thm)],[62914]) ).

thf(1024,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(4586,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)],[1024]) ).

thf(432,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
    <=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).

thf(2839,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) )
      & ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ C )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(542,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
      <=> ( ( B
            = ( c_Groups_Ozero__class_Ozero @ C ) )
          & ( A
            = ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).

thf(3197,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ C )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( ( B
              = ( c_Groups_Ozero__class_Ozero @ C ) )
            & ( A
              = ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
        & ( ( ( B
              = ( c_Groups_Ozero__class_Ozero @ C ) )
            & ( A
              = ( c_Groups_Ozero__class_Ozero @ C ) ) )
         => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(844,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(4073,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)],[844]) ).

thf(1221,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(5093,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)],[1221]) ).

thf(537,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) )
           => ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).

thf(3182,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) )
           => ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(449,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ C )
     => ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) )
      <=> ( ( B
           != ( c_Groups_Ozero__class_Ozero @ C ) )
          | ( A
           != ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).

thf(2896,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ C )
     => ( ( ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) )
         => ( ( B
             != ( c_Groups_Ozero__class_Ozero @ C ) )
            | ( A
             != ( c_Groups_Ozero__class_Ozero @ C ) ) ) )
        & ( ( ( B
             != ( c_Groups_Ozero__class_Ozero @ C ) )
            | ( A
             != ( c_Groups_Ozero__class_Ozero @ C ) ) )
         => ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(611,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(3384,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)],[611]) ).

thf(54618,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_c____ )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_c____ @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ),
    inference(paramod_ordered,[status(thm)],[54339,15154]) ).

thf(54645,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_c____ )
      | ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
       != v_c____ )
      | ( A
       != ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
    inference(simp,[status(thm)],[54618]) ).

thf(54696,plain,
    ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_c____ )
    | ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
     != v_c____ ) ),
    inference(simp,[status(thm)],[54645]) ).

thf(997,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(4509,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)],[997]) ).

thf(205,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).

thf(2025,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(404,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(2742,plain,
    ! [A: $i,B: $i] :
      ( ( class_Orderings_Opreorder @ B )
     => ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(939,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(4332,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)],[939]) ).

thf(17347,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ A )
     != ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_da____ @ v_mazh ) ),
    inference(paramod_ordered,[status(thm)],[4980,1263]) ).

thf(17374,plain,
    ! [A: $i] :
      ( ( tc_RealDef_Oreal != tc_RealDef_Oreal )
      | ( A != v_da____ )
      | ( A != v_mazh ) ),
    inference(simp,[status(thm)],[17347]) ).

thf(17396,plain,
    v_mazh != v_da____,
    inference(simp,[status(thm)],[17374]) ).

thf(642,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(3483,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)],[642]) ).

thf(1014,axiom,
    class_Rings_Ono__zero__divisors @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).

thf(4554,plain,
    class_Rings_Ono__zero__divisors @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).

thf(632,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(3456,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)],[632]) ).

thf(64034,plain,
    ! [B: $i,A: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) )
       != ( class_Rings_Ocomm__semiring__1 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[63965,1491]) ).

thf(64035,plain,
    ! [A: $i] : ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) @ A ),
    inference(pattern_uni,[status(thm)],[64034:[bind(A,$thf( A )),bind(B,$thf( tc_Polynomial_Opoly @ tc_Int_Oint ))]]) ).

thf(1040,axiom,
    class_Groups_Osgn__if @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osgn__if) ).

thf(4635,plain,
    class_Groups_Osgn__if @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).

thf(254,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ C @ A )
       => ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ C @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__zdiffD) ).

thf(2182,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ C @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ C @ A )
       => ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(8301,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ B )
      | ~ ( class_Orderings_Oord @ tc_RealDef_Oreal )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_RealDef_Oreal ) @ D @ C )
      | ( ( c_Groups_Ozero__class_Ozero @ B )
       != v_da____ )
      | ( ( hAPP @ C @ F )
       != v_mazh )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
       != ( hAPP @ D @ F ) ) ),
    inference(paramod_ordered,[status(thm)],[1333,8249]) ).

thf(8302,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ D )
      | ~ ( class_Orderings_Oord @ tc_RealDef_Oreal )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ B )
      | ( ( c_Groups_Ozero__class_Ozero @ D )
       != v_da____ )
      | ( ( hAPP @ B @ A )
       != v_mazh ) ),
    inference(pattern_uni,[status(thm)],[8301:[bind(A,$thf( A )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( hAPP @ ( c_Groups_Otimes__class_Otimes @ J ) @ ( c_Groups_Ozero__class_Ozero @ J ) )),bind(E,$thf( E )),bind(F,$thf( A ))]]) ).

thf(8332,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ D )
      | ~ ( class_Orderings_Oord @ tc_RealDef_Oreal )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ B )
      | ( ( c_Groups_Ozero__class_Ozero @ D )
       != v_da____ )
      | ( ( hAPP @ B @ A )
       != v_mazh ) ),
    inference(simp,[status(thm)],[8302]) ).

thf(8565,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ tc_RealDef_Oreal )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Ozero__class_Ozero @ D ) ) @ B )
      | ( ( c_Groups_Ozero__class_Ozero @ D )
       != v_da____ )
      | ( ( hAPP @ B @ A )
       != v_mazh )
      | ( ( class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex )
       != ( class_RealVector_Oreal__normed__algebra @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[3342,8332]) ).

thf(8566,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oord @ tc_RealDef_Oreal )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) @ B )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex )
       != v_da____ )
      | ( ( hAPP @ B @ A )
       != v_mazh ) ),
    inference(pattern_uni,[status(thm)],[8565:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( tc_Complex_Ocomplex ))]]) ).

thf(8820,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ $true
      | ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) @ B )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex )
       != v_da____ )
      | ( ( hAPP @ B @ A )
       != v_mazh ) ),
    inference(rewrite,[status(thm)],[8566,5099]) ).

thf(8821,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) @ B )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex )
       != v_da____ )
      | ( ( hAPP @ B @ A )
       != v_mazh ) ),
    inference(simp,[status(thm)],[8820]) ).

thf(8859,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) @ B )
      | ( v_cs____ != v_da____ )
      | ( ( hAPP @ B @ A )
       != v_mazh )
      | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
       != ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,8821]) ).

thf(8882,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) @ B )
      | ( v_cs____ != v_da____ )
      | ( ( hAPP @ B @ A )
       != v_mazh )
      | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
       != tc_Complex_Ocomplex ) ),
    inference(simp,[status(thm)],[8859]) ).

thf(9173,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ v_cs____ ) @ B )
      | ( v_cs____ != v_da____ )
      | ( ( hAPP @ B @ A )
       != v_mazh )
      | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
       != tc_Complex_Ocomplex )
      | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
       != ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,8882]) ).

thf(9195,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ v_cs____ ) @ B )
      | ( v_cs____ != v_da____ )
      | ( ( hAPP @ B @ A )
       != v_mazh )
      | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
       != tc_Complex_Ocomplex )
      | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
       != tc_Complex_Ocomplex ) ),
    inference(simp,[status(thm)],[9173]) ).

thf(9206,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_RealDef_Oreal ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ v_cs____ ) @ B )
      | ( v_cs____ != v_da____ )
      | ( ( hAPP @ B @ A )
       != v_mazh )
      | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
       != tc_Complex_Ocomplex ) ),
    inference(simp,[status(thm)],[9195]) ).

thf(17608,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ v_da____ )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh ) ) ),
    inference(paramod_ordered,[status(thm)],[1527,17349]) ).

thf(17623,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ v_da____ )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_da____ )
      | ( A != v_mazh ) ),
    inference(simp,[status(thm)],[17608]) ).

thf(17637,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ v_da____ )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_da____ ) ),
    inference(simp,[status(thm)],[17623]) ).

thf(971,axiom,
    class_Rings_Ozero__neq__one @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).

thf(4430,plain,
    class_Rings_Ozero__neq__one @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).

thf(57,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).

thf(1471,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(92434,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) )
       != ( class_Rings_Ocomm__ring @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[90561,1575]) ).

thf(92435,plain,
    class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[92434:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ))]]) ).

thf(727,axiom,
    class_Rings_Ocomm__ring__1 @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).

thf(3747,plain,
    class_Rings_Ocomm__ring__1 @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).

thf(1199,axiom,
    class_Groups_Ogroup__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).

thf(5035,plain,
    class_Groups_Ogroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).

thf(168,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Rings_Odvd__class_Odvd @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A )
       => ( c_Rings_Odvd__class_Odvd @ D @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__right) ).

thf(1877,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Rings_Odvd__class_Odvd @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A )
       => ( c_Rings_Odvd__class_Odvd @ D @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(978,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ B ) ) @ A ) )
    <=> ( ( B
         != ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
        | ( A
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__zpower__abs__iff) ).

thf(4445,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ B ) ) @ A ) )
       => ( ( B
           != ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
          | ( A
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
      & ( ( ( B
           != ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
          | ( A
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ B ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).

thf(490,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
    <=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ C @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__reduce) ).

thf(3027,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
       => ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ C @ B ) )
      & ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ C @ B )
       => ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ C @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(1122,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(4880,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)],[1122]) ).

thf(4881,plain,
    ! [A: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      = A ),
    inference(cnf,[status(esa)],[4880]) ).

thf(4882,plain,
    ! [A: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      = A ),
    inference(lifteq,[status(thm)],[4881]) ).

thf(1554,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Olinordered__ring__strict @ C )
      | ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) )
       != ( c_Groups_Ozero__class_Ozero @ C ) )
      | ( B
        = ( c_Groups_Ozero__class_Ozero @ C ) ) ),
    inference(cnf,[status(esa)],[1552]) ).

thf(1557,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) )
       != ( c_Groups_Ozero__class_Ozero @ C ) )
      | ( B
        = ( c_Groups_Ozero__class_Ozero @ C ) )
      | ~ ( class_Rings_Olinordered__ring__strict @ C ) ),
    inference(lifteq,[status(thm)],[1554]) ).

thf(1109,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(4833,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)],[1109]) ).

thf(90341,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) )
       != ( class_Rings_Ocomm__ring @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[89104,1575]) ).

thf(90342,plain,
    class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[90341:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ))]]) ).

thf(1019,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(4569,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)],[1019]) ).

thf(840,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(4064,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)],[840]) ).

thf(1104,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(4818,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)],[1104]) ).

thf(131,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( 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(1731,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(745,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(3800,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)],[745]) ).

thf(670,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(3572,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)],[670]) ).

thf(1127,axiom,
    class_Groups_Oabs__if @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oabs__if) ).

thf(4897,plain,
    class_Groups_Oabs__if @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).

thf(1169,axiom,
    class_Groups_Oone @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).

thf(4985,plain,
    class_Groups_Oone @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).

thf(164,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(1862,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)],[164]) ).

thf(881,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(4181,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)],[881]) ).

thf(492,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).

thf(3034,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(20,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oidom @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
       => ~ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ ( c_Nat_OSuc @ ( c_Polynomial_Oorder @ C @ A @ B ) ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__2) ).

thf(1325,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oidom @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
       => ~ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ ( c_Nat_OSuc @ ( c_Polynomial_Oorder @ C @ A @ B ) ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(1114,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(4850,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)],[1114]) ).

thf(482,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).

thf(3006,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(631,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(3451,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)],[631]) ).

thf(1553,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Olinordered__ring__strict @ C )
      | ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) )
       != ( c_Groups_Ozero__class_Ozero @ C ) )
      | ( A
        = ( c_Groups_Ozero__class_Ozero @ C ) ) ),
    inference(cnf,[status(esa)],[1552]) ).

thf(1556,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) )
       != ( c_Groups_Ozero__class_Ozero @ C ) )
      | ( A
        = ( c_Groups_Ozero__class_Ozero @ C ) )
      | ~ ( class_Rings_Olinordered__ring__strict @ C ) ),
    inference(lifteq,[status(thm)],[1553]) ).

thf(87150,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( class_Rings_Ocomm__ring @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      | ( A
       != ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ),
    inference(paramod_ordered,[status(thm)],[4121,87089]) ).

thf(87151,plain,
    ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) )
    | ( class_Rings_Ocomm__ring @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(pattern_uni,[status(thm)],[87150:[bind(A,$thf( tc_Polynomial_Opoly @ tc_RealDef_Oreal ))]]) ).

thf(458,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).

thf(2928,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(331,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__abs) ).

thf(2461,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ B ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(8280,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ A )
       != ( c_Groups_Ozero__class_Ozero @ A ) )
      | ( ( class_Rings_Ozero__neq__one @ tc_Complex_Ocomplex )
       != ( class_Rings_Ozero__neq__one @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4430,2315]) ).

thf(8281,plain,
    ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
   != ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
    inference(pattern_uni,[status(thm)],[8280:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(527,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).

thf(3150,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ B ) ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(1059,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(4684,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ A )
     => ( class_Groups_Oone @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).

thf(641,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(3480,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)],[641]) ).

thf(416,axiom,
    ! [A: $i,B: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
      = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).

thf(2770,plain,
    ! [A: $i,B: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
      = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(160,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Oring @ F )
     => ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C )
          = ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
      <=> ( C
          = ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( 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(1841,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Oring @ F )
     => ( ( ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C )
            = ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
         => ( C
            = ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) @ A ) ) )
        & ( ( C
            = ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) @ A ) )
         => ( ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C )
            = ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(121,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
        = ( hAPP @ ( hAPP @ ( 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(1699,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( c_Groups_Oplus__class_Oplus @ D @ C @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(245,axiom,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__cube) ).

thf(2156,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(119,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).

thf(1694,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(609,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__div__pos__le) ).

thf(3380,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(468,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Odiff) ).

thf(2962,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ D @ B @ A ) )
        = ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(83679,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != A )
      | ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) ) )
       != ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2178,82959]) ).

thf(83719,plain,
    ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
   != ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(simp,[status(thm)],[83679]) ).

thf(84703,plain,
    ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
   != ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
    inference(rewrite,[status(thm)],[83719,2178]) ).

thf(731,axiom,
    class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).

thf(3759,plain,
    class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).

thf(414,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(2765,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)],[414]) ).

thf(60828,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( class_Groups_Oab__group__add @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      | ( A
       != ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ),
    inference(paramod_ordered,[status(thm)],[4121,21007]) ).

thf(60829,plain,
    ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) )
    | ( class_Groups_Oab__group__add @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(pattern_uni,[status(thm)],[60828:[bind(A,$thf( tc_Polynomial_Opoly @ tc_Int_Oint ))]]) ).

thf(1152,axiom,
    class_Groups_Ozero @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).

thf(4955,plain,
    class_Groups_Ozero @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).

thf(6929,plain,
    ! [A: $i] :
      ( ( ( c_Polynomial_OpCons @ A @ ( c_Groups_Ozero__class_Ozero @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
      | ( ( class_Groups_Ozero @ tc_RealDef_Oreal )
       != ( class_Groups_Ozero @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4955,1272]) ).

thf(6930,plain,
    ( ( c_Polynomial_OpCons @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) )
    = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ),
    inference(pattern_uni,[status(thm)],[6929:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(372,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 @ ( hAPP @ ( hAPP @ ( 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(2620,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(241,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(2139,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)],[241]) ).

thf(707,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(3687,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)],[707]) ).

thf(530,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).

thf(3159,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(308,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) @ B )
          = ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__pos) ).

thf(2369,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
       => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) @ B )
          = ( c_Groups_Oabs__class_Oabs @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(951,axiom,
    class_Orderings_Olinorder @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).

