Leo-III---1.8.0.THM-Ref.s

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SWW222+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 09:09:42 AM UTC 2026

% Result   : Theorem 66.59s 17.78s
% Output   : Refutation 69.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      : 1251
% Syntax   : Number of formulae    : 2504 ( 844 unt;   0 typ;   0 def)
%            Number of atoms       : 6447 (1721 equ;   0 cnn)
%            Maximal formula atoms :   18 (   2 avg)
%            Number of connectives : 32489 ( 371   ~; 120   |; 699   &;28175   @)
%                                         ( 277 <=>;2847  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  114 ( 112 usr;  15 con; 0-3 aty)
%            Number of variables   : 4913 (   0   ^;4840   !;  73   ?;4913   :)

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

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

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

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

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

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

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

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

thf(v_wa_____decl,type,
    v_wa____: $i ).

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

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

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

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

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

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

thf(c_Int_OBit0_decl,type,
    c_Int_OBit0: $i > $i ).

thf(c_Int_OBit1_decl,type,
    c_Int_OBit1: $i > $i ).

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

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

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

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

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

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

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

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

thf(class_Rings_Ocomm__semiring__1_decl,type,
    class_Rings_Ocomm__semiring__1: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(class_Rings_Ocomm__semiring__0_decl,type,
    class_Rings_Ocomm__semiring__0: $i > $o ).

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

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

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

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

thf(class_Rings_Ocomm__ring__1_decl,type,
    class_Rings_Ocomm__ring__1: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(class_Rings_Olinordered__semiring__1_decl,type,
    class_Rings_Olinordered__semiring__1: $i > $o ).

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

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

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

thf(class_Rings_Olinordered__semiring__1__strict_decl,type,
    class_Rings_Olinordered__semiring__1__strict: $i > $o ).

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

thf(class_Rings_Oring__1__no__zero__divisors_decl,type,
    class_Rings_Oring__1__no__zero__divisors: $i > $o ).

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

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

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

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

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

thf(class_Rings_Oring__1_decl,type,
    class_Rings_Oring__1: $i > $o ).

thf(class_Rings_Osemiring__1_decl,type,
    class_Rings_Osemiring__1: $i > $o ).

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

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

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

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

thf(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct_decl,type,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).

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

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

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

thf(c_Int_Oiszero_decl,type,
    c_Int_Oiszero: $i > $i > $o ).

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

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

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

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

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

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

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

thf(class_Int_Oring__char__0_decl,type,
    class_Int_Oring__char__0: $i > $o ).

thf(class_RealVector_Oreal__normed__algebra__1_decl,type,
    class_RealVector_Oreal__normed__algebra__1: $i > $o ).

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

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

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

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

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

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

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

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

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

thf(251,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Ocancel__semigroup__add )
     => ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
          = ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__cancel) ).

thf(2163,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Ocancel__semigroup__add )
     => ( ( ( B = A )
         => ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
            = ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) )
        & ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
            = ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(120,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__ge__self) ).

thf(1665,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(746,axiom,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).

thf(3873,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).

thf(1134,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Int_Onumber__ring )
     => ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
        = ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__number__of__diff2) ).

thf(5116,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Int_Onumber__ring )
     => ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
        = ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).

thf(825,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Int_Onumber__ring )
        & ( B @ class_Fields_Ofield ) )
     => ( ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__numeral__1) ).

thf(4094,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Int_Onumber__ring )
        & ( B @ class_Fields_Ofield ) )
     => ( ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).

thf(1121,axiom,
    tc_RealDef_Oreal @ class_Rings_Oring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).

thf(5088,plain,
    tc_RealDef_Oreal @ class_Rings_Oring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).

thf(1140,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
      = ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__real__of__nat__cancel) ).

thf(5136,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
      = ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).

thf(864,axiom,
    ( ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
    = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__1__eq__Suc__0) ).

thf(4262,plain,
    ( ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
    = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).

thf(549,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).

thf(3167,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B = A )
       => ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
          = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
      & ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
          = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(461,axiom,
    tc_Nat_Onat @ class_Groups_Ocancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).

thf(2876,plain,
    tc_Nat_Onat @ class_Groups_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(369,axiom,
    v_f____ @ c_SEQ_Osubseq,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fz_I1_J) ).

thf(2559,plain,
    v_f____ @ c_SEQ_Osubseq,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(298,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Odivision__ring )
     => ( ( C
         != ( D @ c_Groups_Ozero__class_Ozero ) )
       => ( ( B
            = ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) )
         => ( ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
            = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__imp) ).

thf(2331,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Odivision__ring )
     => ( ( C
         != ( D @ c_Groups_Ozero__class_Ozero ) )
       => ( ( B
            = ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) )
         => ( ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
            = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(168,axiom,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != ( A @ c_Nat_OSuc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).

thf(1818,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != ( A @ c_Nat_OSuc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(93,axiom,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
        = ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) )
    <=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__0__number__of) ).

thf(1554,plain,
    ! [A: $i] :
      ( ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
          = ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ) )
      & ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
          = ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) )
       => ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(1215,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( C @ ( B @ hAPP ) )
          = ( C @ ( A @ hAPP ) ) )
     => ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).

thf(5422,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( C @ ( B @ hAPP ) )
          = ( C @ ( A @ hAPP ) ) )
     => ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).

thf(32,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
        = ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__add__abs) ).

thf(1337,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
        = ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(296,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( ( B @ c_Groups_Ozero__class_Ozero )
          = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
      <=> ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Int_Oiszero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__special_I1_J) ).

thf(2306,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Int_Oiszero ) )
         => ( ( B @ c_Groups_Ozero__class_Ozero )
            = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) )
        & ( ( ( B @ c_Groups_Ozero__class_Ozero )
            = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
         => ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Int_Oiszero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(597,axiom,
    tc_Int_Oint @ class_Rings_Ono__zero__divisors,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).

thf(3345,plain,
    tc_Int_Oint @ class_Rings_Ono__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(928,axiom,
    ! [A: $i] :
      ( ( A
       != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
     => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ c_Transcendental_Oarctan )
        = ( A @ c_Transcendental_Oarctan @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arctan__inverse) ).

thf(4464,plain,
    ! [A: $i] :
      ( ( A
       != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
     => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ c_Transcendental_Oarctan )
        = ( A @ c_Transcendental_Oarctan @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).

thf(301,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
      = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0) ).

thf(2341,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
      = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

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

thf(3008,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(64,axiom,
    ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
    = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__0) ).

thf(1454,plain,
    ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
    = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(615,axiom,
    ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero )
   != ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).

thf(3399,plain,
    ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero )
   != ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(282,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__1) ).

thf(2263,plain,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(694,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mono) ).

thf(3698,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).

thf(780,axiom,
    ! [A: $i] :
      ( ( A @ class_Int_Onumber__ring )
     => ( ( A @ c_Groups_Oone__class_Oone )
        = ( c_Int_OPls @ c_Int_OBit1 @ ( A @ c_Int_Onumber__class_Onumber__of ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I110_J) ).

thf(3979,plain,
    ! [A: $i] :
      ( ( A @ class_Int_Onumber__ring )
     => ( ( A @ c_Groups_Oone__class_Oone )
        = ( c_Int_OPls @ c_Int_OBit1 @ ( A @ c_Int_Onumber__class_Onumber__of ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).

thf(665,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( ( B
          = ( A @ c_Nat_OSuc ) )
        | ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__eq) ).

thf(3581,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B
            = ( A @ c_Nat_OSuc ) )
          | ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
       => ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( B
            = ( A @ c_Nat_OSuc ) )
          | ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(1051,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
          = ( B @ c_Groups_Oone__class_Oone ) )
      <=> ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Int_Oiszero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__special_I4_J) ).

thf(4852,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Int_Oiszero ) )
         => ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
            = ( B @ c_Groups_Oone__class_Oone ) ) )
        & ( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
            = ( B @ c_Groups_Oone__class_Oone ) )
         => ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Int_Oiszero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).

thf(25,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( B != A )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).

thf(1315,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( B != A )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(735,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__eq) ).

thf(3830,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).

thf(436,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__int__code_I16_J) ).

thf(2787,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(333,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oordered__cancel__semiring )
     => ( ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
          | ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
       => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).

thf(2427,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oordered__cancel__semiring )
     => ( ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
          | ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
       => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(205,axiom,
    tc_Int_Oint @ class_Rings_Oordered__comm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).

thf(1982,plain,
    tc_Int_Oint @ class_Rings_Oordered__comm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(129,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__ring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).

thf(1686,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__ring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(843,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__diff__conv) ).

thf(4166,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).

thf(802,axiom,
    ~ ! [A: $i] :
        ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ~ ! [B: $i] :
              ( ( ( A @ ( v_z____ @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
                & ( v_z____ @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
             => ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( B @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bd_O_A_091_124_A0_A_060_Ad_059_AALL_Aw_O_A0_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_A_N_N_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).

thf(4037,plain,
    ~ ! [A: $i] :
        ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ~ ! [B: $i] :
              ( ( ( A @ ( v_z____ @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
                & ( v_z____ @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
             => ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( B @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).

thf(266,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( A
          = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__zero__iff) ).

thf(2210,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(480,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ozero )
     => ( ( ( A @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
      <=> ( A
          = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psize__eq__0__iff) ).

thf(2940,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ozero )
     => ( ( ( A
            = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) )
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
        & ( ( ( A @ ( B @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) )
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
         => ( A
            = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(939,axiom,
    tc_Complex_Ocomplex @ class_Groups_Oab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).

thf(4500,plain,
    tc_Complex_Ocomplex @ class_Groups_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).

thf(892,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) )
      = ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__average__minus__first) ).

thf(4339,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) )
      = ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).

thf(105,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).

thf(1618,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(484,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oone )
     => ( ( ( B @ c_Groups_Oone__class_Oone )
          = A )
      <=> ( A
          = ( B @ c_Groups_Oone__class_Oone ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__reorient) ).

thf(2953,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oone )
     => ( ( ( A
            = ( B @ c_Groups_Oone__class_Oone ) )
         => ( ( B @ c_Groups_Oone__class_Oone )
            = A ) )
        & ( ( ( B @ c_Groups_Oone__class_Oone )
            = A )
         => ( A
            = ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(291,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__ring__strict )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
          | ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).

thf(2282,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__ring__strict )
     => ( ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
              & ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
            | ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
              & ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
              & ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
            | ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
              & ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(240,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Fields_Olinordered__field )
     => ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
             => ( B @ ( C @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__le) ).

thf(2114,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Fields_Olinordered__field )
     => ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
             => ( B @ ( C @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(978,axiom,
    ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) )
   != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pi__half__neq__zero) ).

thf(4623,plain,
    ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) )
   != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).

thf(1194,axiom,
    ! [A: $i] :
      ( ( A @ c_Int_OBit1 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I5_J) ).

thf(5348,plain,
    ! [A: $i] :
      ( ( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ c_Int_OBit1 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ c_Int_OBit1 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).

thf(610,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( A
        = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__pred_H) ).

thf(3382,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( A
        = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(311,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).

thf(2363,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(230,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Rings_Olinordered__idom )
        & ( B @ class_Int_Onumber__ring ) )
     => ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__special_I2_J) ).

thf(2077,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Rings_Olinordered__idom )
        & ( B @ class_Int_Onumber__ring ) )
     => ( ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(804,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( D @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__sum__triangle__ineq) ).

thf(4043,plain,
    ! [A: $i,B: $i,C: $i,D: $i] : ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( D @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).

thf(647,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__left__mono) ).

thf(3534,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(690,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__real__le) ).

thf(3681,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).

thf(784,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
            <=> ( A @ c_Transcendental_Otan @ ( B @ c_Transcendental_Otan @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tan__monotone_H) ).

thf(3990,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( ( A @ c_Transcendental_Otan @ ( B @ c_Transcendental_Otan @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
               => ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
              & ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
               => ( A @ c_Transcendental_Otan @ ( B @ c_Transcendental_Otan @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).

thf(883,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__eq__diff) ).

thf(4311,plain,
    ! [A: $i,B: $i] :
      ( ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).

thf(713,axiom,
    tc_Int_Oint @ class_Rings_Osemiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).

thf(3762,plain,
    tc_Int_Oint @ class_Rings_Osemiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).

thf(399,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
        & ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).

thf(2644,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
          & ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
       => ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
          & ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(729,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__group__add__abs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs) ).

thf(3813,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__group__add__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).

thf(319,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucE) ).

thf(2381,plain,
    ! [A: $i,B: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(1115,axiom,
    ! [A: $i] :
      ( ( ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
          = A ) )
      & ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
          = ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__abs__def) ).

thf(5069,plain,
    ! [A: $i] :
      ( ( ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
          = A ) )
      & ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
          = ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).

thf(472,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ class_Rings_Oordered__ring )
     => ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__iff2) ).

thf(2908,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ class_Rings_Oordered__ring )
     => ( ( ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(224,axiom,
    tc_Int_Oint @ class_Groups_Omonoid__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).

thf(2062,plain,
    tc_Int_Oint @ class_Groups_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(1093,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Odivision__ring )
     => ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__divide__left) ).

thf(5000,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Odivision__ring )
     => ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).

thf(166,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).

thf(1808,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(620,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__ring__strict )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).

thf(3417,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__ring__strict )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(608,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring__strict )
     => ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).

thf(3377,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring__strict )
     => ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(904,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ? [B: $i] :
        ! [C: $i] :
          ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( v_z____ @ ( C @ ( v_f____ @ hAPP ) @ v_g____ @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fz_I2_J) ).

thf(4391,plain,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ? [B: $i] :
        ! [C: $i] :
          ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( v_z____ @ ( C @ ( v_f____ @ hAPP ) @ v_g____ @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).

thf(634,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).

thf(3460,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(481,axiom,
    tc_Nat_Onat @ class_Groups_Ozero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).

thf(2947,plain,
    tc_Nat_Onat @ class_Groups_Ozero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(193,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( c_Transcendental_Opi @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Ocos @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__monotone__0__pi_H) ).