thf(4362,plain,
    class_Orderings_Olinorder @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).

thf(408,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing) ).

thf(2752,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Oone__class_Oone @ D ) @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(1434,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) ) ),
    inference(cnf,[status(esa)],[1433]) ).

thf(1435,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A ) )
      = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ C @ B ) ) @ A ) ),
    inference(lifteq,[status(thm)],[1434]) ).

thf(1136,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(4918,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)],[1136]) ).

thf(584,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(3310,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)],[584]) ).

thf(10149,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
      | ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_da____ @ A )
      | ( B != v_mazh ) ),
    inference(paramod_ordered,[status(thm)],[1362,1263]) ).

thf(10150,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ A )
      | ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ v_mazh )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_da____ @ A ) ),
    inference(pattern_uni,[status(thm)],[10149:[bind(A,$thf( A )),bind(B,$thf( v_mazh ))]]) ).

thf(15057,plain,
    ! [B: $i,A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ B )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_da____ @ B )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ v_mazh ) ) ),
    inference(paramod_ordered,[status(thm)],[1527,10150]) ).

thf(15058,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
    | ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_da____ @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
    inference(pattern_uni,[status(thm)],[15057:[bind(A,$thf( v_mazh )),bind(B,$thf( c_Groups_Oone__class_Oone @ tc_Nat_Onat ))]]) ).

thf(46420,plain,
    ! [A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_da____ @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1527,15058]) ).

thf(46436,plain,
    ! [A: $i] :
      ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_da____ @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_mazh )
      | ( A
       != ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
    inference(simp,[status(thm)],[46420]) ).

thf(46476,plain,
    ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_da____ @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_mazh ) ),
    inference(simp,[status(thm)],[46436]) ).

thf(716,axiom,
    class_Groups_Omonoid__mult @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).

thf(3706,plain,
    class_Groups_Omonoid__mult @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(590,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(3325,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(524,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
       => ( c_Rings_Odvd__class_Odvd @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__power__dvd) ).

thf(3142,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
       => ( c_Rings_Odvd__class_Odvd @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(230,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mono) ).

thf(2101,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(926,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(4304,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)],[926]) ).

thf(18818,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh )
    | ( v_cs____ != v_da____ )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,17635]) ).

thf(18831,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh )
    | ( v_cs____ != v_da____ )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[18818]) ).

thf(1151,axiom,
    class_Groups_Osgn__if @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Osgn__if) ).

thf(4954,plain,
    class_Groups_Osgn__if @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).

thf(992,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(4497,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)],[992]) ).

thf(14010,plain,
    ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
   != ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_da____ @ v_mazh ) ),
    inference(paramod_ordered,[status(thm)],[4575,1263]) ).

thf(14049,plain,
    ( ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
     != v_da____ )
    | ( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
     != v_mazh ) ),
    inference(simp,[status(thm)],[14010]) ).

thf(476,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
        & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ C ) )
     => ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
       => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__trans) ).

thf(2984,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
        & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ C ) )
     => ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
       => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(192,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(1973,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)],[192]) ).

thf(14417,plain,
    ( ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( v_cs____ != v_da____ )
    | ( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
     != v_mazh )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,14049]) ).

thf(14427,plain,
    ( ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( v_cs____ != v_da____ )
    | ( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
     != v_mazh )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[14417]) ).

thf(986,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(4481,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)],[986]) ).

thf(149,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
        = ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__right) ).

thf(1805,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
        = ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(483,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono2) ).

thf(3009,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(76378,plain,
    ! [A: $i] :
      ( ( class_Orderings_Olinorder @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Olinordered__idom @ tc_Int_Oint )
       != ( class_Rings_Olinordered__idom @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[3913,1534]) ).

thf(76379,plain,
    class_Orderings_Olinorder @ ( tc_Polynomial_Opoly @ tc_Int_Oint ),
    inference(pattern_uni,[status(thm)],[76378:[bind(A,$thf( tc_Int_Oint ))]]) ).

thf(76417,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( class_Orderings_Olinorder @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      | ( A
       != ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ),
    inference(paramod_ordered,[status(thm)],[4121,76379]) ).

thf(76418,plain,
    ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) )
    | ( class_Orderings_Olinorder @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(pattern_uni,[status(thm)],[76417:[bind(A,$thf( tc_Polynomial_Opoly @ tc_Int_Oint ))]]) ).

thf(795,axiom,
    class_Groups_Ogroup__add @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).

thf(3936,plain,
    class_Groups_Ogroup__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).

thf(703,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(3672,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)],[703]) ).

thf(209,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).

thf(2037,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(1472,plain,
    ! [D: $i,C: $i,B: $i,A: $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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ),
    inference(cnf,[status(esa)],[1471]) ).

thf(576,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(3292,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)],[576]) ).

thf(762,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__left__mono) ).

thf(3849,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).

thf(216,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oring @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__minus) ).

thf(2054,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oring @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(969,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(4426,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)],[969]) ).

thf(186,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A )
    <=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I1_J) ).

thf(1948,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A )
       => ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) @ A ) )
      & ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ B ) @ A )
       => ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(961,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(4405,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)],[961]) ).

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

thf(4690,plain,
    class_Rings_Olinordered__semiring @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).

thf(1582,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Ocomm__semiring__1 @ C )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
    inference(cnf,[status(esa)],[1581]) ).

thf(1583,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) )
      | ~ ( class_Rings_Ocomm__semiring__1 @ C ) ),
    inference(lifteq,[status(thm)],[1582]) ).

thf(958,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(4394,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)],[958]) ).

thf(55853,plain,
    ! [B: $i,A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A ) )
     != ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[3515,55044]) ).

thf(55899,plain,
    ! [B: $i,A: $i] :
      ( ( tc_RealDef_Oreal != tc_RealDef_Oreal )
      | ( A
       != ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
      | ( ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ A )
       != ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ B ) ) ),
    inference(simp,[status(thm)],[55853]) ).

thf(55940,plain,
    ! [A: $i] :
      ( ( c_RealVector_Onorm__class_Onorm @ tc_RealDef_Oreal @ A )
     != ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
    inference(simp,[status(thm)],[55899]) ).

thf(369,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ E )
     => ( ( c_Rings_Odvd__class_Odvd @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
         => ( c_Rings_Odvd__class_Odvd @ E @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ E ) @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power__le) ).

thf(2614,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ E )
     => ( ( c_Rings_Odvd__class_Odvd @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
         => ( c_Rings_Odvd__class_Odvd @ E @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ E ) @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(540,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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1) ).

thf(3193,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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(820,axiom,
    ! [A: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ A )
     => ? [B: $i] :
          ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
          & ! [C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ A @ C ) ) @ ( c_RealVector_Onorm__class_Onorm @ A @ D ) ) ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ononneg__bounded) ).

thf(4013,plain,
    ! [A: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ A )
     => ? [B: $i] :
          ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B )
          & ! [C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ A @ C ) ) @ ( c_RealVector_Onorm__class_Onorm @ A @ D ) ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).

thf(911,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(4260,plain,
    class_Groups_Ocancel__ab__semigroup__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).

thf(478,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff1) ).

thf(2994,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(1189,axiom,
    class_Orderings_Olinorder @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).

thf(5025,plain,
    class_Orderings_Olinorder @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).

thf(420,axiom,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) @ A )
      = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__0) ).

thf(2784,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( 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)],[420]) ).

thf(281,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oring @ C )
     => ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( 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(2271,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oring @ C )
     => ( ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(979,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( class_Power_Opower @ C )
        & ( class_Rings_Omult__zero @ C )
        & ( class_Rings_Ono__zero__divisors @ C )
        & ( class_Rings_Ozero__neq__one @ C ) )
     => ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A )
          = ( c_Groups_Ozero__class_Ozero @ C ) )
      <=> ( ( B
            = ( c_Groups_Ozero__class_Ozero @ C ) )
          & ( A
           != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).

thf(4456,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( class_Power_Opower @ C )
        & ( class_Rings_Omult__zero @ C )
        & ( class_Rings_Ono__zero__divisors @ C )
        & ( class_Rings_Ozero__neq__one @ C ) )
     => ( ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A )
            = ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( ( B
              = ( c_Groups_Ozero__class_Ozero @ C ) )
            & ( A
             != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
        & ( ( ( B
              = ( c_Groups_Ozero__class_Ozero @ C ) )
            & ( A
             != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
         => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A )
            = ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).

thf(381,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ C @ B ) ) @ A )
      = ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).

thf(2652,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ C @ B ) ) @ A )
      = ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(1027,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(4598,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)],[1027]) ).

thf(47842,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
       != ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2851,37077]) ).

thf(47929,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) )
       != ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) )
      | ( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
       != A ) ),
    inference(simp,[status(thm)],[47842]) ).

thf(47993,plain,
    ! [A: $i] :
      ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) )
     != ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[47929]) ).

thf(443,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(2878,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)],[443]) ).

thf(43120,plain,
    ! [A: $i] :
      ( ( A
       != ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
       != ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2838,42687]) ).

thf(43278,plain,
    ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) )
     != ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
    inference(simp,[status(thm)],[43120]) ).

thf(43387,plain,
    ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) )
   != ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[43278]) ).

thf(932,axiom,
    class_Groups_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).

thf(4319,plain,
    class_Groups_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).

thf(329,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ C )
     => ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__over) ).

thf(2449,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ C )
     => ( ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Rings_Oinverse__class_Odivide @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(389,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
        = ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ominus) ).

thf(2684,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
        = ( c_Groups_Ouminus__class_Ouminus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(262,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
         => ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).

thf(2202,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
         => ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(787,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(3921,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)],[787]) ).

thf(433,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
      = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__assoc) ).

thf(2846,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
      = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(358,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B )
          = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) )
      <=> ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).

thf(2564,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B )
            = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) )
         => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B )
            = A ) )
        & ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ B )
            = A )
         => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ B )
            = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(86,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Nat_OSuc @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Nat_OSuc @ B ) ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__base) ).

thf(1550,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Nat_OSuc @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Nat_OSuc @ B ) ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(1551,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Olinordered__semidom @ D )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ ( c_Nat_OSuc @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ ( c_Nat_OSuc @ B ) ) )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
      | ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ),
    inference(cnf,[status(esa)],[1550]) ).

thf(1179,axiom,
    class_Groups_Ocancel__semigroup__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).

thf(5003,plain,
    class_Groups_Ocancel__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).

thf(1170,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(4986,plain,
    class_Groups_Olinordered__ab__group__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).

thf(879,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(4168,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)],[879]) ).

thf(362,axiom,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ A )
     != A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).

thf(2582,plain,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ A )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(831,axiom,
    class_Groups_Ocomm__monoid__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).

thf(4045,plain,
    class_Groups_Ocomm__monoid__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).

thf(136,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
         => ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).

thf(1748,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ B )
         => ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(75801,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[69314,1510]) ).

thf(75802,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[75801:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ) ))]]) ).

thf(57053,plain,
    ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != tc_Nat_Onat )
    | ( tc_Int_Oint != v_cs____ )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,56079]) ).

thf(57066,plain,
    ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != tc_Nat_Onat )
    | ( tc_Int_Oint != v_cs____ )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[57053]) ).

thf(77726,plain,
    ( ( tc_Nat_Onat != v_cs____ )
    | ( tc_Int_Oint != v_cs____ )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,57066]) ).

thf(77741,plain,
    ( ( tc_Nat_Onat != v_cs____ )
    | ( tc_Int_Oint != v_cs____ )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[77726]) ).

thf(77752,plain,
    ( ( tc_Nat_Onat != v_cs____ )
    | ( tc_Int_Oint != v_cs____ )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[77741]) ).

thf(71303,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
     != ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ A ) ),
    inference(paramod_ordered,[status(thm)],[63419,3379]) ).

thf(71333,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != A )
      | ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
       != A ) ),
    inference(simp,[status(thm)],[71303]) ).

thf(71367,plain,
    ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
   != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[71333]) ).

thf(757,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(3833,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)],[757]) ).

thf(54749,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_mazh )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Complex_Ocomplex @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh ) ) ),
    inference(paramod_ordered,[status(thm)],[54352,17638]) ).

thf(54793,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_mazh )
      | ( tc_Nat_Onat != tc_Complex_Ocomplex )
      | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
       != v_da____ )
      | ( A != v_mazh ) ),
    inference(simp,[status(thm)],[54749]) ).

thf(54823,plain,
    ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_mazh )
    | ( tc_Nat_Onat != tc_Complex_Ocomplex )
    | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
     != v_da____ ) ),
    inference(simp,[status(thm)],[54793]) ).

thf(429,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Olinordered__idom @ E )
     => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oabs__class_Oabs @ E @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oabs__class_Oabs @ E @ B ) @ A )
         => ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Oabs__class_Oabs @ E @ D ) ) @ ( c_Groups_Oabs__class_Oabs @ E @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__less) ).

thf(2831,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Olinordered__idom @ E )
     => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oabs__class_Oabs @ E @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless @ E @ ( c_Groups_Oabs__class_Oabs @ E @ B ) @ A )
         => ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Oabs__class_Oabs @ E @ D ) ) @ ( c_Groups_Oabs__class_Oabs @ E @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(146,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 @ ( hAPP @ ( hAPP @ ( 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(1798,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(4117,plain,
    ! [A: $i] :
      ( ~ ( 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(cnf,[status(esa)],[4116]) ).

thf(4119,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(lifteq,[status(thm)],[4117]) ).

thf(4120,plain,
    ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[4119]) ).

thf(5223,plain,
    ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ v_cs____ )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,4120]) ).

thf(5229,plain,
    ( ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ v_cs____ )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[5223]) ).

thf(725,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(3737,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)],[725]) ).

thf(68566,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) ) ) ) ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[67859,1510]) ).

thf(68567,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[68566:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) ) ) ) ) ))]]) ).

thf(75627,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) ) ) ) ) ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[68567,1510]) ).

thf(75628,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[75627:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) ) ) ) ) ) ))]]) ).

thf(693,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(3640,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)],[693]) ).

thf(72,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ B )
     => ? [C: $i] :
        ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Obounded) ).

thf(1516,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ B )
     => ? [C: $i] :
        ! [D: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(14653,plain,
    ! [A: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ A ) @ A )
      | ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
       != ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[14613,1339]) ).

thf(14654,plain,
    c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ),
    inference(pattern_uni,[status(thm)],[14653:[bind(A,$thf( c_Groups_Oone__class_Oone @ tc_Nat_Onat ))]]) ).

thf(302,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
    <=> ( ( B
          = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
        & ( A
          = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).

thf(2337,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
          = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
       => ( ( B
            = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
          & ( A
            = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
      & ( ( ( B
            = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
          & ( A
            = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
       => ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
          = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(2338,plain,
    ( ! [A: $i,B: $i] :
        ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
          = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
       => ( ( B
            = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
          & ( A
            = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) )
    & ! [A: $i,B: $i] :
        ( ( ( B
            = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
          & ( A
            = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) )
       => ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
          = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
    inference(miniscope,[status(thm)],[2337]) ).

thf(2339,plain,
    ! [B: $i,A: $i] :
      ( ( B
       != ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      | ( A
       != ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
    inference(cnf,[status(esa)],[2338]) ).

thf(2342,plain,
    ! [B: $i,A: $i] :
      ( ( B
       != ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      | ( A
       != ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
        = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
    inference(lifteq,[status(thm)],[2339]) ).

thf(2343,plain,
    ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
    = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[2342]) ).

thf(20768,plain,
    c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ),
    inference(rewrite,[status(thm)],[14654,2343]) ).

thf(52026,plain,
    ( ~ ( c_Orderings_Oord__class_Oless__eq @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ v_da____ @ v_mazh )
    | ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
     != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
    inference(paramod_ordered,[status(thm)],[20768,15065]) ).

thf(52044,plain,
    ( ~ ( c_Orderings_Oord__class_Oless__eq @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ v_da____ @ v_mazh )
    | ( tc_Nat_Onat != tc_Nat_Onat )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != tc_RealDef_Oreal )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
    inference(simp,[status(thm)],[52026]) ).

thf(52086,plain,
    ( ~ ( c_Orderings_Oord__class_Oless__eq @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ v_da____ @ v_mazh )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[52044]) ).

thf(586,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(3315,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ A )
     => ( class_Rings_Osemiring @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(950,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(4360,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)],[950]) ).

thf(19848,plain,
    ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_da____ )
    | ( v_cs____ != v_mazh )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,18838]) ).

thf(19862,plain,
    ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_da____ )
    | ( v_cs____ != v_mazh )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[19848]) ).

thf(384,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) )
    <=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).

thf(2661,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) ) )
      & ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(21603,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( ( c_Nat_OSuc @ A )
       != v_mzh )
      | ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
       != ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ v_mazh @ v_ma ) ) ),
    inference(paramod_ordered,[status(thm)],[3499,14801]) ).

thf(21626,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( ( c_Nat_OSuc @ A )
       != v_mzh )
      | ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_mazh )
      | ( A != v_ma ) ),
    inference(simp,[status(thm)],[21603]) ).

thf(21643,plain,
    ( ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( ( c_Nat_OSuc @ v_ma )
     != v_mzh )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_mazh ) ),
    inference(simp,[status(thm)],[21626]) ).

thf(54761,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_da____ )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Complex_Ocomplex @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ v_da____ ) ) ),
    inference(paramod_ordered,[status(thm)],[54352,17637]) ).

thf(54803,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_da____ )
      | ( tc_Nat_Onat != tc_Complex_Ocomplex )
      | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
       != v_mazh )
      | ( A != v_da____ ) ),
    inference(simp,[status(thm)],[54761]) ).

thf(54838,plain,
    ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_da____ )
    | ( tc_Nat_Onat != tc_Complex_Ocomplex )
    | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
     != v_mazh ) ),
    inference(simp,[status(thm)],[54803]) ).

thf(1232,axiom,
    class_Rings_Ono__zero__divisors @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).

thf(5111,plain,
    class_Rings_Ono__zero__divisors @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).

thf(135,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oidom @ C )
     => ( ( ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A )
          = ( c_Groups_Ozero__class_Ozero @ C ) )
      <=> ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__0__iff__dvd) ).

thf(1743,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oidom @ C )
     => ( ( ( ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A )
            = ( c_Groups_Ozero__class_Ozero @ C ) )
         => ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) @ B ) )
        & ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) @ B )
         => ( ( hAPP @ ( c_Polynomial_Opoly @ C @ B ) @ A )
            = ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(1143,axiom,
    class_Rings_Osemiring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).

thf(4939,plain,
    class_Rings_Osemiring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).

thf(561,axiom,
    class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).

thf(3260,plain,
    class_Groups_Ocancel__semigroup__add @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(401,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(2732,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)],[401]) ).

thf(634,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__le__div__pos) ).

thf(3462,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(138,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Groups_Ominus__class_Ominus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
          = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__divide__eq__iff) ).

thf(1753,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Groups_Ominus__class_Ominus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
          = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(1157,axiom,
    class_Rings_Oordered__comm__semiring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).

thf(4961,plain,
    class_Rings_Oordered__comm__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).

thf(314,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Oordered__ring @ F )
     => ( ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
      <=> ( c_Orderings_Oord__class_Oless @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff2) ).

thf(2386,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Oordered__ring @ F )
     => ( ( ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
         => ( c_Orderings_Oord__class_Oless @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) @ A ) ) )
        & ( ( c_Orderings_Oord__class_Oless @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) @ A ) )
         => ( c_Orderings_Oord__class_Oless @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(740,axiom,
    class_Fields_Ofield @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).

thf(3786,plain,
    class_Fields_Ofield @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).

thf(1164,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(4971,plain,
    class_RealVector_Oreal__normed__algebra__1 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).

thf(771,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(3872,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)],[771]) ).

thf(1218,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(5079,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).

thf(1038,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(4630,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)],[1038]) ).

thf(3606,plain,
    ! [B: $i,A: $i] :
      ( ( B != A )
      | ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
    inference(cnf,[status(esa)],[3604]) ).

thf(3607,plain,
    ! [B: $i,A: $i] :
      ( ( B != A )
      | ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
    inference(lifteq,[status(thm)],[3606]) ).

thf(3608,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ A ),
    inference(simp,[status(thm)],[3607]) ).

thf(57052,plain,
    ( ( tc_Nat_Onat != v_cs____ )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != tc_Int_Oint )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,56079]) ).

thf(57069,plain,
    ( ( tc_Nat_Onat != v_cs____ )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != tc_Int_Oint )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[57052]) ).

thf(974,axiom,
    class_Groups_Oone @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).

thf(4437,plain,
    class_Groups_Oone @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).

thf(942,axiom,
    class_Rings_Odvd @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).

thf(4346,plain,
    class_Rings_Odvd @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).

thf(18,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oidom @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
       => ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ ( c_Polynomial_Oorder @ C @ A @ B ) ) @ B )
          & ~ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ ( c_Nat_OSuc @ ( c_Polynomial_Oorder @ C @ A @ B ) ) ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order) ).

thf(1317,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oidom @ C )
     => ( ( B
         != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
       => ( ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ ( c_Polynomial_Oorder @ C @ A @ B ) ) @ B )
          & ~ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ ( c_Nat_OSuc @ ( c_Polynomial_Oorder @ C @ A @ B ) ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(50858,plain,
    ! [B: $i,A: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ A @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ 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 ) @ B ) @ B ) ),
    inference(paramod_ordered,[status(thm)],[46754,4201]) ).

thf(50947,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Int_Oint != tc_Int_Oint )
      | ( A
       != ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ B ) )
      | ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A )
       != B ) ),
    inference(simp,[status(thm)],[50858]) ).

thf(50980,plain,
    ! [A: $i] :
      ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) )
     != A ),
    inference(simp,[status(thm)],[50947]) ).

thf(487,axiom,
    ! [A: $i,B: $i] :
      ( ( B
       != ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
     => ( ( A
         != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ? [C: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ C ) @ A ) ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reduce__poly__simple) ).

thf(3019,plain,
    ! [A: $i,B: $i] :
      ( ( B
       != ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
     => ( ( A
         != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       => ? [C: $i] : ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ C ) @ A ) ) ) ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(406,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
     => ( ( C
          = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ C )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).

thf(2747,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
     => ( ( C
          = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ B @ C )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(1499,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Olinordered__semidom @ C )
      | ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ B )
      | ~ ( c_Orderings_Oord__class_Oless @ C @ B @ ( c_Groups_Oone__class_Oone @ C ) )
      | ( c_Orderings_Oord__class_Oless @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ),
    inference(cnf,[status(esa)],[1498]) ).

thf(960,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(4398,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)],[960]) ).

thf(226,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ E )
     => ( ( c_Rings_Odvd__class_Odvd @ E @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ E ) @ D ) @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ C )
         => ( c_Rings_Odvd__class_Odvd @ E @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ E ) @ D ) @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__dvd) ).

thf(2092,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ E )
     => ( ( c_Rings_Odvd__class_Odvd @ E @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ E ) @ D ) @ C ) @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ C )
         => ( c_Rings_Odvd__class_Odvd @ E @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ E ) @ D ) @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(852,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(4092,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)],[852]) ).

thf(797,axiom,
    class_Rings_Osemiring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).

thf(3940,plain,
    class_Rings_Osemiring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).

thf(270,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono1) ).

thf(2224,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(581,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(3305,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)],[581]) ).

thf(47,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oone__class_Oone @ D ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing) ).

thf(1431,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oone__class_Oone @ D ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(1432,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Olinordered__semidom @ D )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ C @ B )
      | ~ ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Oone__class_Oone @ D ) @ A )
      | ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) ) ),
    inference(cnf,[status(esa)],[1431]) ).

thf(884,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(4190,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).

thf(248,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(2165,plain,
    ! [A: $i] :
      ( ( class_Rings_Oidom @ A )
     => ( class_Rings_Oidom @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(775,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(3885,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)],[775]) ).

thf(152,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).

thf(1813,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(1297,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Groups_Ozero @ C )
      | ( ( c_Polynomial_OpCons @ C @ B @ A )
       != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
      | ( B
        = ( c_Groups_Ozero__class_Ozero @ C ) ) ),
    inference(cnf,[status(esa)],[1295]) ).

thf(1300,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Polynomial_OpCons @ C @ B @ A )
       != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
      | ( B
        = ( c_Groups_Ozero__class_Ozero @ C ) )
      | ~ ( class_Groups_Ozero @ C ) ),
    inference(lifteq,[status(thm)],[1297]) ).

thf(1452,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Olinordered__semiring__strict @ C )
      | ~ ( c_Orderings_Oord__class_Oless @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( hAPP @ ( hAPP @ ( 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(cnf,[status(esa)],[1451]) ).

thf(106,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
    <=> ( ( B = A )
        | ( C
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel1) ).

thf(1637,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
          = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
       => ( ( B = A )
          | ( C
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
      & ( ( ( B = A )
          | ( C
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
       => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
          = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(594,axiom,
    class_Rings_Oordered__semiring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).

thf(3334,plain,
    class_Rings_Oordered__semiring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(1183,axiom,
    class_Groups_Ominus @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ominus) ).

thf(5015,plain,
    class_Groups_Ominus @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).

thf(822,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(4020,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)],[822]) ).

thf(54601,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ v_da____ )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh ) ) ),
    inference(paramod_ordered,[status(thm)],[54339,17349]) ).

thf(54639,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ v_da____ )
      | ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
       != v_da____ )
      | ( A != v_mazh ) ),
    inference(simp,[status(thm)],[54601]) ).

thf(54688,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ v_da____ )
    | ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
     != v_da____ ) ),
    inference(simp,[status(thm)],[54639]) ).

thf(869,axiom,
    class_Rings_Oordered__ring__abs @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).

thf(4145,plain,
    class_Rings_Oordered__ring__abs @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).

thf(1194,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(5030,plain,
    class_Groups_Oordered__ab__group__add__abs @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).

thf(1257,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(5154,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)],[1257]) ).

thf(1255,axiom,
    class_Groups_Oab__semigroup__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).

thf(5152,plain,
    class_Groups_Oab__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255]) ).

thf(866,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(4132,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)],[866]) ).

thf(109,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
      = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zpower) ).

thf(1658,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ B ) ) @ A )
      = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(296,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 ) )
         => ( ( hAPP @ ( hAPP @ ( 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(2322,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 ) )
         => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
           != ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(393,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) )
      = ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).

thf(2701,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ B @ A ) )
      = ( c_Groups_Ominus__class_Ominus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(353,axiom,
    ( ( v_cs____
     != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
   => ? [A: $i] :
      ! [B: $i] :
        ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_da____ @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ v_aa____ @ ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ v_c____ @ v_cs____ ) ) ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_calculation) ).

thf(2545,plain,
    ( ( v_cs____
     != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
   => ? [A: $i] :
      ! [B: $i] :
        ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ B ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_da____ @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ v_aa____ @ ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ v_c____ @ v_cs____ ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(61723,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( A != v_da____ )
      | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_da____ )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[4121,18841]) ).

thf(61724,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( A != v_da____ )
      | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_da____ ) ),
    inference(pattern_uni,[status(thm)],[61723:[]]) ).

thf(63328,plain,
    ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ v_da____ )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_da____ ) ),
    inference(simp,[status(thm)],[61724]) ).

thf(1167,axiom,
    class_Int_Oring__char__0 @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).

thf(4982,plain,
    class_Int_Oring__char__0 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).

thf(115,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
        & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ C ) )
     => ( ( B = A )
       => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__less__eq__trans) ).

thf(1679,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
        & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ C ) )
     => ( ( B = A )
       => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(1095,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(4781,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)],[1095]) ).

thf(592,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(3329,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)],[592]) ).

thf(15667,plain,
    ( ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ v_cs____ )
     != ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,15632]) ).

thf(15676,plain,
    ( ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ v_cs____ )
     != ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[15667]) ).

thf(495,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
        <=> ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).

thf(3041,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B ) )
          & ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(735,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(3769,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)],[735]) ).

thf(1121,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(4875,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)],[1121]) ).

thf(181,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).

thf(1934,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(1155,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(4959,plain,
    class_Groups_Oordered__comm__monoid__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).

thf(122,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(1702,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)],[122]) ).

thf(352,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ B ) @ A ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ A )
         => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ C )
           => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).

thf(2543,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ E ) @ B ) @ A ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ A )
         => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ E @ C )
           => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(10,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oab__group__add @ C )
     => ( ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ B @ A ) )
        = ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__code_I2_J) ).

thf(1284,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Groups_Oab__group__add @ C )
     => ( ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ ( c_Polynomial_OpCons @ C @ B @ A ) )
        = ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) @ ( c_Groups_Ouminus__class_Ouminus @ ( tc_Polynomial_Opoly @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(67,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).

thf(1500,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B )
          = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) )
       => ( B = A ) )
      & ( ( B = A )
       => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B )
          = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(1501,plain,
    ( ! [A: $i,B: $i] :
        ( ? [C: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B )
            = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) )
       => ( B = A ) )
    & ! [A: $i,B: $i] :
        ( ( B = A )
       => ! [C: $i] :
            ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B )
            = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) ) ) ),
    inference(miniscope,[status(thm)],[1500]) ).

thf(1503,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B )
       != ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) )
      | ( B = A ) ),
    inference(cnf,[status(esa)],[1501]) ).

thf(1506,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B )
       != ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) )
      | ( B = A ) ),
    inference(lifteq,[status(thm)],[1503]) ).

thf(972,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(4431,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)],[972]) ).

thf(112,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Oordered__ring @ F )
     => ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff2) ).

thf(1670,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Oordered__ring @ F )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) @ A ) ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ F @ C @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ B @ E ) ) @ D ) @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(77473,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( class_Orderings_Oord @ ( tc_fun @ B @ C ) )
      | ( ( class_Orderings_Oord @ ( tc_fun @ A @ tc_RealDef_Oreal ) )
       != ( class_Orderings_Oord @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[77423,1536]) ).

thf(77474,plain,
    ! [B: $i,A: $i] : ( class_Orderings_Oord @ ( tc_fun @ A @ ( tc_fun @ B @ tc_RealDef_Oreal ) ) ),
    inference(pattern_uni,[status(thm)],[77473:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( tc_fun @ D @ tc_RealDef_Oreal ))]]) ).

thf(77489,plain,
    ! [B: $i,A: $i] : ( class_Orderings_Oord @ ( tc_fun @ A @ ( tc_fun @ B @ tc_RealDef_Oreal ) ) ),
    inference(simp,[status(thm)],[77474]) ).

thf(1251,axiom,
    class_Groups_Oab__semigroup__mult @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).

thf(5147,plain,
    class_Groups_Oab__semigroup__mult @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).

thf(318,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).