thf(1939,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( c_Transcendental_Opi @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ c_Transcendental_Ocos @ ( A @ c_Transcendental_Ocos @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(1004,axiom,
    ! [A: $i] :
      ( ( A @ class_Int_Onumber__ring )
     => ( ( c_Int_OPls @ c_Int_OBit1 @ ( A @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_Groups_Oone__class_Oone ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__1__eq__1) ).

thf(4697,plain,
    ! [A: $i] :
      ( ( A @ class_Int_Onumber__ring )
     => ( ( c_Int_OPls @ c_Int_OBit1 @ ( A @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_Groups_Oone__class_Oone ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).

thf(774,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add__abs )
     => ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq4) ).

thf(3959,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add__abs )
     => ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).

thf(405,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ocomm__monoid__mult )
     => ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1) ).

thf(2676,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ocomm__monoid__mult )
     => ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(762,axiom,
    ! [A: $i] :
      ( ( A @ c_Transcendental_Oarctan @ c_Transcendental_Ocos )
     != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__arctan__not__zero) ).

thf(3910,plain,
    ! [A: $i] :
      ( ( A @ c_Transcendental_Oarctan @ c_Transcendental_Ocos )
     != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).

thf(1082,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Int_Onumber__ring )
     => ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Int_Onumber__class_Onumber__of ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__number__of__eq) ).

thf(4960,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Int_Onumber__ring )
     => ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Int_Onumber__class_Onumber__of ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).

thf(141,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).

thf(1728,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(162,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).

thf(1793,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(616,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__comm__monoid__add )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__neg) ).

thf(3402,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__comm__monoid__add )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(74,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
     => ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).

thf(1486,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
     => ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(829,axiom,
    c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pi__half__ge__zero) ).

thf(4105,plain,
    c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).

thf(1101,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add__abs )
     => ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq2) ).

thf(5037,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add__abs )
     => ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).

thf(629,axiom,
    ! [A: $i] :
      ( ( A @ class_Groups_Ocancel__comm__monoid__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ocancel__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).

thf(3439,plain,
    ! [A: $i] :
      ( ( A @ class_Groups_Ocancel__comm__monoid__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ocancel__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(1198,axiom,
    tc_Complex_Ocomplex @ class_Rings_Oring__no__zero__divisors,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).

thf(5361,plain,
    tc_Complex_Ocomplex @ class_Rings_Oring__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).

thf(386,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Osgn__class_Osgn ) )
        = ( A @ ( C @ c_Groups_Osgn__class_Osgn ) @ ( B @ ( C @ c_Groups_Osgn__class_Osgn ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__times) ).

thf(2607,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Osgn__class_Osgn ) )
        = ( A @ ( C @ c_Groups_Osgn__class_Osgn ) @ ( B @ ( C @ c_Groups_Osgn__class_Osgn ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(796,axiom,
    tc_Complex_Ocomplex @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

thf(4026,plain,
    tc_Complex_Ocomplex @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).

thf(340,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__semidom )
     => ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__two) ).

thf(2448,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__semidom )
     => ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(721,axiom,
    tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).

thf(3781,plain,
    tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).

thf(30,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).

thf(1327,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add )
     => ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(342,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Omonoid__add )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).

thf(2459,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Omonoid__add )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(876,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__field )
     => ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide_Ominus) ).

thf(4294,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__field )
     => ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).

thf(663,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Omonoid__mult )
     => ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__left) ).

thf(3577,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Omonoid__mult )
     => ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).

thf(1021,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = ( c_Int_OPls @ c_Int_OBit1 @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__special_I3_J) ).

thf(4762,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = ( c_Int_OPls @ c_Int_OBit1 @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).

thf(739,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).

thf(3848,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).

thf(78,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oab__semigroup__add )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).

thf(1497,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oab__semigroup__add )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(502,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).

thf(3017,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(1216,axiom,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).

thf(5425,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).

thf(707,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Oidom )
     => ( A @ tc_Polynomial_Opoly @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

thf(3745,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Oidom )
     => ( A @ tc_Polynomial_Opoly @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).

thf(916,axiom,
    ! [A: $i] :
      ( ( A @ class_Int_Onumber__ring )
     => ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oplus__class_Oplus ) ) )
        = ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( A @ c_Int_Onumber__class_Onumber__of ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__add__one__is__two) ).

thf(4418,plain,
    ! [A: $i] :
      ( ( A @ class_Int_Onumber__ring )
     => ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oplus__class_Oplus ) ) )
        = ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( A @ c_Int_Onumber__class_Onumber__of ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).

thf(1014,axiom,
    tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).

thf(4739,plain,
    tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).

thf(498,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono) ).

thf(3004,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(220,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Int_Onumber )
        & ( D @ class_Fields_Olinordered__field__inverse__zero ) )
     => ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
               => ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
              & ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
               => ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
          & ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( B @ ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__divide__eq__number__of) ).

thf(2035,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Int_Onumber )
        & ( D @ class_Fields_Olinordered__field__inverse__zero ) )
     => ( ( ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
                & ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
            & ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
         => ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
                & ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
            & ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(591,axiom,
    ! [A: $i] : ( A @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI) ).

thf(3332,plain,
    ! [A: $i] : ( A @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(826,axiom,
    ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) )
    = ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ c_Transcendental_Oarctan @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit1 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ c_Transcendental_Oarctan @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_machin) ).

thf(4097,plain,
    ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) )
    = ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ c_Transcendental_Oarctan @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit1 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ c_Transcendental_Oarctan @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).

thf(771,axiom,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).

thf(3942,plain,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).

thf(603,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).

thf(3365,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(1059,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Oab__group__add )
     => ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
          = ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) )
       => ( ( D = C )
        <=> ( B = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).

thf(4870,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Oab__group__add )
     => ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
          = ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) )
       => ( ( ( B = A )
           => ( D = C ) )
          & ( ( D = C )
           => ( B = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).

thf(174,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).

thf(1867,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(550,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semiring__strict )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__neg) ).

thf(3175,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semiring__strict )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(335,axiom,
    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 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).

thf(2434,plain,
    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 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(176,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B = A )
        | ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).

thf(1872,plain,
    ! [A: $i,B: $i] :
      ( ( ( B = A )
        | ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(349,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring) ).

thf(2476,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(1147,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ class_Orderings_Olinorder )
        & ( C @ class_Int_Onumber ) )
     => ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ~ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__number__of__eq__not__less) ).

thf(5163,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ class_Orderings_Olinorder )
        & ( C @ class_Int_Onumber ) )
     => ( ( ~ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ~ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).

thf(35,axiom,
    ! [A: $i] :
      ( ( A @ class_Groups_Oab__group__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).

thf(1354,plain,
    ! [A: $i] :
      ( ( A @ class_Groups_Oab__group__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(247,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
        = ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).

thf(2146,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
        = ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(81,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Odivision__ring__inverse__zero )
     => ( ( ( A
           != ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
            = ( B @ c_Groups_Oone__class_Oone ) ) )
        & ( ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
            = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__self__if) ).

thf(1507,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Odivision__ring__inverse__zero )
     => ( ( ( A
           != ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
            = ( B @ c_Groups_Oone__class_Oone ) ) )
        & ( ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
            = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(310,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__minus__cancel) ).

thf(2360,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(806,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).

thf(4047,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).

thf(1033,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
      & ( v_r @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_th) ).

thf(4792,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
      & ( v_r @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).

thf(785,axiom,
    ! [A: $i,B: $i] :
      ( ( B != A )
     => ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).

thf(3994,plain,
    ! [A: $i,B: $i] :
      ( ( B != A )
     => ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).

thf(1230,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__int__code_I15_J) ).

thf(5476,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).

thf(37,axiom,
    ! [A: $i] :
      ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).

thf(1359,plain,
    ! [A: $i] :
      ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(574,axiom,
    ! [A: $i] :
      ( ( A @ class_Groups_Ogroup__add )
     => ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__zero) ).

thf(3281,plain,
    ! [A: $i] :
      ( ( A @ class_Groups_Ogroup__add )
     => ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(540,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ozero )
     => ( ( ( B @ c_Groups_Ozero__class_Ozero )
          = A )
      <=> ( A
          = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__reorient) ).

thf(3140,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ozero )
     => ( ( ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( ( B @ c_Groups_Ozero__class_Ozero )
            = A ) )
        & ( ( ( B @ c_Groups_Ozero__class_Ozero )
            = A )
         => ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(361,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Olinordered__ab__group__add )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).

thf(2516,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Olinordered__ab__group__add )
     => ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(1192,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_RealVector_Onorm__class_Onorm ) )
      = ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__norm__def) ).

thf(5342,plain,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_RealVector_Onorm__class_Onorm ) )
      = ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).

thf(1077,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Int_Oring__char__0 )
        & ( B @ class_Int_Onumber__ring ) )
     => ~ ( A @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Int_Oiszero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__number__of__Bit1) ).

thf(4941,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Int_Oring__char__0 )
        & ( B @ class_Int_Onumber__ring ) )
     => ~ ( A @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Int_Oiszero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).

thf(605,axiom,
    tc_Nat_Onat @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).

thf(3370,plain,
    tc_Nat_Onat @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(148,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__ring )
     => ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__square) ).

thf(1746,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__ring )
     => ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(529,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
        = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
    <=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).

thf(3103,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
      & ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(736,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono) ).

thf(3836,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).

thf(894,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Int_Onumber )
        & ( D @ class_Fields_Olinordered__field__inverse__zero ) )
     => ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( ( ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
               => ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
              & ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
               => ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
          & ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__divide__eq__number__of1) ).

thf(4343,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Int_Onumber )
        & ( D @ class_Fields_Olinordered__field__inverse__zero ) )
     => ( ( ( ( ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
                & ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
            & ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) )
         => ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
                & ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
            & ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).

thf(675,axiom,
    tc_Nat_Onat @ class_Rings_Olinordered__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).

thf(3629,plain,
    tc_Nat_Onat @ class_Rings_Olinordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).

thf(305,axiom,
    ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
    = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_One__nat__def) ).

thf(2348,plain,
    ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
    = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(1162,axiom,
    tc_RealDef_Oreal @ class_Rings_Osemiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).

thf(5227,plain,
    tc_RealDef_Oreal @ class_Rings_Osemiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).

thf(488,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Int_Onumber__ring )
     => ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__add) ).

thf(2972,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Int_Onumber__ring )
     => ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(839,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).

thf(4142,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add )
     => ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).

thf(354,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ocomm__monoid__add )
     => ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).

thf(2491,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ocomm__monoid__add )
     => ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(1233,axiom,
    ! [A: $i] :
      ( ( A @ class_Int_Onumber__ring )
     => ( c_Int_OPls @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Int_Oiszero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__Numeral0) ).

thf(5486,plain,
    ! [A: $i] :
      ( ( A @ class_Int_Onumber__ring )
     => ( c_Int_OPls @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Int_Oiszero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233]) ).

thf(160,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( B @ ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__less) ).

thf(1782,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( B @ ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(494,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
     => ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).

thf(2985,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
     => ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(271,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semiring__strict )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__neg__pos) ).

thf(2227,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semiring__strict )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(568,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).

thf(3249,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(901,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ hAPP ) @ hBOOL )
    <=> ( ! [D: $i] :
            ( ( B
              = ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
           => ( D @ ( C @ hAPP ) @ hBOOL ) )
        & ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
         => ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split) ).

thf(4371,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ! [D: $i] :
              ( ( B
                = ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
             => ( D @ ( C @ hAPP ) @ hBOOL ) )
          & ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
           => ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ hAPP ) @ hBOOL ) )
      & ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ hAPP ) @ hBOOL )
       => ( ! [D: $i] :
              ( ( B
                = ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
             => ( D @ ( C @ hAPP ) @ hBOOL ) )
          & ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
           => ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).

thf(820,axiom,
    ( ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
    = c_Int_OPls ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Pls) ).

thf(4079,plain,
    ( ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
    = c_Int_OPls ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).

thf(867,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__real__def) ).

thf(4266,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).

thf(522,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ozero__neq__one )
     => ( ( A @ c_Groups_Oone__class_Oone )
       != ( A @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__neq__zero) ).

thf(3088,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ozero__neq__one )
     => ( ( A @ c_Groups_Oone__class_Oone )
       != ( A @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(719,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
     => ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).

thf(3777,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
     => ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).

thf(213,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq) ).

thf(2010,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(1037,axiom,
    ! [A: $i] :
      ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sum__of__halves) ).

thf(4803,plain,
    ! [A: $i] :
      ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).

thf(114,axiom,
    ! [A: $i] :
      ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).

thf(1650,plain,
    ! [A: $i] :
      ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(1109,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Rings_Oring )
        & ( D @ class_Int_Onumber ) )
     => ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__diff__distrib__number__of) ).

thf(5056,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Rings_Oring )
        & ( D @ class_Int_Onumber ) )
     => ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).

thf(324,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Osgn__if ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Osgn__if) ).

thf(2400,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Osgn__if ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(1020,axiom,
    ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
    = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__3__eq__3) ).

thf(4760,plain,
    ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
    = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).

thf(1083,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) )
      = ( B @ ( A @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__divide__square__eq) ).

thf(4963,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) )
      = ( B @ ( A @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).

thf(447,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__antisym) ).

thf(2825,plain,
    ! [A: $i,B: $i] :
      ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(992,axiom,
    tc_Complex_Ocomplex @ class_Rings_Oring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).

thf(4665,plain,
    tc_Complex_Ocomplex @ class_Rings_Oring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).

thf(749,axiom,
    ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_RComplete_Onatceiling )
    = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__zero) ).

thf(3880,plain,
    ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_RComplete_Onatceiling )
    = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).

thf(748,axiom,
    ! [A: $i] : ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__natceiling) ).

thf(3878,plain,
    ! [A: $i] : ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).

thf(7,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).

thf(1265,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(929,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__vector )
     => ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__triangle__ineq) ).

thf(4467,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__vector )
     => ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).

thf(327,axiom,
    ! [A: $i] :
      ( ( A @ class_Groups_Oab__group__add )
     => ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__poly__code_I1_J) ).

thf(2405,plain,
    ! [A: $i] :
      ( ( A @ class_Groups_Oab__group__add )
     => ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(107,axiom,
    tc_Int_Oint @ class_Rings_Olinordered__semiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).

thf(1623,plain,
    tc_Int_Oint @ class_Rings_Olinordered__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).

thf(1254,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(1025,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__2__right) ).

thf(4775,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).

thf(458,axiom,
    tc_Nat_Onat @ class_Rings_Ono__zero__divisors,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).

thf(2869,plain,
    tc_Nat_Onat @ class_Rings_Ono__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(50,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse) ).

thf(1409,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(559,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Ocancel__semigroup__add )
     => ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
          = ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
       => ( C = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).

thf(3221,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Ocancel__semigroup__add )
     => ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
          = ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
       => ( C = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(555,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ class_Rings_Olinordered__semiring__1__strict )
     => ( ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
             => ( ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
                  = ( F @ c_Groups_Oone__class_Oone ) )
               => ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convex__bound__lt) ).

thf(3195,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ class_Rings_Olinordered__semiring__1__strict )
     => ( ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
             => ( ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
                  = ( F @ c_Groups_Oone__class_Oone ) )
               => ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(816,axiom,
    tc_Complex_Ocomplex @ class_Rings_Oring__1__no__zero__divisors,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).

thf(4070,plain,
    tc_Complex_Ocomplex @ class_Rings_Oring__1__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).

thf(692,axiom,
    ! [A: $i,B: $i] :
      ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).

thf(3689,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).

thf(662,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Odivision__ring )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__divide__distrib) ).

thf(3574,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Odivision__ring )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(1152,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
          = A )
      <=> ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__equation__iff) ).

thf(5188,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
            = B )
         => ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
            = A ) )
        & ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
            = A )
         => ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
            = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).

thf(1026,axiom,
    tc_RealDef_Oreal @ class_Groups_Oordered__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).

thf(4778,plain,
    tc_RealDef_Oreal @ class_Groups_Oordered__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).

thf(1150,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Odivision__ring )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__divide__distrib) ).

thf(5182,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Odivision__ring )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).

thf(468,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).

thf(2897,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(859,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Odivision__ring )
     => ( ( B
         != ( C @ c_Groups_Ozero__class_Ozero ) )
       => ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) )
          = ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__minus__divide__divide) ).

thf(4243,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Odivision__ring )
     => ( ( B
         != ( C @ c_Groups_Ozero__class_Ozero ) )
       => ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) )
          = ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).

thf(755,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Omult__zero )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__left) ).

thf(3891,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Omult__zero )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).

thf(984,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
          & ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__less__iff) ).

thf(4637,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
            & ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
            & ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).

thf(384,axiom,
    tc_Nat_Onat @ class_Rings_Olinordered__semiring__strict,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).

thf(2603,plain,
    tc_Nat_Onat @ class_Rings_Olinordered__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(474,axiom,
    ! [A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
        = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
    <=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of__0) ).

thf(2916,plain,
    ! [A: $i] :
      ( ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
      & ( ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
       => ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(1057,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( c_Int_OPls @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( B @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
        = ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__eq__diff__pred) ).

thf(4866,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( c_Int_OPls @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( B @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
        = ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).

thf(1067,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ class_Rings_Olinordered__idom )
        & ( C @ class_Int_Onumber__ring ) )
     => ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__number__of) ).

thf(4896,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ class_Rings_Olinordered__idom )
        & ( C @ class_Int_Onumber__ring ) )
     => ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).

thf(537,axiom,
    tc_Int_Oint @ class_Rings_Oring__no__zero__divisors,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).

thf(3131,plain,
    tc_Int_Oint @ class_Rings_Oring__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(118,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Oidom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oring__1__no__zero__divisors ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).

thf(1660,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Oidom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oring__1__no__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(914,axiom,
    tc_RealDef_Oreal @ class_Fields_Ofield__inverse__zero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).

thf(4415,plain,
    tc_RealDef_Oreal @ class_Fields_Ofield__inverse__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).

thf(284,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__add__strict) ).

thf(2269,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(182,axiom,
    ! [A: $i] : ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__Suc__gt__zero) ).

thf(1907,plain,
    ! [A: $i] : ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(1112,axiom,
    c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pi__half__le__two) ).

thf(5064,plain,
    c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).

thf(6,axiom,
    tc_Nat_Onat @ class_Rings_Oordered__cancel__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).

thf(1264,plain,
    tc_Nat_Onat @ class_Rings_Oordered__cancel__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(267,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
        <=> ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__divide__eq) ).

thf(2217,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
          & ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(28,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono1) ).

thf(1323,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(541,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
        <=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__iff) ).

thf(3148,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
          & ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(682,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
        & ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).

thf(3653,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
          & ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
          & ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

thf(837,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( c_Int_OPls @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
          = ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) ) )
      & ( ( c_Int_OPls @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__mult__left) ).

thf(4130,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( c_Int_OPls @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
          = ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) ) )
      & ( ( c_Int_OPls @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).

thf(652,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff1) ).

thf(3542,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(24,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__ring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Onumber__ring) ).

thf(1313,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__ring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(871,axiom,
    ! [A: $i] :
      ( ( A @ c_Int_OBit0 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I4_J) ).

thf(4275,plain,
    ! [A: $i] :
      ( ( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ c_Int_OBit0 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ c_Int_OBit0 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).

thf(1139,axiom,
    ! [A: $i] :
      ( ( A @ c_SEQ_Osubseq )
    <=> ! [B: $i] : ( B @ c_Nat_OSuc @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subseq__Suc__iff) ).

thf(5130,plain,
    ! [A: $i] :
      ( ( ! [B: $i] : ( B @ c_Nat_OSuc @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ c_SEQ_Osubseq ) )
      & ( ( A @ c_SEQ_Osubseq )
       => ! [B: $i] : ( B @ c_Nat_OSuc @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).

thf(99,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ? [C: $i] :
          ( A
          = ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__add) ).

thf(1577,plain,
    ! [A: $i,B: $i] :
      ( ( ? [C: $i] :
            ( A
            = ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ? [C: $i] :
            ( A
            = ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(345,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
        <=> ( A @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__le__divide__eq) ).

thf(2466,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( ( A @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
          & ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( A @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(1131,axiom,
    v_r @ ( v_w____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wr) ).

thf(5108,plain,
    v_r @ ( v_w____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).

thf(1023,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__number__of__int__code) ).

thf(4766,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).

thf(742,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Oidom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oring__no__zero__divisors ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).

thf(3855,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Oidom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oring__no__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).

thf(424,axiom,
    tc_Int_Oint @ class_Rings_Olinordered__semiring__strict,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).

thf(2745,plain,
    tc_Int_Oint @ class_Rings_Olinordered__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

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

thf(2356,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semiring__strict )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(1054,axiom,
    ~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bin__less__0__simps_I1_J) ).

thf(4862,plain,
    ~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).

thf(1138,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oab__group__add )
     => ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Limits_Ominus__diff__minus) ).

thf(5127,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oab__group__add )
     => ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).

thf(958,axiom,
    tc_Complex_Ocomplex @ class_Groups_Ocancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).

thf(4551,plain,
    tc_Complex_Ocomplex @ class_Groups_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).

thf(866,axiom,
    tc_RealDef_Oreal @ class_Rings_Oring__no__zero__divisors,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).

thf(4265,plain,
    tc_RealDef_Oreal @ class_Rings_Oring__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).

thf(1116,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__pos__neg) ).

thf(5077,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).

thf(188,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ class_Rings_Oring )
     => ( ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
          = ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) )
      <=> ( C
          = ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__add__iff2) ).

thf(1922,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ class_Rings_Oring )
     => ( ( ( C
            = ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) )
         => ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
            = ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) )
        & ( ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
            = ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) )
         => ( C
            = ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(411,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( ? [C: $i] :
            ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
            & ( B
              = ( C @ c_Nat_OSuc ) ) )
        | ( B
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).

thf(2691,plain,
    ! [A: $i,B: $i] :
      ( ( ( ? [C: $i] :
              ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
              & ( B
                = ( C @ c_Nat_OSuc ) ) )
          | ( B
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
       => ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( ? [C: $i] :
              ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
              & ( B
                = ( C @ c_Nat_OSuc ) ) )
          | ( B
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(527,axiom,
    tc_Nat_Onat @ class_Rings_Ocomm__semiring__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).

thf(3099,plain,
    tc_Nat_Onat @ class_Rings_Ocomm__semiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(1191,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ c_Int_OBit0 )
     != ( A @ c_Int_OBit1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I49_J) ).

thf(5338,plain,
    ! [A: $i,B: $i] :
      ( ( B @ c_Int_OBit0 )
     != ( A @ c_Int_OBit1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).

thf(835,axiom,
    ! [A: $i] :
      ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I1_J) ).

thf(4119,plain,
    ! [A: $i] :
      ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).

thf(787,axiom,
    tc_Complex_Ocomplex @ class_Int_Onumber__ring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber__ring) ).

thf(3998,plain,
    tc_Complex_Ocomplex @ class_Int_Onumber__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).

thf(1196,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( B @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__antisym) ).

thf(5355,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( B @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).

thf(45,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Odivision__ring )
     => ( ( A
         != ( B @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
          = ( B @ c_Groups_Oone__class_Oone ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__self) ).

thf(1379,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Odivision__ring )
     => ( ( A
         != ( B @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
          = ( B @ c_Groups_Oone__class_Oone ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(611,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Odiff__left) ).

thf(3385,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(1173,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__linear) ).

thf(5256,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).

thf(680,axiom,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
      = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__Suc) ).

thf(3638,plain,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
      = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(82,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__number__of__Bit0) ).

thf(1514,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(315,axiom,
    ! [A: $i] :
      ( ( A @ class_Groups_Ozero )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).

thf(2373,plain,
    ! [A: $i] :
      ( ( A @ class_Groups_Ozero )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(977,axiom,
    tc_Complex_Ocomplex @ class_Groups_Oab__semigroup__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).

thf(4622,plain,
    tc_Complex_Ocomplex @ class_Groups_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).

thf(1188,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( B
          = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
      <=> ( A
          = ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equation__minus__iff) ).

thf(5323,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( ( A
            = ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
         => ( B
            = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) )
        & ( ( B
            = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
         => ( A
            = ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).

thf(1044,axiom,
    ! [A: $i] :
      ( ( A @ c_Int_OBit1 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I22_J) ).

thf(4830,plain,
    ! [A: $i] :
      ( ( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ c_Int_OBit1 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ c_Int_OBit1 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).

thf(884,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field )
     => ( ( B
         != ( C @ c_Groups_Ozero__class_Ozero ) )
       => ( ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
          = ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__abs__divide) ).

thf(4317,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field )
     => ( ( B
         != ( C @ c_Groups_Ozero__class_Ozero ) )
       => ( ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
          = ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).

thf(1107,axiom,
    tc_RealDef_Oreal @ class_Rings_Oordered__ring__abs,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring__abs) ).

thf(5052,plain,
    tc_RealDef_Oreal @ class_Rings_Oordered__ring__abs,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).

thf(997,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__neg__neg) ).

thf(4675,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).

thf(501,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Rings_Osemiring )
        & ( D @ class_Int_Onumber ) )
     => ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__distrib__number__of) ).

thf(3014,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Rings_Osemiring )
        & ( D @ class_Int_Onumber ) )
     => ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(362,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I31_J) ).

thf(2520,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(418,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ono__zero__divisors )
     => ( ( B
         != ( C @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A
           != ( C @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
           != ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_no__zero__divisors) ).

thf(2730,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ono__zero__divisors )
     => ( ( B
         != ( C @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A
           != ( C @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
           != ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(495,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Int_Onumber )
        & ( D @ class_Fields_Olinordered__field__inverse__zero ) )
     => ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
               => ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
              & ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
               => ( C @ ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
          & ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__le__eq__number__of) ).

thf(2989,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Int_Onumber )
        & ( D @ class_Fields_Olinordered__field__inverse__zero ) )
     => ( ( ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
                & ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( C @ ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
            & ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
         => ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
                & ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( C @ ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
            & ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(38,axiom,
    ! [A: $i,B: $i] :
      ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__le__0__iff) ).

thf(1362,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(903,axiom,
    v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_e) ).

thf(4390,plain,
    v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).

thf(1123,axiom,
    tc_Complex_Ocomplex @ class_Rings_Oidom,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).

thf(5091,plain,
    tc_Complex_Ocomplex @ class_Rings_Oidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).

thf(942,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Olinordered__idom )
     => ( ( C @ ( D @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( D @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__less) ).

thf(4507,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Olinordered__idom )
     => ( ( C @ ( D @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( D @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).

thf(658,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__less__div__pos) ).

thf(3557,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(1237,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).

thf(5493,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).

thf(947,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__0 )
     => ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Opoly ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__0) ).

thf(4514,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__0 )
     => ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Opoly ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).

thf(321,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Olinordered__ab__group__add )
     => ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).

thf(2388,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Olinordered__ab__group__add )
     => ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(745,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( B
          = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
      <=> ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
          = ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).

thf(3866,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
            = ( C @ c_Groups_Ozero__class_Ozero ) )
         => ( B
            = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) )
        & ( ( B
            = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
         => ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
            = ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).

thf(1085,axiom,
    ! [A: $i] :
      ( ( A @ c_Transcendental_Otan @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) )
      = ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ c_Transcendental_Otan ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tan__inverse) ).

thf(4967,plain,
    ! [A: $i] :
      ( ( A @ c_Transcendental_Otan @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) )
      = ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ c_Transcendental_Otan ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).

thf(789,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
        = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__minus__iff) ).

thf(4008,plain,
    ! [A: $i,B: $i] :
      ( ( ( B = A )
       => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
      & ( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).

thf(994,axiom,
    ! [A: $i] : ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__refl) ).

thf(4669,plain,
    ! [A: $i] : ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).