thf(2411,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(339,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( class_Rings_Odvd @ C )
        & ( class_Rings_Osemiring__0 @ C ) )
     => ( ? [D: $i] : ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ D ) ) )
      <=> ? [D: $i] :
            ( ( c_Rings_Odvd__class_Odvd @ C @ A @ ( c_Groups_Oplus__class_Oplus @ C @ D @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
            & ( hBOOL @ ( hAPP @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unity__coeff__ex) ).

thf(2500,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( class_Rings_Odvd @ C )
        & ( class_Rings_Osemiring__0 @ C ) )
     => ( ( ? [D: $i] : ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ D ) ) )
         => ? [D: $i] :
              ( ( c_Rings_Odvd__class_Odvd @ C @ A @ ( c_Groups_Oplus__class_Oplus @ C @ D @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
              & ( hBOOL @ ( hAPP @ B @ D ) ) ) )
        & ( ? [D: $i] :
              ( ( c_Rings_Odvd__class_Odvd @ C @ A @ ( c_Groups_Oplus__class_Oplus @ C @ D @ ( c_Groups_Ozero__class_Ozero @ C ) ) )
              & ( hBOOL @ ( hAPP @ B @ D ) ) )
         => ? [D: $i] : ( hBOOL @ ( hAPP @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(839,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(4057,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)],[839]) ).

thf(699,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(3652,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)],[699]) ).

thf(806,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(3970,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)],[806]) ).

thf(54602,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ v_da____ ) ) ),
    inference(paramod_ordered,[status(thm)],[54339,17349]) ).

thf(54664,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh )
      | ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
       != v_mazh )
      | ( A != v_da____ ) ),
    inference(simp,[status(thm)],[54602]) ).

thf(54677,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh )
    | ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
     != v_mazh ) ),
    inference(simp,[status(thm)],[54664]) ).

thf(89302,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
       != v_mazh )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh ) ) ),
    inference(paramod_ordered,[status(thm)],[54339,54677]) ).

thf(89351,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
       != v_mazh )
      | ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
       != v_da____ )
      | ( A != v_mazh ) ),
    inference(simp,[status(thm)],[89302]) ).

thf(89366,plain,
    ( ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
     != v_mazh )
    | ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
     != v_da____ ) ),
    inference(simp,[status(thm)],[89351]) ).

thf(323,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
    <=> ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
        & ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).

thf(2426,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
          & ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) )
      & ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
          & ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(284,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
      = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).

thf(2279,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ B @ A ) )
      = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(1081,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(4748,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)],[1081]) ).

thf(77426,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Oord @ ( tc_fun @ A @ B ) )
      | ( ( class_Orderings_Oord @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) )
       != ( class_Orderings_Oord @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[67494,1536]) ).

thf(77427,plain,
    ! [A: $i] : ( class_Orderings_Oord @ ( tc_fun @ A @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ),
    inference(pattern_uni,[status(thm)],[77426:[bind(A,$thf( A )),bind(B,$thf( tc_Polynomial_Opoly @ tc_RealDef_Oreal ))]]) ).

thf(868,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(4143,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)],[868]) ).

thf(832,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(4046,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)],[832]) ).

thf(1426,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) ) @ A )
      = ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ),
    inference(cnf,[status(esa)],[1425]) ).

thf(1427,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
      = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ C @ B ) ) @ A ) ),
    inference(lifteq,[status(thm)],[1426]) ).

thf(903,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(4235,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)],[903]) ).

thf(890,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(4202,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)],[890]) ).

thf(342,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
       != ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
     => ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C )
          = ( hAPP @ ( hAPP @ ( 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(2511,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
       != ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
     => ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C )
            = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ C )
            = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(517,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Rings_Odvd__class_Odvd @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A )
       => ( c_Rings_Odvd__class_Odvd @ D @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__left) ).

thf(3117,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Rings_Odvd__class_Odvd @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ A )
       => ( c_Rings_Odvd__class_Odvd @ D @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(2859,plain,
    ( ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal )
   != ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    inference(polarity_switch,[status(thm)],[2858]) ).

thf(2860,plain,
    ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
   != ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(lifteq,[status(thm)],[2859]) ).

thf(464,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B )
          = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) )
      <=> ( B
          = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).

thf(2949,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B )
            = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) )
         => ( B
            = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) )
        & ( ( B
            = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) )
         => ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B )
            = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(914,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(4267,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)],[914]) ).

thf(502,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ E )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).

thf(3071,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ E )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(1226,axiom,
    class_Rings_Oordered__ring__abs @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring__abs) ).

thf(5100,plain,
    class_Rings_Oordered__ring__abs @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).

thf(529,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ B )
     => ( ( hAPP @ ( hAPP @ ( 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(3156,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ B )
     => ( ( hAPP @ ( hAPP @ ( 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)],[529]) ).

thf(783,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(3914,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)],[783]) ).

thf(653,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(3520,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)],[653]) ).

thf(603,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(3366,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)],[603]) ).

thf(1001,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(4516,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)],[1001]) ).

thf(910,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(4257,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)],[910]) ).

thf(1053,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(4671,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)],[1053]) ).

thf(47834,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A )
       != ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1836,37077]) ).

thf(47912,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
       != ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) )
      | ( ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B )
       != A ) ),
    inference(simp,[status(thm)],[47834]) ).

thf(47974,plain,
    ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
   != ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[47912]) ).

thf(965,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(4414,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)],[965]) ).

thf(706,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ ( c_RealVector_Onorm__class_Onorm @ D @ A ) ) )
         => ( B
            = ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__ratiotest__lemma) ).

thf(3684,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__vector @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ D @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ ( c_RealVector_Onorm__class_Onorm @ D @ A ) ) )
         => ( B
            = ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(575,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(3288,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)],[575]) ).

thf(896,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(4217,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)],[896]) ).

thf(101,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( c_Rings_Odvd__class_Odvd @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__right) ).

thf(1617,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( c_Rings_Odvd__class_Odvd @ B @ A @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(1042,axiom,
    class_Groups_Ominus @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ominus) ).

thf(4639,plain,
    class_Groups_Ominus @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).

thf(48333,plain,
    ! [A: $i] :
      ( ( A
       != ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
       != ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2851,47985]) ).

thf(48366,plain,
    ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) )
     != ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) )
    | ( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
     != ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
    inference(simp,[status(thm)],[48333]) ).

thf(48406,plain,
    ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) )
   != ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) ),
    inference(simp,[status(thm)],[48366]) ).

thf(667,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(3565,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)],[667]) ).

thf(500,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(3067,plain,
    ! [A: $i,B: $i] :
      ( ( class_Orderings_Oorder @ B )
     => ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(1176,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(4997,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)],[1176]) ).

thf(1517,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ B )
      | ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_RealVector_Onorm__class_Onorm @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ C ) ) @ ( sk3 @ B @ A ) ) ) ),
    inference(cnf,[status(esa)],[1516]) ).

thf(297,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult__less) ).

thf(2325,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(142,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__1__mult) ).

thf(1781,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(686,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_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A )
         => ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ A @ B )
           => ( B = A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__antisym__nonneg) ).

thf(3625,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_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A )
         => ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ A @ B )
           => ( B = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(679,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(3593,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)],[679]) ).

thf(5487,plain,
    ! [A: $i] :
      ( ( ( c_Polynomial_OpCons @ A @ ( c_Groups_Oone__class_Oone @ A ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ A ) ) )
        = ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ A ) ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[4691,1316]) ).

thf(5488,plain,
    ( ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
    = ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
    inference(pattern_uni,[status(thm)],[5487:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(19517,plain,
    ( ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) @ v_cs____ )
    = ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
    inference(rewrite,[status(thm)],[5488,1280]) ).

thf(93100,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat != tc_Complex_Ocomplex )
      | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
       != v_mazh )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Complex_Ocomplex @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh ) ) ),
    inference(paramod_ordered,[status(thm)],[54352,54833]) ).

thf(93137,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat != tc_Complex_Ocomplex )
      | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
       != v_mazh )
      | ( tc_Nat_Onat != tc_Complex_Ocomplex )
      | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
       != v_da____ )
      | ( A != v_mazh ) ),
    inference(simp,[status(thm)],[93100]) ).

thf(93162,plain,
    ( ( tc_Nat_Onat != tc_Complex_Ocomplex )
    | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
     != v_mazh )
    | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
     != v_da____ ) ),
    inference(simp,[status(thm)],[93137]) ).

thf(1419,plain,
    ~ ? [A: $i] :
        ( ( c_Nat_OSuc @ A )
        = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(miniscope,[status(thm)],[1418]) ).

thf(1420,plain,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ A )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(cnf,[status(esa)],[1419]) ).

thf(1421,plain,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ A )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(lifteq,[status(thm)],[1420]) ).

thf(56027,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != tc_Nat_Onat )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Nat_Onat @ tc_Int_Oint ) ) ),
    inference(paramod_ordered,[status(thm)],[54339,54260]) ).

thf(56056,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != tc_Nat_Onat )
      | ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
       != tc_Nat_Onat )
      | ( A != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[56027]) ).

thf(56087,plain,
    ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != tc_Nat_Onat )
    | ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[56056]) ).

thf(640,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
         => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
           => ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__mono) ).

thf(3478,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
         => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
           => ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(617,axiom,
    ! [A: $i,B: $i] :
      ( ( B
       != ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ A @ B )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A ) @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__imp__le__int) ).

thf(3400,plain,
    ! [A: $i,B: $i] :
      ( ( B
       != ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ A @ B )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ A ) @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(456,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) )
           => ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__left__mono) ).

thf(2924,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) )
           => ( c_Orderings_Oord__class_Oless @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(624,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(3433,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)],[624]) ).

thf(922,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(4289,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)],[922]) ).

thf(177,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oring__no__zero__divisors @ C )
     => ( ( ( hAPP @ ( hAPP @ ( 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(1918,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oring__no__zero__divisors @ C )
     => ( ( ( ( hAPP @ ( hAPP @ ( 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 ) ) )
         => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A )
            = ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(935,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(4325,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).

thf(5359,plain,
    ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ v_cs____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,3133]) ).

thf(5362,plain,
    ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ v_cs____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[5359]) ).

thf(6958,plain,
    ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ v_cs____ ) @ v_cs____ ) )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_RealDef_Oreal )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,5362]) ).

thf(6981,plain,
    ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ v_cs____ ) @ v_cs____ ) )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_RealDef_Oreal )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[6958]) ).

thf(6985,plain,
    ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ v_cs____ ) @ v_cs____ ) )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[6981]) ).

thf(68051,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Rings_Oinverse__class_Odivide @ B @ A @ ( c_Groups_Oone__class_Oone @ B ) )
        = A )
      | ( ( class_Rings_Odivision__ring @ tc_RealDef_Oreal )
       != ( class_Rings_Odivision__ring @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[5067,1522]) ).

thf(68052,plain,
    ! [A: $i] :
      ( ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ A @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
      = A ),
    inference(pattern_uni,[status(thm)],[68051:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal ))]]) ).

thf(533,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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).

thf(3171,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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(467,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__one__le__power) ).

thf(2960,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B )
     => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(1120,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(4873,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)],[1120]) ).

thf(1319,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Oidom @ C )
      | ( B
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
      | ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ ( c_Polynomial_Oorder @ C @ A @ B ) ) @ B ) ),
    inference(cnf,[status(esa)],[1317]) ).

thf(1321,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
      | ~ ( class_Rings_Oidom @ C )
      | ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ ( c_Polynomial_Oorder @ C @ A @ B ) ) @ B ) ),
    inference(lifteq,[status(thm)],[1319]) ).

thf(108,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_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
       => ? [C: $i] :
            ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
            & ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ B )
              = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__pos__nth) ).

thf(1654,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_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
       => ? [C: $i] :
            ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
            & ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ B )
              = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(479,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).

thf(2997,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(64112,plain,
    ! [B: $i,A: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) )
       != ( class_Rings_Ocomm__semiring__1 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[63979,1491]) ).

thf(64113,plain,
    ! [A: $i] : ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) @ A ),
    inference(pattern_uni,[status(thm)],[64112:[bind(A,$thf( A )),bind(B,$thf( tc_Polynomial_Opoly @ tc_RealDef_Oreal ))]]) ).

thf(589,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(3320,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)],[589]) ).

thf(454,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
        & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ C ) )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
       => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__le__trans) ).

thf(2919,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ B )
        & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ C ) )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
       => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(1239,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(5124,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)],[1239]) ).

thf(271,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oring__1 @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus) ).

thf(2226,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oring__1 @ C )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ B ) ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ ( c_Groups_Ouminus__class_Ouminus @ C @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(380,axiom,
    ! [A: $i,B: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
        = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
    <=> ( ( B
          = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
        & ( A
          = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).

thf(2643,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
          = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
       => ( ( B
            = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
          & ( A
            = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
      & ( ( ( B
            = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
          & ( A
            = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
       => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A )
          = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(64073,plain,
    ! [B: $i,A: $i] :
      ( ( c_Rings_Odvd__class_Odvd @ B @ ( c_Groups_Oone__class_Oone @ B ) @ A )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) )
       != ( class_Rings_Ocomm__semiring__1 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[63977,1491]) ).

thf(64074,plain,
    ! [A: $i] : ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) @ A ),
    inference(pattern_uni,[status(thm)],[64073:[bind(A,$thf( A )),bind(B,$thf( tc_Polynomial_Opoly @ tc_Nat_Onat ))]]) ).

thf(383,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ F ) @ E ) @ D )
        = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C )
         => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ D )
           => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
             => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ F )
               => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ E @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).

thf(2658,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ F ) @ E ) @ D )
        = ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ A @ C )
         => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ D )
           => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ C )
             => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ C @ F )
               => ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ E @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(791,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(3929,plain,
    class_Groups_Oordered__ab__group__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).

thf(43142,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
       != ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[2838,37074]) ).

thf(43351,plain,
    ! [A: $i] :
      ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
       != ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) )
      | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != A ) ),
    inference(simp,[status(thm)],[43142]) ).

thf(43457,plain,
    ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
   != ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[43351]) ).

thf(132,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(1734,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)],[132]) ).

thf(929,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(4310,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)],[929]) ).

thf(1079,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(4730,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)],[1079]) ).

thf(1055,axiom,
    class_Groups_Omonoid__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).

thf(4678,plain,
    class_Groups_Omonoid__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).

thf(14507,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
     != ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_c____ ) ) ),
    inference(paramod_ordered,[status(thm)],[4081,3258]) ).

thf(14552,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( A
       != ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_c____ )
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(simp,[status(thm)],[14507]) ).

thf(14571,plain,
    ( ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_c____ )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(simp,[status(thm)],[14552]) ).

thf(494,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).

thf(3039,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(249,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(2167,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Olinordered__idom @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(1058,axiom,
    class_Rings_Olinordered__semiring @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).

thf(4683,plain,
    class_Rings_Olinordered__semiring @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).

thf(1072,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(4715,plain,
    class_Rings_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).

thf(728,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(3748,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)],[728]) ).

thf(471,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ E )
     => ( ( c_Rings_Odvd__class_Odvd @ E @ D @ C )
       => ( ( c_Rings_Odvd__class_Odvd @ E @ B @ A )
         => ( c_Rings_Odvd__class_Odvd @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__dvd__mono) ).

thf(2971,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ E )
     => ( ( c_Rings_Odvd__class_Odvd @ E @ D @ C )
       => ( ( c_Rings_Odvd__class_Odvd @ E @ B @ A )
         => ( c_Rings_Odvd__class_Odvd @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(1162,axiom,
    class_Groups_Ocomm__monoid__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).

thf(4969,plain,
    class_Groups_Ocomm__monoid__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).

thf(320,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
    <=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
        & ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).

thf(2416,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) )
       => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
          & ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) ) )
      & ( ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B )
          & ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A ) )
       => ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(1129,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(4900,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)],[1129]) ).

thf(912,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(4261,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)],[912]) ).

thf(636,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(3465,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)],[636]) ).

thf(1212,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(5055,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)],[1212]) ).

thf(768,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(3864,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)],[768]) ).

thf(54746,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_da____ )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Complex_Ocomplex @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ v_mazh ) ) ),
    inference(paramod_ordered,[status(thm)],[54352,17635]) ).

thf(54783,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_da____ )
      | ( tc_Nat_Onat != tc_Complex_Ocomplex )
      | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
       != v_da____ )
      | ( A != v_mazh ) ),
    inference(simp,[status(thm)],[54746]) ).

thf(54856,plain,
    ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_da____ )
    | ( tc_Nat_Onat != tc_Complex_Ocomplex )
    | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
     != v_da____ ) ),
    inference(simp,[status(thm)],[54783]) ).

thf(251,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__self) ).

thf(2174,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__idom @ B )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) ) @ ( c_Groups_Oabs__class_Oabs @ B @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(315,axiom,
    ! [A: $i,B: $i] :
      ( ( ( class_Power_Opower @ B )
        & ( class_Rings_Osemiring__0 @ B ) )
     => ( ( ( A
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
         => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
            = ( c_Groups_Oone__class_Oone @ B ) ) )
        & ( ( A
           != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
         => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
            = ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__left) ).

thf(2389,plain,
    ! [A: $i,B: $i] :
      ( ( ( class_Power_Opower @ B )
        & ( class_Rings_Osemiring__0 @ B ) )
     => ( ( ( A
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
         => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
            = ( c_Groups_Oone__class_Oone @ B ) ) )
        & ( ( A
           != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
         => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
            = ( c_Groups_Ozero__class_Ozero @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(287,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(2290,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)],[287]) ).

thf(1032,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(4615,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)],[1032]) ).

thf(47851,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
       != ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ B ) )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
       != ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[2838,37077]) ).

thf(47909,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) )
       != ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) )
      | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != B ) ),
    inference(simp,[status(thm)],[47851]) ).

thf(47969,plain,
    ! [A: $i] :
      ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) )
     != ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[47909]) ).

thf(8916,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Rings_Omult__zero @ B )
      | ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ v_cs____ @ ( c_Groups_Ozero__class_Ozero @ B ) )
      | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
       != tc_RealDef_Oreal )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ A )
       != ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1352,5361]) ).

thf(8917,plain,
    ( ~ ( class_Rings_Omult__zero @ tc_RealDef_Oreal )
    | ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ v_cs____ @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_RealDef_Oreal ) ),
    inference(pattern_uni,[status(thm)],[8916:[bind(A,$thf( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal )),bind(B,$thf( tc_RealDef_Oreal ))]]) ).

thf(9101,plain,
    ( ~ $true
    | ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ v_cs____ @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_RealDef_Oreal ) ),
    inference(rewrite,[status(thm)],[8917,5068]) ).

thf(9102,plain,
    ( ~ ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ v_cs____ @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[9101]) ).

thf(40188,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) ) @ A )
       != ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[1836,37074]) ).

thf(40315,plain,
    ! [A: $i] :
      ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
       != ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) )
      | ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
       != A ) ),
    inference(simp,[status(thm)],[40188]) ).

thf(40460,plain,
    ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) )
   != ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[40315]) ).

thf(981,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 @ B @ A )
       => ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__not__less) ).

thf(4468,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 @ B @ A )
       => ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).

thf(54615,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_da____ )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ v_da____ ) ) ),
    inference(paramod_ordered,[status(thm)],[54339,17637]) ).

thf(54643,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_da____ )
      | ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
       != v_mazh )
      | ( A != v_da____ ) ),
    inference(simp,[status(thm)],[54615]) ).

thf(54693,plain,
    ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_da____ )
    | ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
     != v_mazh ) ),
    inference(simp,[status(thm)],[54643]) ).

thf(1508,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Fields_Olinordered__field @ D )
      | ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
      | ~ ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) @ A )
      | ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ),
    inference(cnf,[status(esa)],[1507]) ).

thf(1243,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(5132,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)],[1243]) ).

thf(481,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).

thf(3003,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ E @ D )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Groups_Ominus__class_Ominus @ tc_Nat_Onat @ D @ E ) ) @ C ) @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ E ) @ C ) @ B ) @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ D ) @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(819,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(4010,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)],[819]) ).

thf(1068,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__field @ B )
     => ? [C: $i] :
          ( ( c_Orderings_Oord__class_Oless__eq @ 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 @ ( c_Rings_Oinverse__class_Odivide @ B @ D @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Ononneg__bounded) ).

thf(4705,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__field @ B )
     => ? [C: $i] :
          ( ( c_Orderings_Oord__class_Oless__eq @ 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 @ ( c_Rings_Oinverse__class_Odivide @ B @ D @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).

thf(46684,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint )
       != B )
      | ( ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) @ A )
       != ( c_Groups_Oplus__class_Oplus @ tc_Int_Oint @ B @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4907,45743]) ).

thf(46685,plain,
    ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
   != ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) ),
    inference(pattern_uni,[status(thm)],[46684:[bind(A,$thf( c_Groups_Oone__class_Oone @ tc_Int_Oint )),bind(B,$thf( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ))]]) ).

thf(604,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(3368,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)],[604]) ).

thf(462,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).

thf(2944,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(201,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semidom @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
       => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__power) ).

thf(2009,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__semidom @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oone__class_Oone @ C ) @ B )
       => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(888,axiom,
    class_Rings_Olinordered__semiring__strict @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).

thf(4197,plain,
    class_Rings_Olinordered__semiring__strict @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).

thf(1262,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(5162,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262]) ).

thf(299,axiom,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__minus__mult__self__le) ).

thf(2330,plain,
    ! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Ouminus__class_Ouminus @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(1512,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Fields_Ofield__inverse__zero @ D )
      | ( C
        = ( c_Groups_Ozero__class_Ozero @ D ) )
      | ( ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
        = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) ) @ C ) ) ),
    inference(cnf,[status(esa)],[1511]) ).

thf(1513,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( c_Groups_Ozero__class_Ozero @ D ) )
      | ( ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) ) @ C )
        = ( c_Groups_Oplus__class_Oplus @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) )
      | ~ ( class_Fields_Ofield__inverse__zero @ D ) ),
    inference(lifteq,[status(thm)],[1512]) ).

thf(110,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ D )
     => ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__mult) ).

thf(1661,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ D )
     => ( ( hAPP @ ( c_Polynomial_Opoly @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ D ) ) @ C ) @ B ) ) @ A )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ C ) @ A ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ D @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(236,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ E )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ C ) ) @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ A ) )
        = ( c_Rings_Oinverse__class_Odivide @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__times__eq) ).

thf(2120,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ E )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Rings_Oinverse__class_Odivide @ E @ D @ C ) ) @ ( c_Rings_Oinverse__class_Odivide @ E @ B @ A ) )
        = ( c_Rings_Oinverse__class_Odivide @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(661,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(3552,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)],[661]) ).

thf(1034,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Olinordered__semiring__1__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).

thf(4619,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Olinordered__semiring__1__strict @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).

thf(100,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
          = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__num) ).

thf(1614,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield__inverse__zero @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
          = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(117,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) ) @ A )
          = ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__power__divide) ).

thf(1689,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) ) @ A )
          = ( c_Rings_Oinverse__class_Odivide @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(810,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(3978,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)],[810]) ).

thf(335,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(2475,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)],[335]) ).

thf(1029,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(4602,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)],[1029]) ).

thf(1159,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(4964,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)],[1159]) ).

thf(453,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_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
       => ? [C: $i] :
            ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
            & ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ B )
              = A )
            & ! [D: $i] :
                ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ D )
                  & ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ D ) @ B )
                    = A ) )
               => ( D = C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__pos__nth__unique) ).

thf(2912,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_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
       => ? [C: $i] :
            ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
            & ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ C ) @ B )
              = A )
            & ! [D: $i] :
                ( ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ D )
                  & ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_RealDef_Oreal ) @ D ) @ B )
                    = A ) )
               => ( D = C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(211,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
       != ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A )
      <=> ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mono) ).

thf(2041,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
       != ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) )
     => ( ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A )
         => ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) ) )
        & ( ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ C ) @ A ) )
         => ( c_Rings_Odvd__class_Odvd @ tc_Int_Oint @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(58199,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != tc_Int_Oint )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Complex_Ocomplex @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Int_Oint @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[54352,54263]) ).

thf(58234,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != tc_Int_Oint )
      | ( tc_Nat_Onat != tc_Complex_Ocomplex )
      | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
       != tc_Int_Oint )
      | ( A != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[58199]) ).

thf(58260,plain,
    ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != tc_Int_Oint )
    | ( tc_Nat_Onat != tc_Complex_Ocomplex )
    | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
     != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[58234]) ).

thf(674,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(3585,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)],[674]) ).

thf(1026,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(4591,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)],[1026]) ).

thf(81509,plain,
    ! [B: $i,A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ A ) )
     != ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ B ) ),
    inference(paramod_ordered,[status(thm)],[3417,81500]) ).

thf(81575,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( c_Nat_OSuc @ B )
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      | ( ( c_Nat_OSuc @ A )
       != B ) ),
    inference(simp,[status(thm)],[81509]) ).

thf(81614,plain,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ ( c_Nat_OSuc @ A ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[81575]) ).

thf(1230,axiom,
    class_RealVector_Oreal__field @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__field) ).

thf(5109,plain,
    class_RealVector_Oreal__field @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).

thf(1203,axiom,
    class_Orderings_Oorder @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).

thf(5040,plain,
    class_Orderings_Oorder @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).

thf(1092,axiom,
    class_Power_Opower @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).

thf(4774,plain,
    class_Power_Opower @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).

thf(925,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(4299,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)],[925]) ).

thf(985,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(4478,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)],[985]) ).

thf(218,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
       => ( c_Rings_Odvd__class_Odvd @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult) ).

thf(2066,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
       => ( c_Rings_Odvd__class_Odvd @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(90762,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) )
       != ( class_Rings_Ocomm__ring @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[90342,1575]) ).

thf(90763,plain,
    class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[90762:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ))]]) ).

thf(13419,plain,
    ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ v_cs____ )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,12931]) ).

thf(13428,plain,
    ( ~ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ v_cs____ )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[13419]) ).

thf(14649,plain,
    ! [A: $i] :
      ( ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
       != tc_Nat_Onat )
      | ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
       != ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ A @ v_cs____ ) ) ),
    inference(paramod_ordered,[status(thm)],[14613,5298]) ).

thf(14687,plain,
    ! [A: $i] :
      ( ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
       != tc_Nat_Onat )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != A )
      | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != v_cs____ ) ),
    inference(simp,[status(thm)],[14649]) ).

thf(14700,plain,
    ( ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_cs____ ) ),
    inference(simp,[status(thm)],[14687]) ).

thf(39042,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ) ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[29260,1417]) ).

thf(39043,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[39042:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(46175,plain,
    ! [A: $i] :
      ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ) ) ) ) ) ) )
       != ( class_Groups_Oab__group__add @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[39043,1417]) ).

thf(46176,plain,
    class_Groups_Oab__group__add @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[46175:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ) ) ) ) ) ) ) ) ) ))]]) ).

thf(1241,axiom,
    class_Rings_Oidom @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).

thf(5128,plain,
    class_Rings_Oidom @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).

thf(44297,plain,
    ! [A: $i] :
      ( ( A
       != ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) )
      | ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
       != ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2851,41177]) ).

thf(44529,plain,
    ( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) )
     != ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) )
    | ( ( c_Groups_Oone__class_Oone @ tc_Int_Oint )
     != ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
    inference(simp,[status(thm)],[44297]) ).

thf(44748,plain,
    ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) )
   != ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) ),
    inference(simp,[status(thm)],[44529]) ).

thf(1135,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(4917,plain,
    class_Groups_Oordered__comm__monoid__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).

thf(343,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
        <=> ( c_Orderings_Oord__class_Oless @ D @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__divide__eq) ).

thf(2517,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) )
           => ( c_Orderings_Oord__class_Oless @ D @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) ) )
          & ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ C ) )
           => ( c_Orderings_Oord__class_Oless @ D @ B @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(779,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(3907,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)],[779]) ).

thf(683,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(3601,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)],[683]) ).

thf(49344,plain,
    ! [A: $i] :
      ( ( tc_Int_Oint != tc_RealDef_Oreal )
      | ( A
       != ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ A ) )
       != ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4626,46014]) ).

thf(49363,plain,
    ( ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( tc_Int_Oint != tc_Int_Oint )
    | ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
     != ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
    inference(simp,[status(thm)],[49344]) ).

thf(49373,plain,
    ( ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( ( c_Groups_Ouminus__class_Ouminus @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
     != ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
    inference(simp,[status(thm)],[49363]) ).

thf(989,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(4491,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)],[989]) ).

thf(1204,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(5041,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).

thf(242,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ C )
     => ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( 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(2142,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring__strict @ C )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ ( hAPP @ ( hAPP @ ( 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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(861,axiom,
    class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).

thf(4125,plain,
    class_Groups_Ocomm__monoid__mult @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).

thf(459,axiom,
    ! [A: $i,B: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A )
      = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__commute) ).

thf(2930,plain,
    ! [A: $i,B: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ B ) @ A )
      = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(237,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
       => ( c_Rings_Odvd__class_Odvd @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult2) ).

thf(2123,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ D )
     => ( ( c_Rings_Odvd__class_Odvd @ D @ C @ B )
       => ( c_Rings_Odvd__class_Odvd @ D @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(310,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
        = ( hAPP @ ( hAPP @ ( 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(2374,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( c_Groups_Oplus__class_Oplus @ B @ A @ A )
        = ( hAPP @ ( hAPP @ ( 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)],[310]) ).

thf(286,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(2287,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)],[286]) ).

thf(58123,plain,
    ( ( tc_Nat_Onat != v_cs____ )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != tc_Nat_Onat )
    | ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
     != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,56089]) ).

thf(58134,plain,
    ( ( tc_Nat_Onat != v_cs____ )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != tc_Nat_Onat )
    | ( ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[58123]) ).

thf(1577,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Ocomm__semiring__1 @ C )
      | ( ( c_Groups_Oplus__class_Oplus @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ B ) ) ),
    inference(cnf,[status(esa)],[1576]) ).

thf(1578,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Groups_Oplus__class_Oplus @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ B ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ A @ ( c_Groups_Oone__class_Oone @ C ) ) ) @ B ) )
      | ~ ( class_Rings_Ocomm__semiring__1 @ C ) ),
    inference(lifteq,[status(thm)],[1577]) ).

thf(858,axiom,
    class_Int_Oring__char__0 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).

thf(4114,plain,
    class_Int_Oring__char__0 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).

thf(1242,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(5129,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)],[1242]) ).

thf(983,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(4472,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)],[983]) ).

thf(766,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(3860,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)],[766]) ).

thf(348,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(2534,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Oordered__ring @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(276,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).

thf(2255,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ C @ B )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(908,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(4254,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)],[908]) ).

thf(1180,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(5004,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)],[1180]) ).

thf(774,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(3882,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)],[774]) ).

thf(815,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(3987,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)],[815]) ).

thf(1076,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(4719,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)],[1076]) ).

thf(345,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Oordered__ring @ F )
     => ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) @ C ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff1) ).