thf(173,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Ofield__inverse__zero )
     => ( ( C
          = ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) )
      <=> ( ( ( A
              = ( D @ c_Groups_Ozero__class_Ozero ) )
           => ( C
              = ( D @ c_Groups_Ozero__class_Ozero ) ) )
          & ( ( A
             != ( D @ c_Groups_Ozero__class_Ozero ) )
           => ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
              = B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__eq) ).

thf(1847,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Ofield__inverse__zero )
     => ( ( ( ( ( A
                = ( D @ c_Groups_Ozero__class_Ozero ) )
             => ( C
                = ( D @ c_Groups_Ozero__class_Ozero ) ) )
            & ( ( A
               != ( D @ c_Groups_Ozero__class_Ozero ) )
             => ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
                = B ) ) )
         => ( C
            = ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) )
        & ( ( C
            = ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) )
         => ( ( ( A
                = ( D @ c_Groups_Ozero__class_Ozero ) )
             => ( C
                = ( D @ c_Groups_Ozero__class_Ozero ) ) )
            & ( ( A
               != ( D @ c_Groups_Ozero__class_Ozero ) )
             => ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
                = B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(211,axiom,
    tc_Nat_Onat @ class_Groups_Oordered__comm__monoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).

thf(2007,plain,
    tc_Nat_Onat @ class_Groups_Oordered__comm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(483,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
      = ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__commute) ).

thf(2950,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
      = ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(21,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Oordered__ab__group__add )
     => ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
          = ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) )
       => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
        <=> ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).

thf(1302,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Oordered__ab__group__add )
     => ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
          = ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) )
       => ( ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) )
          & ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(964,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ c_Transcendental_Otan @ ( B @ c_Transcendental_Otan @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tan__monotone) ).

thf(4578,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ c_Transcendental_Otan @ ( B @ c_Transcendental_Otan @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).

thf(877,axiom,
    ! [A: $i] :
      ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ? [B: $i] :
          ( ( ( B @ c_Transcendental_Otan )
            = A )
          & ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
          & ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tan__total__pi4) ).

thf(4297,plain,
    ! [A: $i] :
      ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ? [B: $i] :
          ( ( ( B @ c_Transcendental_Otan )
            = A )
          & ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
          & ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).

thf(686,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
        = ( C @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc) ).

thf(3670,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
        = ( C @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(546,axiom,
    tc_Nat_Onat @ class_Groups_Ocomm__monoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).

thf(3163,plain,
    tc_Nat_Onat @ class_Groups_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(274,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).

thf(2236,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(464,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
    <=> ? [C: $i] :
          ( A
          = ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).

thf(2880,plain,
    ! [A: $i,B: $i] :
      ( ( ? [C: $i] :
            ( A
            = ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ? [C: $i] :
            ( A
            = ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(1011,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Oordered__ab__group__add )
     => ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
          = ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) )
       => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
        <=> ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).

thf(4724,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Oordered__ab__group__add )
     => ( ( ( C @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
          = ( A @ ( B @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) )
       => ( ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
           => ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) ) )
          & ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
           => ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).

thf(601,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Oordered__comm__semiring )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).

thf(3357,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Oordered__comm__semiring )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(542,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Oordered__semiring )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__mono) ).

thf(3152,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Oordered__semiring )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(889,axiom,
    c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).

thf(4329,plain,
    c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).

thf(753,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Fields_Ofield__inverse__zero )
     => ( ( A @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__divide__times__eq) ).

thf(3887,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Fields_Ofield__inverse__zero )
     => ( ( A @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).

thf(966,axiom,
    ( ? [A: $i] :
        ( ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
        & ( v_r @ ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
  <=> ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_J_A_061_A_I_N_As_A_060_A_N_As_J_096) ).

thf(4583,plain,
    ( ( ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ? [A: $i] :
          ( ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
          & ( v_r @ ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
    & ( ? [A: $i] :
          ( ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
          & ( v_r @ ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
     => ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).

thf(217,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ c_Int_OBit0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Bit0) ).

thf(2027,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ c_Int_OBit0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(1245,axiom,
    tc_Complex_Ocomplex @ class_Rings_Odivision__ring__inverse__zero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).

thf(5526,plain,
    tc_Complex_Ocomplex @ class_Rings_Odivision__ring__inverse__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).

thf(770,axiom,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A
        = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc0) ).

thf(3934,plain,
    ! [A: $i] :
      ( ( ( A
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
       => ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).

thf(41,axiom,
    tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).

thf(1373,plain,
    tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(700,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Ocancel__ab__semigroup__add )
     => ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
          = ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__imp__eq) ).

thf(3724,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Ocancel__ab__semigroup__add )
     => ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
          = ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).

thf(926,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__vector )
     => ( ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( A
         != ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__norm__iff) ).

thf(4454,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__vector )
     => ( ( ( A
           != ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
         => ( A
           != ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).

thf(971,axiom,
    ( ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
    = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__numeral__1__eq__1) ).

thf(4600,plain,
    ( ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
    = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).

thf(579,axiom,
    tc_Nat_Onat @ class_Groups_Oab__semigroup__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).

thf(3295,plain,
    tc_Nat_Onat @ class_Groups_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(433,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).

thf(2782,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(644,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).

thf(3527,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__cancel__ab__semigroup__add )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(697,axiom,
    ! [A: $i,B: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
        = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
    <=> ( ( ( A
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
          & ( B
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
        | ( ( A
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
          & ( B
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__add) ).

thf(3702,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( ( A
              = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
            & ( B
              = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
          | ( ( A
              = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
            & ( B
              = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) )
       => ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
          = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
      & ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
          = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
       => ( ( ( A
              = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
            & ( B
              = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
          | ( ( A
              = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
            & ( B
              = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).

thf(807,axiom,
    tc_RealDef_Oreal @ class_Groups_Oordered__comm__monoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).

thf(4050,plain,
    tc_RealDef_Oreal @ class_Groups_Oordered__comm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).

thf(243,axiom,
    ! [A: $i] :
      ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A
        = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zabs__less__one__iff) ).

thf(2122,plain,
    ! [A: $i] :
      ( ( ( A
          = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
       => ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A
          = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(172,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Int_Onumber )
        & ( D @ class_Fields_Ofield__inverse__zero ) )
     => ( ( C
          = ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) )
      <=> ( ( ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) )
              = ( D @ c_Groups_Ozero__class_Ozero ) )
           => ( C
              = ( D @ c_Groups_Ozero__class_Ozero ) ) )
          & ( ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) )
             != ( D @ c_Groups_Ozero__class_Ozero ) )
           => ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
              = B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of1) ).

thf(1828,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Int_Onumber )
        & ( D @ class_Fields_Ofield__inverse__zero ) )
     => ( ( ( ( ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) )
                = ( D @ c_Groups_Ozero__class_Ozero ) )
             => ( C
                = ( D @ c_Groups_Ozero__class_Ozero ) ) )
            & ( ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) )
               != ( D @ c_Groups_Ozero__class_Ozero ) )
             => ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
                = B ) ) )
         => ( C
            = ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) )
        & ( ( C
            = ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) )
         => ( ( ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) )
                = ( D @ c_Groups_Ozero__class_Ozero ) )
             => ( C
                = ( D @ c_Groups_Ozero__class_Ozero ) ) )
            & ( ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) )
               != ( D @ c_Groups_Ozero__class_Ozero ) )
             => ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
                = B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(672,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__right) ).

thf(3621,plain,
    ! [A: $i,B: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(779,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I13_J) ).

thf(3973,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).

thf(203,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).

thf(1978,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(766,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__0) ).

thf(3923,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).

thf(577,axiom,
    tc_Int_Oint @ class_Rings_Oidom,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).

thf(3290,plain,
    tc_Int_Oint @ class_Rings_Oidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(1035,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__ring )
     => ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__diff) ).

thf(4798,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__ring )
     => ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).

thf(1000,axiom,
    c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_e2) ).

thf(4686,plain,
    c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).

thf(299,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).

thf(2335,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(223,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff2) ).

thf(2058,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(1048,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__vector )
     => ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__triangle__ineq3) ).

thf(4842,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__vector )
     => ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).

thf(1201,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__right__mono) ).

thf(5375,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).

thf(1127,axiom,
    tc_Complex_Ocomplex @ class_Rings_Oring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).

thf(5101,plain,
    tc_Complex_Ocomplex @ class_Rings_Oring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).

thf(941,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Ofield__inverse__zero )
     => ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__divide__right) ).

thf(4504,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Ofield__inverse__zero )
     => ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).

thf(1041,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__numeral__code_I6_J) ).

thf(4825,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).

thf(396,axiom,
    tc_Int_Oint @ class_Rings_Oordered__ring__abs,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).

thf(2639,plain,
    tc_Int_Oint @ class_Rings_Oordered__ring__abs,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(589,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1) ).

thf(3327,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(427,axiom,
    ! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__cube) ).

thf(2750,plain,
    ! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(195,axiom,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != ( A @ c_Nat_OSuc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).

thf(1943,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != ( A @ c_Nat_OSuc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(95,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Int_Onumber__ring )
     => ( ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__number__of__diff1) ).

thf(1564,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Int_Onumber__ring )
     => ( ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(430,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__comm__monoid__add )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).

thf(2762,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__comm__monoid__add )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(1103,axiom,
    tc_Complex_Ocomplex @ class_Groups_Omonoid__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).

thf(5045,plain,
    tc_Complex_Ocomplex @ class_Groups_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).

thf(1110,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__vector )
     => ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__diff__ineq) ).

thf(5059,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__vector )
     => ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).

thf(1009,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oab__group__add )
     => ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
        = ( B @ ( A @ ( C @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__diff__eq) ).

thf(4718,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oab__group__add )
     => ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
        = ( B @ ( A @ ( C @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).

thf(990,axiom,
    tc_Complex_Ocomplex @ class_Rings_Ocomm__ring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).

thf(4660,plain,
    tc_Complex_Ocomplex @ class_Rings_Ocomm__ring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).

thf(857,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__vector )
     => ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__triangle__ineq4) ).

thf(4230,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__vector )
     => ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).

thf(44,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__comm__monoid__add )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).

thf(1377,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__comm__monoid__add )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(800,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( A @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Bit1) ).

thf(4033,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( A @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).

thf(450,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).

thf(2833,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(1125,axiom,
    ~ ( c_Int_OPls @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I2_J) ).

thf(5096,plain,
    ~ ( c_Int_OPls @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).

thf(622,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add2) ).

thf(3421,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(897,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__ge__minus__self) ).

thf(4364,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).

thf(491,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__ring__abs ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring__abs) ).

thf(2979,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__ring__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(1169,axiom,
    tc_RealDef_Oreal @ class_Rings_Oring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).

thf(5246,plain,
    tc_RealDef_Oreal @ class_Rings_Oring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).

thf(880,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__div__algebra,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).

thf(4307,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__div__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).

thf(209,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__pred) ).

thf(2002,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(710,axiom,
    tc_Int_Oint @ class_Rings_Ocomm__ring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).

thf(3756,plain,
    tc_Int_Oint @ class_Rings_Ocomm__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).

thf(441,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__ring__strict )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
        <=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).

thf(2809,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__ring__strict )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
          & ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(439,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Int_Onumber__ring )
     => ( ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__number__of__left) ).

thf(2804,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Int_Onumber__ring )
     => ( ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(949,axiom,
    tc_RealDef_Oreal @ class_Groups_Oordered__ab__group__add__abs,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).

thf(4519,plain,
    tc_RealDef_Oreal @ class_Groups_Oordered__ab__group__add__abs,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).

thf(133,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ocomm__monoid__add )
     => ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).

thf(1697,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ocomm__monoid__add )
     => ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(659,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Olinordered__ab__group__add )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).

thf(3559,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Olinordered__ab__group__add )
     => ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(322,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv) ).

thf(2392,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(760,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Oordered__ab__semigroup__add )
     => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mono) ).

thf(3906,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Oordered__ab__semigroup__add )
     => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).

thf(967,axiom,
    tc_RealDef_Oreal @ class_Groups_Ogroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).

thf(4588,plain,
    tc_RealDef_Oreal @ class_Groups_Ogroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).

thf(415,axiom,
    tc_Int_Oint @ class_Rings_Oordered__ring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).

thf(2718,plain,
    tc_Int_Oint @ class_Rings_Oordered__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(264,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( A @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__cancel) ).

thf(2205,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( A @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(552,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( B @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).

thf(3184,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(931,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oab__group__add )
     => ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__poly__code_I1_J) ).

thf(4475,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oab__group__add )
     => ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).

thf(380,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ominus__left) ).

thf(2586,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(627,axiom,
    tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).

thf(3435,plain,
    tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(1005,axiom,
    ! [A: $i] :
      ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ c_Transcendental_Otan @ c_Transcendental_Oarctan )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arctan__tan) ).

thf(4700,plain,
    ! [A: $i] :
      ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ c_Transcendental_Otan @ c_Transcendental_Oarctan )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).

thf(758,axiom,
    tc_Int_Oint @ class_Groups_Oabs__if,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oabs__if) ).

thf(3899,plain,
    tc_Int_Oint @ class_Groups_Oabs__if,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).

thf(526,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ c_SEQ_Osubseq )
     => ( A @ ( B @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_seq__suble) ).

thf(3097,plain,
    ! [A: $i,B: $i] :
      ( ( B @ c_SEQ_Osubseq )
     => ( A @ ( B @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(563,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__assoc) ).

thf(3229,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(743,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0) ).

thf(3857,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).

thf(1248,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ? [D: $i] :
          ( ! [E: $i] :
              ( ( ( D @ ( B @ ( E @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
                & ( B @ ( E @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
             => ( C @ ( B @ ( A @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( E @ ( A @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
          & ( D @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__cont) ).

thf(5530,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ? [D: $i] :
          ( ! [E: $i] :
              ( ( ( D @ ( B @ ( E @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
                & ( B @ ( E @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
             => ( C @ ( B @ ( A @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( E @ ( A @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
          & ( D @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).

thf(131,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
          = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).

thf(1691,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
          = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(741,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Oring )
     => ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__diff__mult) ).

thf(3852,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Oring )
     => ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).

thf(1148,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
      = ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sgn__eq) ).

thf(5167,plain,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
      = ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).

thf(1142,axiom,
    ( ( ( v_d____ @ ( v_z____ @ ( v_wa____ @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
      & ( v_z____ @ ( v_wa____ @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
   => ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( v_wa____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__0960_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_061_061_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096) ).

thf(5142,plain,
    ( ( ( v_d____ @ ( v_z____ @ ( v_wa____ @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
      & ( v_z____ @ ( v_wa____ @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
   => ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( v_wa____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).

thf(1100,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ogroup__add )
     => ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__minus) ).

thf(5034,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ogroup__add )
     => ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).

thf(185,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring__strict )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).

thf(1915,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring__strict )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(1136,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add__abs )
     => ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq3) ).

thf(5122,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add__abs )
     => ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).

thf(853,axiom,
    tc_RealDef_Oreal @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

thf(4216,plain,
    tc_RealDef_Oreal @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).

thf(666,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semiring__strict )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).

thf(3591,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semiring__strict )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(968,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__vector )
     => ( ? [C: $i] :
            ( ! [D: $i] : ( C @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
      <=> ? [C: $i] :
          ! [D: $i] : ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lemma__NBseq__def) ).

thf(4589,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__vector )
     => ( ( ? [C: $i] :
            ! [D: $i] : ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ? [C: $i] :
              ( ! [D: $i] : ( C @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
              & ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) )
        & ( ? [C: $i] :
              ( ! [D: $i] : ( C @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
              & ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
         => ? [C: $i] :
            ! [D: $i] : ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).

thf(981,axiom,
    ! [A: $i] : ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ v_g____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_g_I2_J) ).

thf(4629,plain,
    ! [A: $i] : ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ v_g____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).

thf(347,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__comm__monoid__add )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__pos__pos) ).

thf(2473,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__comm__monoid__add )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(374,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__mono2) ).

thf(2574,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(1211,axiom,
    ! [A: $i] :
      ( ( ( v_d____ @ ( v_z____ @ ( A @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
        & ( v_z____ @ ( A @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
     => ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_d_I2_J) ).

thf(5411,plain,
    ! [A: $i] :
      ( ( ( v_d____ @ ( v_z____ @ ( A @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
        & ( v_z____ @ ( A @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
     => ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).

thf(646,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( A @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__cancel) ).

thf(3531,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( A @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(679,axiom,
    ! [A: $i] :
      ( ( A @ class_Groups_Osgn__if )
     => ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Osgn__class_Osgn ) )
        = ( A @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn0) ).

thf(3635,plain,
    ! [A: $i] :
      ( ( A @ class_Groups_Osgn__if )
     => ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Osgn__class_Osgn ) )
        = ( A @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).

thf(221,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
          = A )
      <=> ( B
          = ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).

thf(2047,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( ( B
            = ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
         => ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
            = A ) )
        & ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
            = A )
         => ( B
            = ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(586,axiom,
    ! [A: $i] : ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc) ).

thf(3318,plain,
    ! [A: $i] : ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(1213,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ c_Transcendental_Oarctan )
      = ( A @ c_Transcendental_Oarctan @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arctan__minus) ).

thf(5416,plain,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ c_Transcendental_Oarctan )
      = ( A @ c_Transcendental_Oarctan @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213]) ).

thf(819,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
      = ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__add__cancel) ).

thf(4076,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
      = ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).

thf(900,axiom,
    tc_RealDef_Oreal @ class_Rings_Olinordered__ring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).

thf(4370,plain,
    tc_RealDef_Oreal @ class_Rings_Olinordered__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).

thf(23,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__semidom )
     => ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__le__zero) ).

thf(1311,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__semidom )
     => ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(273,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Olinordered__ab__group__add )
     => ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).

thf(2232,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Olinordered__ab__group__add )
     => ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(294,axiom,
    tc_Int_Oint @ class_Groups_Oordered__ab__group__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).

thf(2296,plain,
    tc_Int_Oint @ class_Groups_Oordered__ab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(1069,axiom,
    ! [A: $i] :
      ( ( A @ class_Int_Onumber__ring )
     => ( ( c_Int_OPls @ ( A @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Pls) ).

thf(4910,plain,
    ! [A: $i] :
      ( ( A @ class_Int_Onumber__ring )
     => ( ( c_Int_OPls @ ( A @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).

thf(1243,axiom,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__div__algebra,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).

thf(5519,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__div__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).

thf(798,axiom,
    tc_RealDef_Oreal @ class_Groups_Osgn__if,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Osgn__if) ).

thf(4031,plain,
    tc_RealDef_Oreal @ class_Groups_Osgn__if,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).

thf(391,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add )
     => ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).

thf(2621,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add )
     => ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(154,axiom,
    tc_Int_Oint @ class_Rings_Olinordered__semidom,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).

thf(1768,plain,
    tc_Int_Oint @ class_Rings_Olinordered__semidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(471,axiom,
    ! [A: $i] :
      ( ( A @ class_RealVector_Oreal__normed__algebra__1 )
     => ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Osgn__class_Osgn ) )
        = ( A @ c_Groups_Oone__class_Oone ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__one) ).

thf(2905,plain,
    ! [A: $i] :
      ( ( A @ class_RealVector_Oreal__normed__algebra__1 )
     => ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Osgn__class_Osgn ) )
        = ( A @ c_Groups_Oone__class_Oone ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(654,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring__strict )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).

thf(3550,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring__strict )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(844,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__order) ).

thf(4172,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).

thf(1092,axiom,
    tc_RealDef_Oreal @ class_Groups_Omonoid__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).

thf(4999,plain,
    tc_RealDef_Oreal @ class_Groups_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).

thf(278,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Ofield )
     => ( ( C
         != ( D @ c_Groups_Ozero__class_Ozero ) )
       => ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
          = ( C @ ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__divide__eq__iff) ).

thf(2249,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Ofield )
     => ( ( C
         != ( D @ c_Groups_Ozero__class_Ozero ) )
       => ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
          = ( C @ ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(365,axiom,
    ! [A: $i] :
      ( ( A
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
    <=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neq0__conv) ).

thf(2541,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A
         != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
      & ( ( A
         != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
       => ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(289,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono) ).

thf(2277,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(1060,axiom,
    ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ c_Transcendental_Oarctan )
    = ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arctan1__eq__pi4) ).

thf(4878,plain,
    ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ c_Transcendental_Oarctan )
    = ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).

thf(1177,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__vector )
     => ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__ge__zero) ).

thf(5266,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__vector )
     => ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).

thf(1225,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( B != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl3) ).

thf(5455,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).

thf(783,axiom,
    tc_RealDef_Oreal @ class_Rings_Oordered__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).

thf(3989,plain,
    tc_RealDef_Oreal @ class_Rings_Oordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).

thf(938,axiom,
    tc_RealDef_Oreal @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).

thf(4499,plain,
    tc_RealDef_Oreal @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).

thf(991,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__idom )
     => ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).

thf(4661,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__idom )
     => ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).

thf(594,axiom,
    c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pi__ge__zero) ).

thf(3339,plain,
    c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(12,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Odivision__ring )
     => ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__divide__eq__right) ).

thf(1274,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Odivision__ring )
     => ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(1155,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zminus) ).

thf(5206,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).

thf(1105,axiom,
    tc_Complex_Ocomplex @ class_Rings_Ozero__neq__one,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).

thf(5049,plain,
    tc_Complex_Ocomplex @ class_Rings_Ozero__neq__one,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).

thf(381,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
        <=> ( B @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__divide__less__eq) ).

thf(2589,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( ( B @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
          & ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( B @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(48,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B
          = ( A @ c_Nat_OSuc ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucE) ).

thf(1387,plain,
    ! [A: $i,B: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B
          = ( A @ c_Nat_OSuc ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(139,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__semidom )
     => ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__less__zero) ).

thf(1723,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__semidom )
     => ~ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(419,axiom,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
      = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0__right) ).

thf(2733,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
      = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(790,axiom,
    tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).

thf(4016,plain,
    tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).

thf(370,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ c_RComplete_Onatceiling )
          = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__eq) ).

thf(2560,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ c_RComplete_Onatceiling )
          = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(97,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( ( B @ c_Nat_OSuc )
         != A )
       => ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessI) ).

thf(1570,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( ( B @ c_Nat_OSuc )
         != A )
       => ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(124,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__SucI) ).

thf(1676,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(606,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Osemiring__1 )
     => ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_Oiszero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__0) ).

thf(3371,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Osemiring__1 )
     => ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_Oiszero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(1228,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).

thf(5470,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).

thf(479,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Opi @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_Transcendental_Otan )
      = ( A @ c_Transcendental_Otan ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tan__periodic__pi) ).

thf(2937,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Opi @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_Transcendental_Otan )
      = ( A @ c_Transcendental_Otan ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(543,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leD) ).

thf(3154,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(924,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__algebra )
     => ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__mult__ineq) ).

thf(4449,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__algebra )
     => ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).

thf(937,axiom,
    ! [A: $i] :
      ( ( c_Int_OPls @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I10_J) ).

thf(4493,plain,
    ! [A: $i] :
      ( ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( c_Int_OPls @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( c_Int_OPls @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).

thf(1120,axiom,
    ! [A: $i] :
      ( ( A @ class_RealVector_Oreal__normed__vector )
     => ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_RealVector_Onorm__class_Onorm ) )
        = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__zero) ).

thf(5085,plain,
    ! [A: $i] :
      ( ( A @ class_RealVector_Oreal__normed__vector )
     => ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_RealVector_Onorm__class_Onorm ) )
        = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).

thf(1242,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Int_Onumber )
        & ( D @ class_Fields_Olinordered__field__inverse__zero ) )
     => ( ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( ( ~ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
               => ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
              & ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
               => ( C @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
          & ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__eq__number__of1) ).

thf(5507,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Int_Onumber )
        & ( D @ class_Fields_Olinordered__field__inverse__zero ) )
     => ( ( ( ( ~ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
                & ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( C @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
            & ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) )
         => ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( ~ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
                & ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( C @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
            & ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242]) ).

thf(1128,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Rings_Olinordered__idom )
        & ( B @ class_Int_Onumber__ring ) )
     => ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( c_Int_OPls @ c_Int_OBit1 @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I4_J) ).

thf(5102,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Rings_Olinordered__idom )
        & ( B @ class_Int_Onumber__ring ) )
     => ( ( ( c_Int_OPls @ c_Int_OBit1 @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( c_Int_OPls @ c_Int_OBit1 @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).

thf(331,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).

thf(2414,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(1045,axiom,
    tc_Complex_Ocomplex @ class_Rings_Odivision__ring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).

thf(4836,plain,
    tc_Complex_Ocomplex @ class_Rings_Odivision__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).

thf(583,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Ocancel__semigroup__add )
     => ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
          = ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
      <=> ( C = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__cancel) ).

thf(3307,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Ocancel__semigroup__add )
     => ( ( ( C = A )
         => ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
            = ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) )
        & ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
            = ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
         => ( C = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(1236,axiom,
    tc_RealDef_Oreal @ class_Rings_Ocomm__ring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring) ).

thf(5492,plain,
    tc_RealDef_Oreal @ class_Rings_Ocomm__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236]) ).

thf(393,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add1__zle__eq) ).

thf(2628,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(187,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonpos__neg) ).

thf(1920,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(810,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( B @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) )
          = ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__div__pos) ).

thf(4053,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( B @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) )
          = ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).

thf(584,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Osemiring__1 )
     => ~ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Int_Oiszero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__iszero__1) ).

thf(3314,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Osemiring__1 )
     => ~ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Int_Oiszero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(19,axiom,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).

thf(1296,plain,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(262,axiom,
    ( c_Int_OPls
    = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pls__def) ).

thf(2200,plain,
    ( c_Int_OPls
    = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(256,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oordered__cancel__semiring )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).

thf(2179,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oordered__cancel__semiring )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(1088,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__not__less__zero) ).

thf(4979,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).

thf(769,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ocomm__monoid__add )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0) ).

thf(3931,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ocomm__monoid__add )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).

thf(548,axiom,
    tc_Nat_Onat @ class_Rings_Ozero__neq__one,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).

thf(3166,plain,
    tc_Nat_Onat @ class_Rings_Ozero__neq__one,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(339,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Int_Onumber__ring )
     => ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Int_Onumber__class_Onumber__of ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__simps_I32_J) ).

thf(2445,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Int_Onumber__ring )
     => ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Int_Onumber__class_Onumber__of ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(344,axiom,
    ! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le0) ).

thf(2464,plain,
    ! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(460,axiom,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__real__of__nat__less__zero) ).

thf(2873,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(201,axiom,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).

thf(1968,plain,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(556,axiom,
    ! [A: $i,B: $i] :
      ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( ( B = A )
        | ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__add1__eq) ).

thf(3198,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B = A )
          | ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
       => ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( B = A )
          | ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(1019,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( C @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( C @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lemma__MVT) ).

thf(4757,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( C @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( C @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).

thf(515,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).

thf(3065,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(1249,axiom,
    tc_Complex_Ocomplex @ class_Rings_Ocomm__ring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).

thf(5534,plain,
    tc_Complex_Ocomplex @ class_Rings_Ocomm__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).

thf(66,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__ring__1 )
     => ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).

thf(1457,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__ring__1 )
     => ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(756,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__ge__zero) ).

thf(3894,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).

thf(227,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).

thf(2068,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(108,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oordered__ring__abs )
     => ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            | ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
          & ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            | ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
       => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
          = ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__eq__mult) ).

thf(1624,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oordered__ring__abs )
     => ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            | ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
          & ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            | ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
       => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
          = ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(653,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
        <=> ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__divide__eq) ).

thf(3546,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
          & ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(1016,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( tc_Complex_Ocomplex @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__diff__def) ).

thf(4746,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( tc_Complex_Ocomplex @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).

thf(909,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__field )
     => ( ( B
         != ( C @ c_Groups_Ozero__class_Ozero ) )
       => ( ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) )
          = ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__norm__divide) ).