thf(2522,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_Rings_Oordered__ring @ F )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) @ C ) @ A ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Groups_Ominus__class_Ominus @ F @ E @ B ) ) @ D ) @ C ) @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ F @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ B ) @ D ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(513,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__div__algebra @ C )
     => ( ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ C @ B ) ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult) ).

thf(3100,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_RealVector_Oreal__normed__div__algebra @ C )
     => ( ( c_RealVector_Onorm__class_Onorm @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) )
        = ( hAPP @ ( hAPP @ ( 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)],[513]) ).

thf(606,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(3373,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)],[606]) ).

thf(635,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(3464,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(1380,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Ocomm__semiring__1 @ C )
      | ( c_Rings_Odvd__class_Odvd @ C @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ),
    inference(cnf,[status(esa)],[1379]) ).

thf(64891,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != tc_Nat_Onat )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Int_Oint @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[54339,54275]) ).

thf(64930,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != tc_Nat_Onat )
      | ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
       != tc_Int_Oint )
      | ( A != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[64891]) ).

thf(64951,plain,
    ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != tc_Nat_Onat )
    | ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
     != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[64930]) ).

thf(13,axiom,
    ! [A: $i,B: $i] :
      ( ( v_cs____
       != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
     => ? [C: $i] :
        ! [D: $i] :
          ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ D ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ A @ v_cs____ ) ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons_Ohyps) ).

thf(1303,plain,
    ! [A: $i,B: $i] :
      ( ( v_cs____
       != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
     => ? [C: $i] :
        ! [D: $i] :
          ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ C @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ D ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ B @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ A @ v_cs____ ) ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(196,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).

thf(1986,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( c_Orderings_Oord__class_Oless @ D @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(742,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(3790,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)],[742]) ).

thf(596,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(3337,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)],[596]) ).

thf(113,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ B )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_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_mult__poly__0__left) ).

thf(1673,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__0 @ B )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ B ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(963,axiom,
    class_Rings_Ocomm__semiring__0 @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).

thf(4410,plain,
    class_Rings_Ocomm__semiring__0 @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).

thf(5370,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Polynomial_Osynthetic__div @ B @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) @ A )
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ B ) ) )
      | ( ( class_Rings_Ocomm__semiring__0 @ tc_Nat_Onat )
       != ( class_Rings_Ocomm__semiring__0 @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[4410,1266]) ).

thf(5371,plain,
    ! [A: $i] :
      ( ( c_Polynomial_Osynthetic__div @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) @ A )
      = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Nat_Onat ) ) ),
    inference(pattern_uni,[status(thm)],[5370:[bind(A,$thf( A )),bind(B,$thf( tc_Nat_Onat ))]]) ).

thf(214,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).

thf(2050,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(1182,axiom,
    class_Rings_Oordered__cancel__semiring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).

thf(5014,plain,
    class_Rings_Oordered__cancel__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).

thf(709,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(3690,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)],[709]) ).

thf(812,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(3982,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)],[812]) ).

thf(58200,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != tc_Int_Oint )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ tc_Int_Oint @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[54339,54263]) ).

thf(58229,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != tc_Int_Oint )
      | ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
       != tc_Int_Oint )
      | ( A != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[58200]) ).

thf(58255,plain,
    ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != tc_Int_Oint )
    | ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( ( c_Groups_Oone__class_Oone @ tc_RealDef_Oreal )
     != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[58229]) ).

thf(826,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(4029,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)],[826]) ).

thf(772,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(3875,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)],[772]) ).

thf(394,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(2704,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)],[394]) ).

thf(123,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(1710,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)],[123]) ).

thf(1200,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(5036,plain,
    class_Groups_Oordered__ab__group__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).

thf(58,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C = B )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
       => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__eq__le__trans) ).

thf(1473,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C = B )
     => ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
       => ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(46338,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      | ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ A )
       != ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ v_da____ @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4980,15058]) ).

thf(46442,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      | ( tc_RealDef_Oreal != tc_RealDef_Oreal )
      | ( A != v_da____ )
      | ( A
       != ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ) ),
    inference(simp,[status(thm)],[46338]) ).

thf(46482,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_da____ ) ),
    inference(simp,[status(thm)],[46442]) ).

thf(1344,plain,
    ~ ? [A: $i] :
        ( A
        = ( c_Nat_OSuc @ A ) ),
    inference(miniscope,[status(thm)],[1343]) ).

thf(1345,plain,
    ! [A: $i] :
      ( A
     != ( c_Nat_OSuc @ A ) ),
    inference(cnf,[status(esa)],[1344]) ).

thf(1346,plain,
    ! [A: $i] :
      ( ( c_Nat_OSuc @ A )
     != A ),
    inference(lifteq,[status(thm)],[1345]) ).

thf(1231,axiom,
    class_Rings_Oring__1 @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).

thf(5110,plain,
    class_Rings_Oring__1 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).

thf(486,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Odivision__ring @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( ( hAPP @ ( hAPP @ ( 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(3015,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Odivision__ring @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( ( hAPP @ ( hAPP @ ( 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)],[486]) ).

thf(163,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) )
        = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
     => ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ B )
        = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__zmult__eq__1) ).

thf(1859,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A ) )
        = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
     => ( ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ B )
        = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(870,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(4146,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)],[870]) ).

thf(1017,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(4565,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)],[1017]) ).

thf(836,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(4051,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)],[836]) ).

thf(1260,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(5159,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)],[1260]) ).

thf(946,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(4350,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)],[946]) ).

thf(153,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__mono2) ).

thf(1816,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( c_Groups_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C )
     => ( ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ B @ A )
       => ( c_Orderings_Oord__class_Oless @ tc_RealDef_Oreal @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(1084,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(4755,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)],[1084]) ).

thf(301,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(2334,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)],[301]) ).

thf(664,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(3560,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Groups_Oabs__if @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(1126,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(4895,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)],[1126]) ).

thf(256,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(2186,plain,
    ! [A: $i] :
      ( ( class_Groups_Ozero @ A )
     => ( class_Groups_Ozero @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(601,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
        <=> ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__divide__le__eq) ).

thf(3347,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ C )
       => ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) ) )
          & ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(920,axiom,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Oordered__ring__abs @ ( tc_Polynomial_Opoly @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring__abs) ).

thf(4286,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Oordered__ring__abs @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).

thf(570,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(3277,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)],[570]) ).

thf(535,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ E )
     => ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
           => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
             => ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).

thf(3177,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_Rings_Olinordered__semiring__strict @ E )
     => ( ( c_Orderings_Oord__class_Oless @ E @ D @ C )
       => ( ( c_Orderings_Oord__class_Oless @ E @ B @ A )
         => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ D )
           => ( ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Groups_Ozero__class_Ozero @ E ) @ B )
             => ( c_Orderings_Oord__class_Oless @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ C ) @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(747,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(3804,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)],[747]) ).

thf(850,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(4083,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)],[850]) ).

thf(823,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(4024,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)],[823]) ).

thf(360,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(2572,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)],[360]) ).

thf(220,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_RealVector_Oreal__field @ F )
     => ( ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ C ) @ B ) ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ D @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ C ) @ A ) ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__mult__lemma) ).

thf(2070,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( class_RealVector_Oreal__field @ F )
     => ( ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ C ) @ B ) ) @ A )
        = ( c_Groups_Oplus__class_Oplus @ F @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ D @ B ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ ( c_Rings_Oinverse__class_Odivide @ F @ ( c_Groups_Ominus__class_Ominus @ F @ E @ C ) @ A ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(69460,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) ) )
       != ( class_Rings_Ocomm__semiring__1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[68283,1510]) ).

thf(69461,plain,
    class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[69460:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ) ))]]) ).

thf(977,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(4442,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)],[977]) ).

thf(828,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(4034,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)],[828]) ).

thf(734,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(3765,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)],[734]) ).

thf(886,axiom,
    class_Orderings_Opreorder @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).

thf(4193,plain,
    class_Orderings_Opreorder @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).

thf(622,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(3424,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)],[622]) ).

thf(385,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).

thf(2668,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ D )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ ( c_Groups_Oplus__class_Oplus @ D @ B @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(92568,plain,
    ! [A: $i] :
      ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ A ) )
      | ( ( class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) )
       != ( class_Rings_Ocomm__ring @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[90763,1575]) ).

thf(92569,plain,
    class_Rings_Ocomm__ring @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ) ),
    inference(pattern_uni,[status(thm)],[92568:[bind(A,$thf( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ ( tc_Polynomial_Opoly @ tc_Int_Oint ) ) ) ) ) ))]]) ).

thf(179,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Oone__class_Oone @ D ) )
           => ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).

thf(1930,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Rings_Olinordered__semidom @ D )
     => ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
         => ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Oone__class_Oone @ D ) )
           => ( c_Orderings_Oord__class_Oless @ D @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ D ) @ A ) @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(712,axiom,
    class_Groups_Omonoid__mult @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).

thf(3701,plain,
    class_Groups_Omonoid__mult @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).

thf(1254,axiom,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ v_da____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_aa____ ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_c____ ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_z____ ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_h) ).

thf(5151,plain,
    c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Oplus__class_Oplus @ tc_RealDef_Oreal @ ( c_Groups_Oabs__class_Oabs @ tc_RealDef_Oreal @ v_da____ ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_aa____ ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_c____ ) ) @ ( c_RealVector_Onorm__class_Onorm @ tc_Complex_Ocomplex @ v_z____ ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254]) ).

thf(938,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
         => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__left__mono__neg) ).

thf(4330,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
         => ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ B ) )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ C ) @ ( c_Rings_Oinverse__class_Odivide @ D @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).

thf(994,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(4501,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)],[994]) ).

thf(64109,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( class_Rings_Ocomm__semiring__1 @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      | ( A
       != ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) ) ),
    inference(paramod_ordered,[status(thm)],[4121,63979]) ).

thf(64110,plain,
    ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( tc_Polynomial_Opoly @ tc_RealDef_Oreal ) )
    | ( class_Rings_Ocomm__semiring__1 @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(pattern_uni,[status(thm)],[64109:[bind(A,$thf( tc_Polynomial_Opoly @ tc_RealDef_Oreal ))]]) ).

thf(1054,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(4674,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)],[1054]) ).

thf(239,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oidom @ C )
     => ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
          = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
      <=> ( ( B = A )
          | ( B
            = ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__disj) ).

thf(2127,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Oidom @ C )
     => ( ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
            = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) )
         => ( ( B = A )
            | ( B
              = ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) ) )
        & ( ( ( B = A )
            | ( B
              = ( c_Groups_Ouminus__class_Ouminus @ C @ A ) ) )
         => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ B ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
            = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ C ) @ A ) @ ( c_Nat_OSuc @ ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(1112,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(4848,plain,
    class_Groups_Ocancel__ab__semigroup__add @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).

thf(157,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(1829,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)],[157]) ).

thf(489,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(3025,plain,
    ! [A: $i] :
      ( ( class_Rings_Olinordered__idom @ A )
     => ( class_Rings_Olinordered__semidom @ ( tc_Polynomial_Opoly @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(156,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(1827,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)],[156]) ).

thf(1531,plain,
    ! [B: $i,A: $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(cnf,[status(esa)],[1530]) ).

thf(1532,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Nat_OSuc @ B )
        = A )
      | ~ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ B @ A )
      | ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Nat_OSuc @ B ) @ A ) ),
    inference(lifteq,[status(thm)],[1531]) ).

thf(1102,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(4799,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)],[1102]) ).

thf(669,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(3570,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)],[669]) ).

thf(1382,plain,
    ! [B: $i,A: $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 ) ) ),
    inference(cnf,[status(esa)],[1381]) ).

thf(1384,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Groups_Osgn__class_Osgn @ B @ A )
       != ( c_Groups_Ozero__class_Ozero @ B ) )
      | ( A
        = ( c_Groups_Ozero__class_Ozero @ B ) )
      | ~ ( class_Rings_Olinordered__idom @ B ) ),
    inference(lifteq,[status(thm)],[1382]) ).

thf(1165,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(4972,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).

thf(1247,axiom,
    class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).

thf(5140,plain,
    class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).

thf(1378,plain,
    ! [B: $i,A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Int_Oint ) @ ( c_Groups_Oabs__class_Oabs @ tc_Int_Oint @ B ) ) @ A ) ),
    inference(cnf,[status(esa)],[1377]) ).

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

thf(2265,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Ofield @ D )
     => ( ( C
         != ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Groups_Oplus__class_Oplus @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
          = ( c_Rings_Oinverse__class_Odivide @ D @ ( c_Groups_Oplus__class_Oplus @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(769,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(3869,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)],[769]) ).

thf(1213,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(5061,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)],[1213]) ).

thf(1171,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(4987,plain,
    class_Rings_Oring__no__zero__divisors @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).

thf(996,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(4506,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)],[996]) ).

thf(560,axiom,
    class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).

thf(3259,plain,
    class_Rings_Oordered__cancel__semiring @ tc_Nat_Onat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(841,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(4066,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)],[841]) ).

thf(988,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(4484,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)],[988]) ).

thf(644,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(3489,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)],[644]) ).

thf(1207,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(5046,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)],[1207]) ).

thf(658,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ D )
     => ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
      <=> ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ B ) )
          & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
           => ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
              & ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
               => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__divide__eq) ).

thf(3538,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field__inverse__zero @ D )
     => ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) )
         => ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
             => ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ B ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) ) )
        & ( ( ( ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
             => ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) @ B ) )
            & ( ~ ( c_Orderings_Oord__class_Oless @ D @ ( c_Groups_Ozero__class_Ozero @ D ) @ A )
             => ( ( ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ C ) @ A ) ) )
                & ( ~ ( c_Orderings_Oord__class_Oless @ D @ A @ ( c_Groups_Ozero__class_Ozero @ D ) )
                 => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) ) ) ) ) )
         => ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(1142,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(4936,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)],[1142]) ).

thf(390,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
    <=> ( ( C
          = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
        | ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).

thf(2687,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
          = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
       => ( ( C
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
          | ( B = A ) ) )
      & ( ( ( C
            = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
          | ( B = A ) )
       => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B )
          = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(439,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(2864,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)],[439]) ).

thf(726,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(3740,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)],[726]) ).

thf(1884,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A )
        = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    inference(cnf,[status(esa)],[1883]) ).

thf(1887,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A )
        = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
    inference(lifteq,[status(thm)],[1884]) ).

thf(1888,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      = ( c_Nat_OSuc @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(simp,[status(thm)],[1887]) ).

thf(39520,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
      = ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) ),
    inference(rewrite,[status(thm)],[1888,2178]) ).

thf(1296,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Groups_Ozero @ C )
      | ( ( c_Polynomial_OpCons @ C @ B @ A )
       != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
      | ( A
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ),
    inference(cnf,[status(esa)],[1295]) ).

thf(1299,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Polynomial_OpCons @ C @ B @ A )
       != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
      | ( A
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
      | ~ ( class_Groups_Ozero @ C ) ),
    inference(lifteq,[status(thm)],[1296]) ).

thf(504,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
        & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
     => ~ ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__asym_H) ).

thf(3076,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
        & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
     => ~ ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(614,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(3394,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)],[614]) ).

thf(392,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__neg) ).

thf(2699,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 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(749,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(3812,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)],[749]) ).

thf(646,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(3494,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)],[646]) ).

thf(785,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(3918,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)],[785]) ).