thf(4402,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__field )
     => ( ( B
         != ( C @ c_Groups_Ozero__class_Ozero ) )
       => ( ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) )
          = ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).

thf(257,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD1) ).

thf(2181,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(1015,axiom,
    ! [A: $i] :
      ( ( A @ c_Int_OBit0 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I21_J) ).

thf(4740,plain,
    ! [A: $i] :
      ( ( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ c_Int_OBit0 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ c_Int_OBit0 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).

thf(505,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__comm__monoid__add )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).

thf(3028,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__comm__monoid__add )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(767,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).

thf(3926,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).

thf(511,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).

thf(3050,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(303,axiom,
    ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
    = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__zero) ).

thf(2345,plain,
    ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
    = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(302,axiom,
    tc_Int_Oint @ class_Groups_Ogroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).

thf(2344,plain,
    tc_Int_Oint @ class_Groups_Ogroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(714,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).

thf(3763,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

thf(701,axiom,
    tc_Int_Oint @ class_Groups_Oordered__ab__group__add__abs,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).

thf(3727,plain,
    tc_Int_Oint @ class_Groups_Oordered__ab__group__add__abs,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).

thf(14,axiom,
    tc_Int_Oint @ class_Rings_Oordered__cancel__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).

thf(1281,plain,
    tc_Int_Oint @ class_Rings_Oordered__cancel__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(109,axiom,
    tc_Int_Oint @ class_Rings_Omult__zero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).

thf(1634,plain,
    tc_Int_Oint @ class_Rings_Omult__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(927,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__int__def) ).

thf(4461,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).

thf(1013,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
          = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).

thf(4732,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( ( B = A )
         => ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
            = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) )
        & ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
            = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).

thf(98,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ class_Rings_Olinordered__idom )
        & ( C @ class_Int_Onumber__ring ) )
     => ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__number__of) ).

thf(1573,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ class_Rings_Olinordered__idom )
        & ( C @ class_Int_Onumber__ring ) )
     => ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(726,axiom,
    ! [A: $i] :
      ( ( A @ c_Int_OBit1 )
      = ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit1__def) ).

thf(3799,plain,
    ! [A: $i] :
      ( ( A @ c_Int_OBit1 )
      = ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).

thf(632,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__comm__monoid__add )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
              = ( C @ c_Groups_Ozero__class_Ozero ) )
          <=> ( ( A
                = ( C @ c_Groups_Ozero__class_Ozero ) )
              & ( B
                = ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).

thf(3445,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__comm__monoid__add )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( ( ( A
                  = ( C @ c_Groups_Ozero__class_Ozero ) )
                & ( B
                  = ( C @ c_Groups_Ozero__class_Ozero ) ) )
             => ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
                = ( C @ c_Groups_Ozero__class_Ozero ) ) )
            & ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
                = ( C @ c_Groups_Ozero__class_Ozero ) )
             => ( ( A
                  = ( C @ c_Groups_Ozero__class_Ozero ) )
                & ( B
                  = ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(797,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add )
     => ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).

thf(4027,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add )
     => ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).

thf(1114,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__minus) ).

thf(5066,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).

thf(703,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__left__mono) ).

thf(3731,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).

thf(34,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Rings_Olinordered__idom )
        & ( B @ class_Int_Onumber__ring ) )
     => ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( c_Int_OPls @ c_Int_OBit1 @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__special_I4_J) ).

thf(1350,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Rings_Olinordered__idom )
        & ( B @ class_Int_Onumber__ring ) )
     => ( ( ( c_Int_OPls @ c_Int_OBit1 @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( c_Int_OPls @ c_Int_OBit1 @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(935,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
      & ( v_r @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bn_O_AEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_An_J_096) ).

thf(4486,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
      & ( v_r @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).

thf(1239,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
        = ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__special_I2_J) ).

thf(5502,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
        = ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239]) ).

thf(358,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__comm__monoid__add )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).

thf(2509,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__comm__monoid__add )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(1199,axiom,
    tc_Complex_Ocomplex @ class_Groups_Ozero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).

thf(5362,plain,
    tc_Complex_Ocomplex @ class_Groups_Ozero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).

thf(177,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
        = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
    <=> ( ( ( A
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
          & ( B
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
        | ( ( A
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
          & ( B
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__1) ).

thf(1878,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( ( A
              = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
            & ( B
              = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
          | ( ( A
              = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
            & ( B
              = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) )
       => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) )
      & ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
       => ( ( ( A
              = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
            & ( B
              = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
          | ( ( A
              = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
            & ( B
              = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(678,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Ofield__inverse__zero )
     => ( ( C
         != ( D @ c_Groups_Ozero__class_Ozero ) )
       => ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
          = ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__right) ).

thf(3632,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Ofield__inverse__zero )
     => ( ( C
         != ( D @ c_Groups_Ozero__class_Ozero ) )
       => ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
          = ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(1063,axiom,
    ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
    = ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__num__one) ).

thf(4883,plain,
    ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
    = ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).

thf(1119,axiom,
    ? [A: $i] :
      ( ! [B: $i] :
          ( ( ( A @ ( v_z____ @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
            & ( v_z____ @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
         => ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( B @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096EX_Ad_0620_O_AALL_Aw_O_A0_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_A_N_N_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096) ).

thf(5081,plain,
    ? [A: $i] :
      ( ! [B: $i] :
          ( ( ( A @ ( v_z____ @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
            & ( v_z____ @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
         => ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( B @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).

thf(496,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__ring )
     => ~ ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).

thf(3001,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__ring )
     => ~ ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(722,axiom,
    ! [A: $i,B: $i] :
      ~ ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less1) ).

thf(3782,plain,
    ! [A: $i,B: $i] :
      ~ ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).

thf(88,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc2) ).

thf(1541,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(206,axiom,
    tc_Nat_Onat @ class_Groups_Omonoid__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).

thf(1983,plain,
    tc_Nat_Onat @ class_Groups_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(1080,axiom,
    tc_RealDef_Oreal @ class_Fields_Olinordered__field__inverse__zero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).

thf(4957,plain,
    tc_RealDef_Oreal @ class_Fields_Olinordered__field__inverse__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).

thf(1108,axiom,
    ! [A: $i] :
      ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ c_Nat_OSuc @ c_Nat_OSuc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__2__eq__Suc) ).

thf(5053,plain,
    ! [A: $i] :
      ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ c_Nat_OSuc @ c_Nat_OSuc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).

thf(1161,axiom,
    ! [A: $i] :
      ( ( c_Int_OPls @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I27_J) ).

thf(5221,plain,
    ! [A: $i] :
      ( ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( c_Int_OPls @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( c_Int_OPls @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).

thf(619,axiom,
    ! [A: $i,B: $i] :
      ( ( B = A )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__imp__le) ).

thf(3413,plain,
    ! [A: $i,B: $i] :
      ( ( B = A )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(9,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Oordered__semiring )
     => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
             => ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__mono_H) ).

thf(1270,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Oordered__semiring )
     => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
             => ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(1126,axiom,
    ! [A: $i,B: $i] :
      ( ( v_r @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( ( B @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
          = ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) )
       => ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_Bz_Ax_O_A_091_124_Acmod_Az_A_060_061_Ar_059_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_059_A_126_Ax_A_060_A1_A_124_093_A_061_061_062_AFalse_096) ).

thf(5098,plain,
    ! [A: $i,B: $i] :
      ( ( v_r @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( ( B @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
          = ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) )
       => ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).

thf(5,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( A
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr__implies__not0) ).

thf(1259,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( A
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(317,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
     => ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).

thf(2377,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
     => ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(438,axiom,
    ! [A: $i] :
      ( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls) ).

thf(2801,plain,
    ! [A: $i] :
      ( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(1167,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ogroup__add )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0) ).

thf(5238,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ogroup__add )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).

thf(945,axiom,
    tc_RealDef_Oreal @ class_Groups_Omonoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).

thf(4512,plain,
    tc_RealDef_Oreal @ class_Groups_Omonoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).

thf(408,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Olinordered__semiring__strict )
     => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
             => ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).

thf(2685,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Olinordered__semiring__strict )
     => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
             => ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(1095,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_RealVector_Oreal__normed__vector )
     => ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__diff__triangle__ineq) ).

thf(5006,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_RealVector_Oreal__normed__vector )
     => ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).

thf(1193,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Rings_Oring )
        & ( D @ class_Int_Onumber ) )
     => ( ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__diff__distrib__number__of) ).

thf(5345,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Rings_Oring )
        & ( D @ class_Int_Onumber ) )
     => ( ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).

thf(467,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__D1) ).

thf(2895,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(861,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Ofield )
     => ( ( C
         != ( D @ c_Groups_Ozero__class_Ozero ) )
       => ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) )
          = ( C @ ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__divide__eq__iff) ).

thf(4248,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Ofield )
     => ( ( C
         != ( D @ c_Groups_Ozero__class_Ozero ) )
       => ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) )
          = ( C @ ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).

thf(558,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
        = ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).

thf(3218,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
        = ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(1031,axiom,
    ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
    = ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__add__1) ).

thf(4789,plain,
    ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
    = ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).

thf(1073,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__pos) ).

thf(4930,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).

thf(137,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
      = ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__add) ).

thf(1719,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
      = ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(855,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ c_Transcendental_Oarctan @ ( B @ c_Transcendental_Oarctan @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arctan__monotone) ).

thf(4227,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ c_Transcendental_Oarctan @ ( B @ c_Transcendental_Oarctan @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).

thf(831,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
        = ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__divide) ).

thf(4109,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
        = ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).

thf(1165,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__vector )
     => ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__triangle__ineq2) ).

thf(5233,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__vector )
     => ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).

thf(96,axiom,
    ! [A: $i] :
      ( ( A @ c_Transcendental_Oarctan @ c_Transcendental_Otan )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tan__arctan) ).

thf(1567,plain,
    ! [A: $i] :
      ( ( A @ c_Transcendental_Oarctan @ c_Transcendental_Otan )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

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

thf(1964,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
     => ( ( E
         != ( F @ c_Groups_Ozero__class_Ozero ) )
       => ( ( ( B != A )
            & ( D = C ) )
         => ( ( B @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
           != ( A @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(1024,axiom,
    ! [A: $i] :
      ( ( A @ class_RealVector_Oreal__normed__algebra__1 )
     => ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_RealVector_Onorm__class_Onorm ) )
        = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__one) ).

thf(4772,plain,
    ! [A: $i] :
      ( ( A @ class_RealVector_Oreal__normed__algebra__1 )
     => ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_RealVector_Onorm__class_Onorm ) )
        = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).

thf(702,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).

thf(3728,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).

thf(946,axiom,
    tc_RealDef_Oreal @ class_Rings_Odivision__ring__inverse__zero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) ).

thf(4513,plain,
    tc_RealDef_Oreal @ class_Rings_Odivision__ring__inverse__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).

thf(62,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__real__less) ).

thf(1446,plain,
    ! [A: $i,B: $i] :
      ( ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(657,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).

thf(3555,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(976,axiom,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__vector,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).

thf(4621,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__vector,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).

thf(1206,axiom,
    ! [A: $i] : ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__add__one__gt__zero) ).

thf(5387,plain,
    ! [A: $i] : ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).

thf(885,axiom,
    tc_Complex_Ocomplex @ class_Groups_Ocancel__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).

thf(4320,plain,
    tc_Complex_Ocomplex @ class_Groups_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).

thf(127,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__1__mult) ).

thf(1683,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(718,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( B @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__left__mono__neg) ).

thf(3775,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( B @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).

thf(462,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Olinordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).

thf(2877,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Olinordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(1118,axiom,
    tc_RealDef_Oreal @ class_RealVector_Oreal__field,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__field) ).

thf(5080,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__field,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).

thf(1238,axiom,
    ! [A: $i] :
      ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bin__less__0__simps_I4_J) ).

thf(5496,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238]) ).

thf(1130,axiom,
    tc_Complex_Ocomplex @ class_Rings_Ono__zero__divisors,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).

thf(5107,plain,
    tc_Complex_Ocomplex @ class_Rings_Ono__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).

thf(449,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).

thf(2830,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(1010,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Int_Onumber__ring )
        & ( B @ class_Fields_Ofield ) )
     => ( ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__Numeral1) ).

thf(4721,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Int_Onumber__ring )
        & ( B @ class_Fields_Ofield ) )
     => ( ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).

thf(145,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).

thf(1739,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(919,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__idom )
     => ( ( ~ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oabs__class_Oabs ) )
            = A ) )
        & ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oabs__class_Oabs ) )
            = ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__poly__def) ).

thf(4425,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__idom )
     => ( ( ~ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oabs__class_Oabs ) )
            = A ) )
        & ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oabs__class_Oabs ) )
            = ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).

thf(917,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__vector )
     => ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Osgn__class_Osgn ) )
        = ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__minus) ).

thf(4421,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__vector )
     => ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Osgn__class_Osgn ) )
        = ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).

thf(630,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__ring )
     => ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__square__less__zero) ).

thf(3441,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__ring )
     => ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(297,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Int_Onumber )
        & ( D @ class_Fields_Ofield__inverse__zero ) )
     => ( ( ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) )
          = ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) )
      <=> ( ( ( A
              = ( D @ c_Groups_Ozero__class_Ozero ) )
           => ( ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) )
              = ( D @ c_Groups_Ozero__class_Ozero ) ) )
          & ( ( A
             != ( D @ c_Groups_Ozero__class_Ozero ) )
           => ( ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
              = B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of) ).

thf(2312,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Int_Onumber )
        & ( D @ class_Fields_Ofield__inverse__zero ) )
     => ( ( ( ( ( A
                = ( D @ c_Groups_Ozero__class_Ozero ) )
             => ( ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) )
                = ( D @ c_Groups_Ozero__class_Ozero ) ) )
            & ( ( A
               != ( D @ c_Groups_Ozero__class_Ozero ) )
             => ( ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
                = B ) ) )
         => ( ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) )
            = ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) )
        & ( ( ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) )
            = ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) )
         => ( ( ( A
                = ( D @ c_Groups_Ozero__class_Ozero ) )
             => ( ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) )
                = ( D @ c_Groups_Ozero__class_Ozero ) ) )
            & ( ( A
               != ( D @ c_Groups_Ozero__class_Ozero ) )
             => ( ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
                = B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(957,axiom,
    ! [A: $i] :
      ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ c_Transcendental_Oarctan @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
      & ( A @ c_Transcendental_Oarctan @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arctan__bounded) ).

thf(4545,plain,
    ! [A: $i] :
      ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ c_Transcendental_Oarctan @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
      & ( A @ c_Transcendental_Oarctan @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).

thf(1172,axiom,
    ? [A: $i] :
    ! [B: $i] :
      ( ? [C: $i] :
          ( ( ( C @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
            = ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) )
          & ( v_r @ ( C @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
     => ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mth2) ).

thf(5253,plain,
    ? [A: $i] :
    ! [B: $i] :
      ( ? [C: $i] :
          ( ( ( C @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
            = ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) )
          & ( v_r @ ( C @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
     => ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).

thf(1176,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__diff__def) ).

thf(5263,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).

thf(52,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Ominus) ).

thf(1414,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(260,axiom,
    ! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).

thf(2196,plain,
    ! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(276,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__number__of__int__code) ).

thf(2240,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(1251,axiom,
    tc_RealDef_Oreal @ class_Int_Onumber,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber) ).

thf(5547,plain,
    tc_RealDef_Oreal @ class_Int_Onumber,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).

thf(134,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Oring__1__no__zero__divisors )
     => ( ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
          = ( B @ c_Groups_Oone__class_Oone ) )
      <=> ( ( A
            = ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
          | ( A
            = ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).

thf(1700,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Oring__1__no__zero__divisors )
     => ( ( ( ( A
              = ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
            | ( A
              = ( B @ c_Groups_Oone__class_Oone ) ) )
         => ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
            = ( B @ c_Groups_Oone__class_Oone ) ) )
        & ( ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
            = ( B @ c_Groups_Oone__class_Oone ) )
         => ( ( A
              = ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
            | ( A
              = ( B @ c_Groups_Oone__class_Oone ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(1157,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__less__mono2) ).

thf(5213,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).

thf(388,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring )
     => ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).

thf(2613,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring )
     => ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(192,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semiring__strict )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).

thf(1937,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semiring__strict )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(167,axiom,
    ! [A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
        = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
    <=> ( A
        = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__zero__iff) ).

thf(1810,plain,
    ! [A: $i] :
      ( ( ( A
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
      & ( ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
       => ( A
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(1053,axiom,
    tc_RealDef_Oreal @ class_Rings_Omult__zero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).

thf(4861,plain,
    tc_RealDef_Oreal @ class_Rings_Omult__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).

thf(253,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).

thf(2172,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(565,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1) ).

thf(3242,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(170,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__1) ).

thf(1825,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(1086,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( A
         != ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__abs__iff) ).

thf(4970,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( ( A
           != ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( A
           != ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).

thf(190,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__0 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).

thf(1932,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__0 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(377,axiom,
    ! [A: $i] :
      ( ( A @ class_Groups_Ocomm__monoid__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).

thf(2581,plain,
    ! [A: $i] :
      ( ( A @ class_Groups_Ocomm__monoid__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(1008,axiom,
    tc_Complex_Ocomplex @ class_Int_Oring__char__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).

thf(4717,plain,
    tc_Complex_Ocomplex @ class_Int_Oring__char__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).

thf(196,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( ( B != A )
        & ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__le) ).

thf(1947,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B != A )
          & ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( B != A )
          & ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(207,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).

thf(1984,plain,
    ! [A: $i,B: $i] :
      ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( ( B = A )
         => ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(442,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Transcendental_Opi @ ( A @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_Transcendental_Otan )
      = ( B @ c_Transcendental_Otan ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tan__periodic__n) ).

thf(2813,plain,
    ! [A: $i,B: $i] :
      ( ( c_Transcendental_Opi @ ( A @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_Transcendental_Otan )
      = ( B @ c_Transcendental_Otan ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(863,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ c_Transcendental_Ocos )
      = ( A @ c_Transcendental_Ocos ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__minus) ).

thf(4259,plain,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ c_Transcendental_Ocos )
      = ( A @ c_Transcendental_Ocos ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).

thf(1002,axiom,
    tc_RealDef_Oreal @ class_Fields_Ofield,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield) ).

thf(4689,plain,
    tc_RealDef_Oreal @ class_Fields_Ofield,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).

thf(151,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__idom )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_even__less__0__iff) ).

thf(1759,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__idom )
     => ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(158,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel) ).

thf(1776,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(1179,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__vector )
     => ( ? [C: $i] :
            ( ! [D: $i] : ( C @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
      <=> ? [C: $i] :
          ! [D: $i] : ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lemma__NBseq__def2) ).

thf(5273,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__vector )
     => ( ( ? [C: $i] :
            ! [D: $i] : ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
         => ? [C: $i] :
              ( ! [D: $i] : ( C @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
              & ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) )
        & ( ? [C: $i] :
              ( ! [D: $i] : ( C @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
              & ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
         => ? [C: $i] :
            ! [D: $i] : ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( D @ ( A @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).

thf(1050,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__less__iff) ).

thf(4846,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).

thf(341,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B
         != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
          = ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ) )
      & ( ( B
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__if) ).

thf(2450,plain,
    ! [A: $i,B: $i] :
      ( ( ( B
         != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
          = ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ) )
      & ( ( B
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(101,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).

thf(1588,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(535,axiom,
    tc_Nat_Onat @ class_Int_Onumber,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).

thf(3126,plain,
    tc_Nat_Onat @ class_Int_Onumber,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(407,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).

thf(2681,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add )
     => ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(651,axiom,
    tc_Int_Oint @ class_Groups_Osgn__if,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osgn__if) ).

thf(3541,plain,
    tc_Int_Oint @ class_Groups_Osgn__if,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(451,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__mult__distrib) ).

thf(2836,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(65,axiom,
    tc_Int_Oint @ class_Rings_Ocomm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).

thf(1456,plain,
    tc_Int_Oint @ class_Rings_Ocomm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(46,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__mono) ).

thf(1382,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(600,axiom,
    ! [A: $i] :
      ( ( A
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
     => ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0I) ).

thf(3354,plain,
    ! [A: $i] :
      ( ( A
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
     => ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(815,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Int_Onumber__ring )
        & ( B @ class_Fields_Olinordered__field__inverse__zero ) )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
       => ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_half__gt__zero) ).

thf(4068,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Int_Onumber__ring )
        & ( B @ class_Fields_Olinordered__field__inverse__zero ) )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
       => ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).

thf(613,axiom,
    tc_Nat_Onat @ class_Groups_Ocancel__comm__monoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).

thf(3390,plain,
    tc_Nat_Onat @ class_Groups_Ocancel__comm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(1043,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__vector,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

thf(4829,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__vector,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).

thf(1075,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oabs__if )
     => ( ( ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
            = A ) )
        & ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
            = ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__if) ).

thf(4934,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oabs__if )
     => ( ( ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
            = A ) )
        & ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
            = ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).

thf(356,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( ( B != A )
        & ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__le) ).

thf(2497,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B != A )
          & ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( B != A )
          & ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(55,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( C @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
        = ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__assoc) ).

thf(1429,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( C @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
        = ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(777,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__vector )
     => ( ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
        = ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__norm__cancel) ).

thf(3967,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__vector )
     => ( ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
        = ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).

thf(567,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oordered__cancel__semiring )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).

thf(3247,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oordered__cancel__semiring )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(618,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__idom )
     => ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__greater) ).

thf(3409,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__idom )
     => ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(915,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gt__half__sum) ).

thf(4416,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).

thf(765,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).

thf(3920,plain,
    ! [A: $i] :
      ( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).

thf(286,axiom,
    tc_Int_Oint @ class_Rings_Olinordered__idom,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).

thf(2272,plain,
    tc_Int_Oint @ class_Rings_Olinordered__idom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(314,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_RealVector_Oreal__normed__field )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide_Oadd) ).

thf(2370,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_RealVector_Oreal__normed__field )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(84,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
        = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
    <=> ( ( A
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
        & ( B
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__two__squares__add__zero__iff) ).

thf(1525,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A
            = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
          & ( B
            = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
       => ( ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
      & ( ( ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A
            = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
          & ( B
            = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(954,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ? [B: $i] :
          ( ( ( B @ c_Transcendental_Otan )
            = A )
          & ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
          & ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tan__total__pos) ).

thf(4535,plain,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ? [B: $i] :
          ( ( ( B @ c_Transcendental_Otan )
            = A )
          & ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
          & ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).

thf(727,axiom,
    ! [A: $i,B: $i] :
      ~ ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__add__less2) ).

thf(3802,plain,
    ! [A: $i,B: $i] :
      ~ ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).

thf(986,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ class_Rings_Oidom )
        & ( C @ class_Int_Oring__char__0 ) )
     => ( ( ( B @ ( C @ c_Polynomial_Opoly ) )
          = ( A @ ( C @ c_Polynomial_Opoly ) ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__eq__iff) ).

thf(4644,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ class_Rings_Oidom )
        & ( C @ class_Int_Oring__char__0 ) )
     => ( ( ( B = A )
         => ( ( B @ ( C @ c_Polynomial_Opoly ) )
            = ( A @ ( C @ c_Polynomial_Opoly ) ) ) )
        & ( ( ( B @ ( C @ c_Polynomial_Opoly ) )
            = ( A @ ( C @ c_Polynomial_Opoly ) ) )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).

thf(660,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__ring__strict )
     => ( ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
          = ( C @ c_Groups_Ozero__class_Ozero ) )
      <=> ( ( A
            = ( C @ c_Groups_Ozero__class_Ozero ) )
          & ( B
            = ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).

thf(3563,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__ring__strict )
     => ( ( ( ( A
              = ( C @ c_Groups_Ozero__class_Ozero ) )
            & ( B
              = ( C @ c_Groups_Ozero__class_Ozero ) ) )
         => ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
            = ( C @ c_Groups_Ozero__class_Ozero ) ) )
        & ( ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
            = ( C @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A
              = ( C @ c_Groups_Ozero__class_Ozero ) )
            & ( B
              = ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(325,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__div__pos__le) ).

thf(2402,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(178,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__ring )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).

thf(1895,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__ring )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(1154,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
            & ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
          | ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
            & ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__divide__iff) ).

thf(5198,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
              & ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
            | ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
              & ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) )
         => ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
              & ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
            | ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
              & ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).

thf(963,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__diff) ).

thf(4572,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).

thf(1149,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( A @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
               => ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
              & ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
               => ( C @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
          & ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__eq) ).

thf(5170,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
                & ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( C @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
            & ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) )
         => ( A @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
                & ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( C @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
            & ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).

thf(842,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
          = ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__neg) ).

thf(4163,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
          = ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).

thf(633,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__gt__zero__cancel__iff) ).

thf(3454,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(394,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__comm__monoid__add )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing) ).

thf(2634,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__comm__monoid__add )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(426,axiom,
    tc_Int_Oint @ class_Rings_Ozero__neq__one,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).

thf(2749,plain,
    tc_Int_Oint @ class_Rings_Ozero__neq__one,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(57,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
     => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__le__mono) ).

thf(1434,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
     => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(208,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
        = ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
    <=> ( ( B
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
        | ( C = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel2) ).

thf(1991,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( B
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
          | ( C = A ) )
       => ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
          = ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) ) )
      & ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
          = ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
       => ( ( B
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
          | ( C = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(26,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__lessD1) ).

thf(1318,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(159,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Oring__1 )
     => ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
        = ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__squared__diff__one__factored) ).

thf(1779,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Oring__1 )
     => ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
        = ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(673,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).

thf(3624,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(265,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__comm__monoid__add )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).

thf(2208,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__comm__monoid__add )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(821,axiom,
    ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
    = ( c_Int_OPls @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__is__num__zero) ).

thf(4081,plain,
    ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
    = ( c_Int_OPls @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).

thf(851,axiom,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).

thf(4212,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).

thf(1065,axiom,
    tc_Complex_Ocomplex @ class_Groups_Ocomm__monoid__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).

thf(4889,plain,
    tc_Complex_Ocomplex @ class_Groups_Ocomm__monoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).

thf(1084,axiom,
    tc_RealDef_Oreal @ class_Rings_Olinordered__ring__strict,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).

thf(4966,plain,
    tc_RealDef_Oreal @ class_Rings_Olinordered__ring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).

thf(1022,axiom,
    tc_RealDef_Oreal @ class_Rings_Olinordered__semidom,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).

thf(4765,plain,
    tc_RealDef_Oreal @ class_Rings_Olinordered__semidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).

thf(788,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oidom )
     => ( ( ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
          = ( C @ c_Groups_Ozero__class_Ozero ) )
      <=> ( ( ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) )
           != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
          | ( B
            = ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__root) ).

thf(3999,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oidom )
     => ( ( ( ( ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) )
             != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
            | ( B
              = ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
         => ( ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
            = ( C @ c_Groups_Ozero__class_Ozero ) ) )
        & ( ( ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
            = ( C @ c_Groups_Ozero__class_Ozero ) )
         => ( ( ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) )
             != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
            | ( B
              = ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ( A @ class_Groups_Ocomm__monoid__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Omonoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).

thf(1286,plain,
    ! [A: $i] :
      ( ( A @ class_Groups_Ocomm__monoid__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Omonoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(313,axiom,
    ! [A: $i] :
      ( ( A @ class_Groups_Ocancel__comm__monoid__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ocancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).

thf(2368,plain,
    ! [A: $i] :
      ( ( A @ class_Groups_Ocancel__comm__monoid__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ocancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(1214,axiom,
    ! [A: $i] :
      ( ( A @ c_Int_OBit0 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ c_Int_OBit0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I3_J) ).

thf(5419,plain,
    ! [A: $i] :
      ( ( A @ c_Int_OBit0 @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ c_Int_OBit0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).

thf(923,axiom,
    tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__pi__half__less__zero) ).