thf(41664,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      | ( ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ A @ A )
       != ( c_Orderings_Oord__class_Oless__eq @ tc_RealDef_Oreal @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ v_mazh ) ) ),
    inference(paramod_ordered,[status(thm)],[4980,15055]) ).

thf(41776,plain,
    ! [A: $i] :
      ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      | ( tc_RealDef_Oreal != tc_RealDef_Oreal )
      | ( A
       != ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
      | ( A != v_mazh ) ),
    inference(simp,[status(thm)],[41664]) ).

thf(41803,plain,
    ( ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_da____ @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != v_mazh ) ),
    inference(simp,[status(thm)],[41776]) ).

thf(952,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(4363,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)],[952]) ).

thf(309,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).

thf(2372,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__ring @ C )
     => ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Groups_Ozero__class_Ozero @ C ) @ ( c_Groups_Oplus__class_Oplus @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ B ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ C ) @ A ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(409,axiom,
    ! [A: $i,B: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
        & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
     => ~ ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__less) ).

thf(2754,plain,
    ! [A: $i,B: $i] :
      ( ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A )
        & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B ) )
     => ~ ( ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ A @ B )
          & ~ ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(379,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ A ) @ ( hAPP @ C @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ B ) ) ) @ B ) )
      = ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ A ) @ ( hAPP @ C @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ B ) ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__MVT) ).

thf(2640,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ A ) @ ( hAPP @ C @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ B ) ) ) @ B ) )
      = ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_Rings_Oinverse__class_Odivide @ tc_RealDef_Oreal @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ ( hAPP @ C @ A ) @ ( hAPP @ C @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ tc_RealDef_Oreal @ A @ B ) ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(1193,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(5029,plain,
    class_Groups_Ocancel__comm__monoid__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).

thf(788,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(3924,plain,
    class_Groups_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).

thf(1133,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(4908,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)],[1133]) ).

thf(691,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(3637,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)],[691]) ).

thf(1445,plain,
    ! [B: $i,A: $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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ),
    inference(cnf,[status(esa)],[1443]) ).

thf(1449,plain,
    ! [B: $i,A: $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 ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Nat_Onat ) @ B ) @ A ) ) ),
    inference(simp,[status(thm)],[1445]) ).

thf(54767,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_mazh )
      | ( ( c_Rings_Odvd__class_Odvd @ tc_Complex_Ocomplex @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) @ A )
       != ( c_Rings_Odvd__class_Odvd @ tc_Nat_Onat @ v_mazh @ v_da____ ) ) ),
    inference(paramod_ordered,[status(thm)],[54352,17640]) ).

thf(54799,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_mazh )
      | ( tc_Nat_Onat != tc_Complex_Ocomplex )
      | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
       != v_mazh )
      | ( A != v_da____ ) ),
    inference(simp,[status(thm)],[54767]) ).

thf(54832,plain,
    ( ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_mazh )
    | ( tc_Nat_Onat != tc_Complex_Ocomplex )
    | ( ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex )
     != v_mazh ) ),
    inference(simp,[status(thm)],[54799]) ).

thf(730,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(3753,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)],[730]) ).

thf(778,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(3901,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)],[778]) ).

thf(485,axiom,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__square) ).

thf(3013,plain,
    ! [A: $i] : ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ A @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(802,axiom,
    class_Groups_Oab__semigroup__mult @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).

thf(3960,plain,
    class_Groups_Oab__semigroup__mult @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).

thf(673,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(3580,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)],[673]) ).

thf(1318,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Rings_Oidom @ C )
      | ( B
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
      | ~ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ ( c_Nat_OSuc @ ( c_Polynomial_Oorder @ C @ A @ B ) ) ) @ B ) ),
    inference(cnf,[status(esa)],[1317]) ).

thf(1320,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) )
      | ~ ( class_Rings_Oidom @ C )
      | ~ ( c_Rings_Odvd__class_Odvd @ ( tc_Polynomial_Opoly @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ ( tc_Polynomial_Opoly @ C ) ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Ouminus__class_Ouminus @ C @ A ) @ ( c_Polynomial_OpCons @ C @ ( c_Groups_Oone__class_Oone @ C ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ C ) ) ) ) ) @ ( c_Nat_OSuc @ ( c_Polynomial_Oorder @ C @ A @ B ) ) ) @ B ) ),
    inference(lifteq,[status(thm)],[1318]) ).

thf(1003,axiom,
    class_Rings_Oidom @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).

thf(4520,plain,
    class_Rings_Oidom @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).

thf(916,axiom,
    class_Orderings_Oorder @ tc_Int_Oint,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).

thf(4274,plain,
    class_Orderings_Oorder @ tc_Int_Oint,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).

thf(549,axiom,
    ! [A: $i,B: $i] :
      ( ( ( class_Power_Opower @ B )
        & ( class_Rings_Osemiring__0 @ B ) )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Nat_OSuc @ A ) )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__Suc) ).

thf(3227,plain,
    ! [A: $i,B: $i] :
      ( ( ( class_Power_Opower @ B )
        & ( class_Rings_Osemiring__0 @ B ) )
     => ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ B ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) @ ( c_Nat_OSuc @ A ) )
        = ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(1067,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__field @ 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 @ ( c_Rings_Oinverse__class_Odivide @ B @ D @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Opos__bounded) ).

thf(4702,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__field @ 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 @ ( c_Rings_Oinverse__class_Odivide @ B @ D @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).

thf(1037,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ 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 @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Opos__bounded) ).

thf(4627,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ 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 @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).

thf(190,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
     => ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
          = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
      <=> ( ( B
            = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
          & ( A
            = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).

thf(1962,plain,
    ! [A: $i,B: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Int_Oint @ ( c_Groups_Ozero__class_Ozero @ tc_Int_Oint ) @ B )
     => ( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
            = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
         => ( ( B
              = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
            & ( A
              = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) )
        & ( ( ( B
              = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) )
            & ( A
              = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) )
         => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Int_Oint ) @ B ) @ A )
            = ( c_Groups_Oone__class_Oone @ tc_Int_Oint ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(185,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ E )
     => ( ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( 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(1945,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ E )
     => ( ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ A ) )
        = ( c_Groups_Oplus__class_Oplus @ E @ ( c_Groups_Oplus__class_Oplus @ E @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ ( c_Groups_Ominus__class_Ominus @ E @ D @ B ) ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ E ) @ B ) @ ( c_Groups_Ominus__class_Ominus @ E @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(1097,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(4784,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)],[1097]) ).

thf(133,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
      <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).

thf(1737,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
        & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
         => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(764,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(3854,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)],[764]) ).

thf(264,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__ring @ B )
     => ~ ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( 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(2206,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Olinordered__ring @ B )
     => ~ ( c_Orderings_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(1089,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(4767,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)],[1089]) ).

thf(440,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( hAPP @ ( hAPP @ ( 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(2866,plain,
    ! [A: $i,B: $i] :
      ( ( class_Rings_Ocomm__semiring__1 @ B )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ ( c_Groups_Oone__class_Oone @ B ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(875,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(4161,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)],[875]) ).

thf(62308,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( A != v_da____ )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(paramod_ordered,[status(thm)],[4121,15220]) ).

thf(62309,plain,
    ! [A: $i] :
      ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
      | ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( A != v_da____ ) ),
    inference(pattern_uni,[status(thm)],[62308:[]]) ).

thf(63452,plain,
    ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ v_da____ )
    | ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[62309]) ).

thf(325,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).

thf(2438,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(1083,axiom,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ B )
     => ? [C: $i] :
          ( ( c_Orderings_Oord__class_Oless__eq @ 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 @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ononneg__bounded) ).

thf(4752,plain,
    ! [A: $i,B: $i] :
      ( ( class_RealVector_Oreal__normed__algebra @ B )
     => ? [C: $i] :
          ( ( c_Orderings_Oord__class_Oless__eq @ 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 @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ D ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).

thf(930,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
        <=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__divide__le__eq) ).

thf(4313,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( class_Fields_Olinordered__field @ D )
     => ( ( c_Orderings_Oord__class_Oless @ D @ C @ ( c_Groups_Ozero__class_Ozero @ D ) )
       => ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ B ) )
          & ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ D ) @ A ) @ C ) @ B )
           => ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Rings_Oinverse__class_Odivide @ D @ B @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).

thf(628,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(3443,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)],[628]) ).

thf(52183,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != tc_RealDef_Oreal )
      | ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
       != ( c_Orderings_Oord__class_Oless__eq @ ( c_Groups_Oone__class_Oone @ tc_Nat_Onat ) @ v_da____ @ v_mazh ) ) ),
    inference(paramod_ordered,[status(thm)],[3785,52086]) ).

thf(52204,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != tc_RealDef_Oreal )
      | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
       != tc_Nat_Onat )
      | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
       != v_da____ )
      | ( A != v_mazh ) ),
    inference(simp,[status(thm)],[52183]) ).

thf(52227,plain,
    ( ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != tc_RealDef_Oreal )
    | ( ( c_Groups_Oone__class_Oone @ tc_Nat_Onat )
     != tc_Nat_Onat )
    | ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != v_da____ ) ),
    inference(simp,[status(thm)],[52204]) ).

thf(232,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( c_Rings_Odvd__class_Odvd @ C @ B @ ( c_Groups_Oabs__class_Oabs @ C @ A ) )
      <=> ( c_Rings_Odvd__class_Odvd @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__abs__iff) ).

thf(2106,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( class_Rings_Olinordered__idom @ C )
     => ( ( ( c_Rings_Odvd__class_Odvd @ C @ B @ ( c_Groups_Oabs__class_Oabs @ C @ A ) )
         => ( c_Rings_Odvd__class_Odvd @ C @ B @ A ) )
        & ( ( c_Rings_Odvd__class_Odvd @ C @ B @ A )
         => ( c_Rings_Odvd__class_Odvd @ C @ B @ ( c_Groups_Oabs__class_Oabs @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(225,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) )
    <=> ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).

thf(2087,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A ) )
      & ( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ B @ A )
       => ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ C ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(793,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(3933,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)],[793]) ).

thf(1464,plain,
    ! [B: $i,A: $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 ) ) ),
    inference(cnf,[status(esa)],[1463]) ).

thf(1467,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( c_Groups_Ozero__class_Ozero @ B ) )
      | ( ( c_Groups_Osgn__class_Osgn @ B @ A )
        = ( c_Groups_Ozero__class_Ozero @ B ) )
      | ~ ( class_Groups_Osgn__if @ B ) ),
    inference(lifteq,[status(thm)],[1464]) ).

thf(1468,plain,
    ! [A: $i] :
      ( ( ( c_Groups_Osgn__class_Osgn @ A @ ( c_Groups_Ozero__class_Ozero @ A ) )
        = ( c_Groups_Ozero__class_Ozero @ A ) )
      | ~ ( class_Groups_Osgn__if @ A ) ),
    inference(simp,[status(thm)],[1467]) ).

thf(497,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ B ) )
           != ( c_Groups_Oplus__class_Oplus @ F @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).

thf(3047,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 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ B ) )
           != ( c_Groups_Oplus__class_Oplus @ F @ C @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ F ) @ E ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(1144,axiom,
    class_Rings_Oordered__semiring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).

thf(4940,plain,
    class_Rings_Oordered__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).

thf(671,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(3575,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)],[671]) ).

thf(382,axiom,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ocomm__monoid__mult @ B )
     => ( ( hAPP @ ( hAPP @ ( 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(2655,plain,
    ! [A: $i,B: $i] :
      ( ( class_Groups_Ocomm__monoid__mult @ B )
     => ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ B ) @ ( c_Groups_Oone__class_Oone @ B ) ) @ A )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(817,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(4002,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)],[817]) ).

thf(133560,plain,
    $false,
    inference(e,[status(thm)],[5116,2778,2876,4852,15055,3449,4682,4904,2163,16466,81608,2199,1322,56093,2630,47949,1586,4201,2452,1879,1337,76449,1718,2094,1411,4094,1469,2744,2889,2306,3345,2109,2031,14801,3661,45273,3399,3930,3798,1559,3666,14574,1729,3477,3698,3397,20973,3863,3830,2787,2595,5028,4728,1818,1295,1956,4992,1686,4166,2250,1750,2210,2622,3912,4960,4711,3382,2363,1855,3534,3681,25737,2976,46647,4376,2117,5141,1406,3317,4226,87185,4339,4075,1882,1522,3762,3230,5292,5069,2395,3549,5000,1808,3417,88884,3285,3377,4391,3153,12089,1401,1422,2947,1939,2248,8118,2671,1544,2014,2099,2282,1591,2114,59940,1269,4326,4215,2380,37077,2854,1533,1692,4973,1486,4532,4105,1497,4090,47945,3135,2933,1275,4279,4564,65817,1458,22101,22030,5120,4234,5037,59936,3439,23621,24861,4418,1310,1756,4575,4839,3332,4647,22175,3648,3044,8981,15632,30510,2184,2316,3446,4650,2627,13692,1988,3826,67346,1342,3121,5161,4294,19919,3562,3577,66068,54674,4980,1507,2360,4941,2216,2432,76385,3308,3730,2886,1386,3140,4760,2957,3335,21398,54858,22829,3103,3350,86058,3634,2046,2763,2548,1576,5123,3249,4079,1441,22461,4679,3088,3777,4198,46014,2082,4665,12785,4156,1803,2136,1518,54694,2531,7178,1482,3597,4775,2869,5024,24060,4563,2039,4070,3342,3821,4778,5150,2562,81500,4568,4243,1409,64032,3263,1287,29621,4546,4439,22320,3976,2603,4524,21017,3195,4348,1430,3644,4956,87224,4692,3689,4224,1871,4761,3061,1907,60995,4654,1330,1264,1511,2274,4130,1313,4349,1279,4275,1455,3280,2466,5108,1462,4428,12693,1800,3517,4194,3470,3312,1494,1847,1892,5355,1379,4353,4788,2169,1514,4617,90446,56079,5199,4664,2767,20573,1479,4928,1347,1398,4830,3084,3734,59218,2520,4141,3951,2158,2024,4632,3835,65892,1362,4793,5020,3557,44620,2852,4771,3231,4514,68154,3268,4008,3258,54305,2829,83682,67037,2616,3431,41177,4820,1418,4815,5156,67492,3300,3851,2017,2178,4411,1489,4988,1415,1664,56089,2794,4903,4578,1811,1450,5027,3393,5013,1373,3724,17635,38707,3295,15261,1632,2469,1334,3527,3702,2880,21007,20687,4050,3973,1978,64149,29260,5032,2540,2034,4871,4115,1581,4686,23074,4783,81639,1283,2073,3986,48884,2861,5101,67550,4040,2965,5137,2718,5045,2508,4718,4751,2367,3537,92643,64677,6648,4055,1377,4935,2618,2833,14361,5096,2190,17349,4504,1796,3036,21181,1622,2424,2979,1526,4307,22271,4825,64101,1433,2103,2750,3588,4892,1697,21107,4211,3184,4475,2586,1975,4082,4483,3510,5298,2922,81483,3011,3567,1438,3186,5070,5142,5034,4910,5122,25288,2011,3097,3857,5157,3503,3459,47981,4323,3591,2204,4962,4589,4407,3984,3169,3265,43716,5117,1470,64023,1783,64946,4370,2737,1311,2296,4576,2083,4031,2496,24699,1868,2773,4999,2601,18838,64799,4434,46754,1487,4499,4493,86701,5049,2589,1387,63991,1900,1723,3261,4712,1343,4016,2560,1519,4397,4920,1580,2277,4989,1676,3022,67611,4521,4128,3069,3371,4204,1824,4284,54272,3816,1619,5102,68420,3814,54833,2414,4044,1560,2464,92301,2068,3926,1407,1291,1573,66163,70256,3307,3271,2445,63777,3980,1837,1602,4849,1365,2628,87146,3403,21641,2332,2826,16790,4155,2820,4757,3137,3499,3750,20912,65975,4385,5021,3718,4553,3600,1457,4187,2179,3144,4746,1836,77423,4942,2327,2213,90246,14565,2313,48145,4104,3727,1281,1740,1910,17638,3595,4027,4316,1402,2377,81619,21498,1328,16108,3704,5081,3650,69314,1350,77425,17395,1592,3784,2498,3909,1541,1983,4957,5053,3254,1270,5098,1534,1953,86053,4512,4108,2973,49386,2709,1970,3218,4048,75454,4636,1498,1587,15065,1425,4693,1540,3963,2726,63977,2724,4227,2858,3632,4095,3119,3078,4883,3916,3237,3941,3205,4219,2268,3440,4898,4263,4320,4951,1942,3210,22274,77419,2196,42687,2551,3643,3555,47061,4291,3954,4049,4653,4518,3326,5031,14613,88950,4860,3000,3179,4983,3846,5080,1292,3094,4721,4167,1461,4425,1424,3441,4545,2080,63778,4191,1584,4513,3032,1937,4861,4054,1612,4621,4180,3294,8952,2781,3935,45588,1478,1451,2598,2581,2756,1525,12756,3242,3703,2968,1324,1776,1263,4846,3486,2125,60575,2536,2681,3787,1530,1539,2836,1456,1266,4068,4970,5134,1552,2851,1932,4244,89104,2505,3390,3819,4237,10148,4540,2006,59931,3937,4717,2813,4347,3628,1874,67516,3115,3760,3967,3247,3692,2052,2697,1715,4953,4152,1720,28375,5026,3074,4689,3920,4416,77588,3162,4223,1333,4644,4966,3173,37074,2076,5434,2402,5126,3675,8708,4995,4163,3147,12931,4535,3824,2634,5112,4184,1991,82959,3802,5153,67859,2926,4352,21055,4288,3563,2761,2208,4081,3279,4212,46777,4889,3587,2057,1712,8279,3592,3639,2440,1515,23948,2221,14362,1895,3422,21448,2909,55044,3807,4921,2729,62114,2904,1959,3890,3262,4359,24925,51250,5043,3707,1727,1510,4708,64152,4470,4380,5138,2149,2253,3871,3491,1483,81627,1273,5230,21692,21142,2570,4256,4438,1548,1927,4657,5960,5048,2028,3375,3888,2734,87329,3839,5016,3792,25256,18841,2894,1374,3343,2260,3536,3372,4662,4341,3319,1916,3504,2789,2489,3086,3081,4122,90561,4465,3604,4946,5022,3213,81856,3234,2048,6916,3925,68068,4494,1389,4077,77437,3240,48706,2525,3609,2849,2188,2981,5067,4309,4926,3283,2674,4605,5099,1535,1403,5097,1795,15079,4328,24681,1520,4612,2817,4769,24745,64734,64071,3783,5449,1765,4273,3091,3170,47985,1428,3223,4251,4526,4537,54847,2193,5039,5033,4127,3964,5118,2293,3051,2891,2308,4645,3646,25255,4149,3208,3663,1635,2935,4822,3340,4573,1997,5148,4764,2442,2759,4854,4640,3302,19666,3719,87099,2358,2319,68283,62513,4790,2721,86060,2383,1574,13945,5054,3710,3500,1307,21222,2346,4716,5143,23838,3996,3631,2538,2478,3251,2151,2229,25518,2987,2637,3551,2422,3957,37304,3515,3779,2906,3419,4699,1349,2097,3270,77547,2257,1589,2955,1492,1603,2299,4601,3106,3468,63698,1542,4586,2839,3197,4073,5093,3182,2896,3384,54696,1571,1376,4509,1439,2025,2742,4332,17396,3483,4554,3456,64035,4635,2182,9206,17637,4430,1471,92435,3747,5035,1877,4445,3027,4882,1557,2625,4833,90342,4569,4064,4818,4028,23728,87271,1731,3800,3572,4897,4985,1862,4181,3034,1325,64620,4850,3006,3451,1556,87151,2928,1381,2461,8281,3150,4684,3480,2770,1841,2350,1699,8821,4196,2156,1694,3380,2962,84703,3759,3838,2765,60829,5218,6930,1528,2620,2139,3687,3159,2369,4362,22657,2752,1435,4918,3310,46476,1477,3706,3325,3142,2101,4304,18831,4954,4497,4626,21019,66935,14049,2984,1973,14427,4481,1805,3881,3009,76418,3936,3672,2037,1472,64062,15058,3292,3849,2054,4426,1948,4405,4907,4690,2816,1583,4394,55940,2614,3193,4013,4260,2994,5025,2784,2271,4456,2652,4598,45743,47993,2878,43387,4319,2449,1509,3975,64140,2684,2202,3921,1340,2846,2564,1551,5003,4986,4168,2582,4045,1748,75802,77752,71367,1647,3833,54823,2831,1798,5229,3737,75628,3640,1516,52086,2863,3315,24158,4360,4864,3913,19862,2661,21643,54838,5111,1743,4939,3260,4950,2732,3462,1753,4961,89193,2386,3786,1267,4971,3872,5079,4630,67148,3608,1484,15220,57069,4437,76379,4346,54352,1317,1579,50980,3019,2747,1499,4398,2092,4092,4905,3940,2224,3305,1432,4190,2165,68567,3885,1813,1300,1452,1637,3334,5015,4020,54688,1785,4145,2337,5030,5154,5152,4132,1658,2322,2701,2545,63328,4982,1679,3412,4781,3329,67494,15676,3041,3769,4875,1934,1543,4959,1702,2543,1284,1506,4431,1670,77489,1372,1404,5147,2411,2500,4057,3652,2838,3970,89366,2426,1536,15154,4624,1353,2279,4748,77427,2579,4143,4046,1427,4235,4202,2511,3117,63979,2860,10150,2949,2728,4267,3961,3071,1272,5100,3156,3914,3520,3366,19859,4516,4257,4671,47974,4414,3684,3288,4217,48880,1617,4639,63965,48406,3565,3067,57066,4997,1517,2325,1781,3625,3593,19517,93162,1421,56087,3478,3400,2924,3433,4289,54339,21968,1918,1316,4325,6985,68052,3171,2960,4873,1321,1834,22743,17640,1654,1412,2997,64113,4102,3320,1390,2919,5124,1575,2226,1453,2643,64074,2658,3929,43457,1734,5068,4310,4730,4678,14571,3039,4121,2167,1341,4683,4715,3748,2971,54275,4969,2416,4900,4261,3465,1276,1590,5055,3864,54856,2174,2389,2290,4615,47969,8882,9102,40460,4468,54693,1508,5132,4126,4042,21081,3003,4010,1523,4705,63419,46685,3368,2944,2009,1491,4197,5162,3497,4759,2330,87109,1513,1661,2120,3552,4619,1614,1689,3978,2475,4602,4964,2912,2041,58260,3585,4591,3267,81614,5109,5040,4774,4299,4478,20768,2066,90763,13428,14700,1309,46176,5128,2315,44748,1442,4917,2517,1280,3907,3601,47044,49373,87089,5078,4491,5041,2142,3379,4125,2930,2123,2374,4880,2287,58134,1578,4114,5129,4472,4687,3860,3785,2534,2255,4254,5004,22924,3882,3987,4719,2522,3100,3373,3464,1380,54263,64951,4787,1303,1986,3790,1527,3337,1673,5371,2050,5014,3690,3982,58255,4029,1314,4210,3875,2704,22392,1710,5036,1473,46482,1346,5110,3015,54677,1436,1859,4146,4565,4051,5159,4350,1816,1495,4755,2334,3560,4895,2186,3347,4286,3277,3177,3804,4968,39043,4083,20756,4024,2572,2070,3716,1410,69461,4442,4034,64990,3765,4193,3424,2668,92569,1930,89027,3701,5151,4330,4501,64110,4674,45856,2127,4848,21351,1352,3128,1829,54260,3025,1827,1532,4799,3570,1384,1537,4972,5140,1378,2265,3869,3772,5061,1550,4987,4506,3259,4066,4484,3489,1500,4410,5046,3538,10146,4936,2687,2864,3740,39520,1431,4955,1299,3076,3394,4691,2699,3812,3494,58251,3918,41803,4363,2372,1331,2754,2640,5029,3924,67730,1463,41603,4908,3637,1449,54832,1417,3753,3901,3013,3960,3580,1320,4520,4274,3227,4702,4627,1962,1945,37628,4555,64257,4784,1737,3854,2206,4767,14811,2866,4161,63452,2438,1490,4752,4313,3443,1416,52227,2106,2087,3933,4858,1468,3047,4940,3575,2177,2655,4002]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SWW237+1 : TPTP v8.2.0. Released v5.2.0.
% 0.10/0.11  % Command  : run_Leo-III %s %d THM
% 0.11/0.32  % Computer : n022.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Wed Jun 19 07:07:25 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 1.00/1.00  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.35/1.41  % [INFO] 	 Parsing done (409ms). 
% 2.35/1.43  % [INFO] 	 Running in sequential loop mode. 
% 3.25/1.80  % [INFO] 	 eprover registered as external prover. 
% 3.25/1.81  % [INFO] 	 Scanning for conjecture ... 
% 3.82/2.02  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1288 axioms. Running axiom selection ... 
% 5.56/2.41  % [INFO] 	 Axiom selection finished. Selected 1260 axioms (removed 28 axioms). 
% 7.43/3.05  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 7.74/3.11  % [INFO] 	 Type checking passed. 
% 7.74/3.11  % [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 ... 
% 288.63/87.88  % External prover 'e' found a proof!
% 288.63/87.88  % [INFO] 	 Killing All external provers ... 
% 288.63/87.88  % Time passed: 87379ms (effective reasoning time: 86449ms)
% 288.63/87.88  % 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)>
% 288.63/87.89  % Axioms used in derivation (1260): fact_zero__le__divide__iff, fact_dvd_Oord__less__eq__trans, fact_xt1_I1_J, fact_le__SucI, arity_fun__Orderings_Oorder, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_power__abs, fact_dvd_Oless__trans, fact_incr__mult__lemma, fact_zle__refl, fact_neg__le__0__iff__le, arity_Complex__Ocomplex__Rings_Odvd, fact_add__le__less__mono, fact_mult__strict__left__mono__neg, fact_order__le__neq__trans, fact_Nat_Oadd__0__right, fact_one__dvd, fact_right__inverse__eq, fact_real__squared__diff__one__factored, arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra, arity_Polynomial__Opoly__Rings_Osemiring__0, fact_abs__of__pos, fact_real__le__refl, fact_abs__le__D2, arity_Complex__Ocomplex__Rings_Oidom, fact_nat_Osimps_I3_J, arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_mult__right__le__imp__le, fact_zdvd__antisym__abs, fact_real__less__def, arity_Nat__Onat__Groups_Ocancel__semigroup__add, fact_real__le__trans, fact_neg__le__divide__eq, fact_power__strict__decreasing, arity_Complex__Ocomplex__Groups_Omonoid__add, arity_Int__Oint__Rings_Ocomm__semiring, fact_pos__add__strict, arity_Int__Oint__Rings_Osemiring, fact_mult__poly__0__right, arity_RealDef__Oreal__Orderings_Oord, fact_add__strict__right__mono, arity_Int__Oint__Orderings_Olinorder, fact_mult__1__left, fact_diff__0__eq__0, fact_minus__mult__left, fact_neg__divide__le__eq, fact_dvd__mult__cancel__left, fact_zdvd__not__zless, fact_neg__equal__0__iff__equal, fact_inf__period_I4_J, fact_dvdI, fact_abs__minus__commute, fact_abs__if, fact_le__eq__less__or__eq, fact_minus__mult__right, fact_xt1_I4_J, arity_RealDef__Oreal__Groups_Ozero, fact_trans__less__add1, fact_q__pos__lemma, 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_order, 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_dvd_Oeq__iff, fact_order__le__less__trans, fact_mult__left_Ominus, arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors, fact_real__sgn__eq, fact_zdvd__antisym__nonneg, fact_power__inject__base, fact_norm__power, arity_Nat__Onat__Rings_Ono__zero__divisors, fact_nat__less__cases, fact_divide__nonpos__neg, fact_one__is__add, arity_Int__Oint__Rings_Olinordered__semiring__strict, arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add, fact_termination__basic__simps_I5_J, arity_Polynomial__Opoly__Rings_Ocomm__semiring__0, fact_norm__mult__less, fact_odd__nonzero, fact_mult_Opos__bounded, fact_dvd_Oorder__trans, fact_norm__diff__triangle__ineq, fact_zminus__zminus, fact_mult__nonneg__nonpos, fact_poly__eq__0__iff__dvd, fact_less__imp__le__nat, fact_combine__common__factor, fact_le__imp__0__less, fact_n__less__m__mult__n, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_Suc__mono, fact_add__less__mono, fact_real__0__less__add__iff, fact_mult__eq__0__iff, fact_pow__divides__pow__int, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, arity_RealDef__Oreal__Groups_Ominus, arity_Nat__Onat__Orderings_Oorder, fact_mult__right__less__imp__less, fact_dvd__triv__right, fact_add__leD1, fact_abs__eq__mult, fact_split__mult__neg__le, fact_dvd_Oless__asym_H, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_unity__coeff__ex, fact_abs__div__pos, fact_zero__less__power, arity_Nat__Onat__Rings_Ocomm__semiring__0, fact_psize__eq__0__iff, arity_Nat__Onat__Groups_Oordered__comm__monoid__add, fact_less__nat__zero__code, arity_RealDef__Oreal__Rings_Osemiring__0, arity_RealDef__Oreal__Rings_Olinordered__ring, fact_linorder__not__le, fact_poly__bound__exists, arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le, fact_mult__le__less__imp__less, fact_zadd__commute, arity_Nat__Onat__Groups_Omonoid__mult, fact_power__increasing, fact_diff__Suc__less, fact_real__add__le__0__iff, fact_mult__0, fact_abs__triangle__ineq2__sym, fact_order__less__asym_H, fact_mult__poly__0__left, arity_Polynomial__Opoly__Rings_Olinordered__ring__strict, fact_order__eq__refl, fact_linorder__antisym__conv2, fact_abs__poly__def, fact_mult__mono, fact_linorder__neqE, fact_field__power__not__zero, arity_RealDef__Oreal__Rings_Oidom, fact_Suc__le__mono, fact_dvd_Oless__imp__not__less, fact_norm__add__less, arity_Nat__Onat__Rings_Ozero__neq__one, fact_poly__zero, fact_divide_Obounded, fact_eq__neg__iff__add__eq__0, arity_Polynomial__Opoly__Groups_Oab__semigroup__mult, fact_zero__le__zpower__abs, fact_add__right__imp__eq, fact_realpow__two__diff, arity_Complex__Ocomplex__Groups_Oab__semigroup__mult, arity_Polynomial__Opoly__Rings_Oidom, fact_mult_Ononneg__bounded, fact_nat__add__right__cancel, fact_neg__le__iff__le, fact_gr0__conv__Suc, 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% 288.63/87.89  % No. of inferences in proof: 3667
% 288.63/87.89  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 87379 ms resp. 86449 ms w/o parsing
% 290.22/88.40  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 290.39/88.41  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------