thf(4448,plain,
    tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).

thf(328,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__le__add1) ).

thf(2408,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(437,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__nat__number__of) ).

thf(2793,plain,
    ! [A: $i,B: $i] :
      ( ( ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
       => ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(1156,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ c_Int_OBit1 )
     != ( A @ c_Int_OBit0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I50_J) ).

thf(5209,plain,
    ! [A: $i,B: $i] :
      ( ( B @ c_Int_OBit1 )
     != ( A @ c_Int_OBit0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).

thf(234,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).

thf(2089,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(553,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add2) ).

thf(3190,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(268,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Ozero__neq__one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).

thf(2221,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(801,axiom,
    tc_RealDef_Oreal @ class_Groups_Ozero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).

thf(4036,plain,
    tc_RealDef_Oreal @ class_Groups_Ozero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).

thf(738,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Olinordered__ab__group__add )
     => ( ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
          = A )
      <=> ( A
          = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__zero) ).

thf(3841,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Olinordered__ab__group__add )
     => ( ( ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
            = A ) )
        & ( ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
            = A )
         => ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).

thf(390,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
        <=> ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__divide__less__eq) ).

thf(2617,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
          & ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(300,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).

thf(2338,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(688,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ono__zero__divisors )
     => ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
          = ( C @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A
            = ( C @ c_Groups_Ozero__class_Ozero ) )
          | ( B
            = ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divisors__zero) ).

thf(3675,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ono__zero__divisors )
     => ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
          = ( C @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A
            = ( C @ c_Groups_Ozero__class_Ozero ) )
          | ( B
            = ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(881,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__le__trans) ).

thf(4308,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).

thf(683,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oone ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).

thf(3660,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oone ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

thf(330,axiom,
    tc_Int_Oint @ class_Groups_Ocomm__monoid__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).

thf(2413,plain,
    tc_Int_Oint @ class_Groups_Ocomm__monoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(508,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).

thf(3042,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(670,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I34_J) ).

thf(3607,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).

thf(754,axiom,
    tc_Int_Oint @ class_Groups_Oordered__comm__monoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).

thf(3890,plain,
    tc_Int_Oint @ class_Groups_Oordered__comm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).

thf(11,axiom,
    tc_Nat_Onat @ class_Rings_Olinordered__comm__semiring__strict,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).

thf(1273,plain,
    tc_Nat_Onat @ class_Rings_Olinordered__comm__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(988,axiom,
    ! [A: $i] :
      ( ( A @ class_Int_Onumber__ring )
     => ~ ( c_Int_OPls @ c_Int_OBit1 @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Int_Oiszero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__iszero__Numeral1) ).

thf(4657,plain,
    ! [A: $i] :
      ( ( A @ class_Int_Onumber__ring )
     => ~ ( c_Int_OPls @ c_Int_OBit1 @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Int_Oiszero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).

thf(571,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Odivision__ring )
     => ( ( C
         != ( D @ c_Groups_Ozero__class_Ozero ) )
       => ( ( B
            = ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) )
        <=> ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
            = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__eq__divide__eq) ).

thf(3262,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Odivision__ring )
     => ( ( C
         != ( D @ c_Groups_Ozero__class_Ozero ) )
       => ( ( ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
              = A )
           => ( B
              = ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) )
          & ( ( B
              = ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) )
           => ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
              = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(905,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).

thf(4393,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).

thf(706,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Rings_Oidom )
        & ( B @ class_Int_Oring__char__0 ) )
     => ( ( ( A @ ( B @ c_Polynomial_Opoly ) )
          = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Opoly ) ) )
      <=> ( A
          = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__zero) ).

thf(3738,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Rings_Oidom )
        & ( B @ class_Int_Oring__char__0 ) )
     => ( ( ( A
            = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A @ ( B @ c_Polynomial_Opoly ) )
            = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Opoly ) ) ) )
        & ( ( ( A @ ( B @ c_Polynomial_Opoly ) )
            = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Opoly ) ) )
         => ( A
            = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(530,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Omonoid__add )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).

thf(3111,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Omonoid__add )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(42,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__comm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).

thf(1374,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__comm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(1209,axiom,
    ! [A: $i] :
      ( ( A @ c_SEQ_Osubseq )
    <=> ! [B: $i,C: $i] :
          ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subseq__def) ).

thf(5400,plain,
    ! [A: $i] :
      ( ( ! [B: $i,C: $i] :
            ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
           => ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
       => ( A @ c_SEQ_Osubseq ) )
      & ( ( A @ c_SEQ_Osubseq )
       => ! [B: $i,C: $i] :
            ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
           => ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).

thf(1168,axiom,
    ( ( ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
      = ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) )
    & ( v_r @ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096cmod_A0_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A0_J_A_061_A_N_A_I_N_Acmod_A_Ipoly_Ap_A0_J_J_096) ).

thf(5241,plain,
    ( ( ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
      = ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) )
    & ( v_r @ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).

thf(596,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__comm__monoid__add )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing2) ).

thf(3343,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__comm__monoid__add )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(198,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Rings_Osemiring )
        & ( D @ class_Int_Onumber ) )
     => ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__distrib__number__of) ).

thf(1959,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Rings_Osemiring )
        & ( D @ class_Int_Onumber ) )
     => ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(368,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc__shift) ).

thf(2556,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(288,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__comm__monoid__add )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__increasing) ).

thf(2275,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__comm__monoid__add )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(219,axiom,
    ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
    = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__one) ).

thf(2033,plain,
    ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
    = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(248,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add__abs )
     => ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq) ).

thf(2149,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add__abs )
     => ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(974,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I16_J) ).

thf(4613,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).

thf(280,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__0 )
     => ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes ) ) )
        = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__poly__0__left) ).

thf(2253,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__0 )
     => ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes ) ) )
        = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(641,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Ofield__inverse__zero )
     => ( ( ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
          = A )
      <=> ( ( ( B
              = ( D @ c_Groups_Ozero__class_Ozero ) )
           => ( A
              = ( D @ c_Groups_Ozero__class_Ozero ) ) )
          & ( ( B
             != ( D @ c_Groups_Ozero__class_Ozero ) )
           => ( C
              = ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__eq) ).

thf(3491,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Ofield__inverse__zero )
     => ( ( ( ( ( B
                = ( D @ c_Groups_Ozero__class_Ozero ) )
             => ( A
                = ( D @ c_Groups_Ozero__class_Ozero ) ) )
            & ( ( B
               != ( D @ c_Groups_Ozero__class_Ozero ) )
             => ( C
                = ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ) )
         => ( ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
            = A ) )
        & ( ( ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
            = A )
         => ( ( ( B
                = ( D @ c_Groups_Ozero__class_Ozero ) )
             => ( A
                = ( D @ c_Groups_Ozero__class_Ozero ) ) )
            & ( ( B
               != ( D @ c_Groups_Ozero__class_Ozero ) )
             => ( C
                = ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(73,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
        = ( B @ ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).

thf(1483,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
        = ( B @ ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(91,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__field )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide_Ozero) ).

thf(1548,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__field )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(782,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Olinordered__ab__group__add )
     => ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).

thf(3985,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Olinordered__ab__group__add )
     => ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).

thf(868,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__special_I2_J) ).

thf(4269,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).

thf(791,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_RealVector_Oreal__normed__vector )
     => ( ( C @ ( D @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__add__less) ).

thf(4017,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_RealVector_Oreal__normed__vector )
     => ( ( C @ ( D @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).

thf(517,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ogroup__add )
     => ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__minus) ).

thf(3070,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ogroup__add )
     => ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(457,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( ( B = A )
        | ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__Suc__eq) ).

thf(2859,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B = A )
          | ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
       => ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( B = A )
          | ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(492,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oordered__cancel__semiring )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).

thf(2981,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oordered__cancel__semiring )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(521,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__left__mono) ).

thf(3086,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(759,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__eq) ).

thf(3900,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(669,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Ofield__inverse__zero )
     => ( ( C
         != ( D @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
          = ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__left) ).

thf(3604,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Ofield__inverse__zero )
     => ( ( C
         != ( D @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
          = ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(1250,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Int_Onumber )
        & ( D @ class_Fields_Olinordered__field__inverse__zero ) )
     => ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
               => ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
              & ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
               => ( C @ ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
          & ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__eq__number__of) ).

thf(5535,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Int_Onumber )
        & ( D @ class_Fields_Olinordered__field__inverse__zero ) )
     => ( ( ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
                & ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( C @ ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
            & ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) )
         => ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
                & ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( C @ ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
            & ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250]) ).

thf(648,axiom,
    ! [A: $i] :
      ( ( A @ class_Groups_Oab__group__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).

thf(3536,plain,
    ! [A: $i] :
      ( ( A @ class_Groups_Oab__group__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(1030,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).

thf(4786,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).

thf(1078,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Rings_Olinordered__idom )
        & ( B @ class_Int_Onumber__ring ) )
     => ( ( ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oabs__class_Oabs ) )
            = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) )
        & ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oabs__class_Oabs ) )
            = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__number__of) ).

thf(4943,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Rings_Olinordered__idom )
        & ( B @ class_Int_Onumber__ring ) )
     => ( ( ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oabs__class_Oabs ) )
            = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) )
        & ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oabs__class_Oabs ) )
            = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).

thf(874,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Fields_Ofield )
     => ( ( D
         != ( E @ c_Groups_Ozero__class_Ozero ) )
       => ( ( C
           != ( E @ c_Groups_Ozero__class_Ozero ) )
         => ( ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
            = ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__frac__eq) ).

thf(4283,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Fields_Ofield )
     => ( ( D
         != ( E @ c_Groups_Ozero__class_Ozero ) )
       => ( ( C
           != ( E @ c_Groups_Ozero__class_Ozero ) )
         => ( ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
            = ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).

thf(161,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__ring__strict )
     => ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( ( A
           != ( C @ c_Groups_Ozero__class_Ozero ) )
          | ( B
           != ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).

thf(1784,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__ring__strict )
     => ( ( ( ( A
             != ( C @ c_Groups_Ozero__class_Ozero ) )
            | ( B
             != ( C @ c_Groups_Ozero__class_Ozero ) ) )
         => ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( A
             != ( C @ c_Groups_Ozero__class_Ozero ) )
            | ( B
             != ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(1234,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A
            = ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
          | ( A
            = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__pos__lt__two__imp__zero__or__one) ).

thf(5488,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A
            = ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
          | ( A
            = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).

thf(570,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
          = ( C @ c_Groups_Ozero__class_Ozero ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__minus__eq) ).

thf(3255,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( ( B = A )
         => ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
            = ( C @ c_Groups_Ozero__class_Ozero ) ) )
        & ( ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
            = ( C @ c_Groups_Ozero__class_Ozero ) )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(1113,axiom,
    tc_RealDef_Oreal @ class_Rings_Olinordered__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).

thf(5065,plain,
    tc_RealDef_Oreal @ class_Rings_Olinordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).

thf(454,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( B @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__diff__conv2) ).

thf(2849,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( ( B @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(637,axiom,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( A
        = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__0__eq) ).

thf(3472,plain,
    ! [A: $i] :
      ( ( ( A
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
       => ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(353,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__semidom )
     => ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__one) ).

thf(2489,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__semidom )
     => ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(705,axiom,
    ! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__Suc1) ).

thf(3736,plain,
    ! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).

thf(189,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__antisym) ).

thf(1929,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(998,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I14_J) ).

thf(4677,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).

thf(214,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
        = ( B @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__right) ).

thf(2016,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
        = ( B @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(360,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__ab__semigroup__add )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__right__mono) ).

thf(2514,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__ab__semigroup__add )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(1036,axiom,
    ! [A: $i] :
      ( ( v_r @ ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_s1m) ).

thf(4801,plain,
    ! [A: $i] :
      ( ( v_r @ ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).

thf(836,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
        = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
    <=> ( A
        = ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__eq__0__iff) ).

thf(4122,plain,
    ! [A: $i,B: $i] :
      ( ( ( A
          = ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) )
       => ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
      & ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
       => ( A
          = ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).

thf(799,axiom,
    c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos2) ).

thf(4032,plain,
    c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).

thf(1007,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
            & ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
          | ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
            & ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__less__0__iff) ).

thf(4709,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
              & ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
            | ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
              & ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
              & ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
            | ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
              & ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).

thf(973,axiom,
    ! [A: $i] :
      ( ( ( A @ c_Int_OBit0 )
        = c_Int_OPls )
    <=> ( A = c_Int_OPls ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I44_J) ).

thf(4605,plain,
    ! [A: $i] :
      ( ( ( A = c_Int_OPls )
       => ( ( A @ c_Int_OBit0 )
          = c_Int_OPls ) )
      & ( ( ( A @ c_Int_OBit0 )
          = c_Int_OPls )
       => ( A = c_Int_OPls ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).

thf(1106,axiom,
    ! [A: $i,B: $i] : ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__mod__triangle__ineq2) ).

thf(5050,plain,
    ! [A: $i,B: $i] : ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).

thf(85,axiom,
    tc_Int_Oint @ class_Groups_Oab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).

thf(1535,plain,
    tc_Int_Oint @ class_Groups_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(163,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).

thf(1795,plain,
    ! [A: $i,B: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(323,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oordered__cancel__semiring )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).

thf(2398,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oordered__cancel__semiring )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(888,axiom,
    tc_RealDef_Oreal @ class_Groups_Ocancel__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).

thf(4328,plain,
    tc_RealDef_Oreal @ class_Groups_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).

thf(617,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ c_Nat_OSuc )
        = ( A @ c_Nat_OSuc ) )
     => ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).

thf(3404,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ c_Nat_OSuc )
        = ( A @ c_Nat_OSuc ) )
     => ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(444,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ~ ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leE) ).

thf(2817,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ~ ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ogroup__add )
     => ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_left__minus) ).

thf(1256,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ogroup__add )
     => ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(1099,axiom,
    ! [A: $i] :
      ( ? [B: $i] :
          ( ( B @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
          & ? [C: $i] :
              ( ( ( C @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
                = ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) )
              & ( v_r @ ( C @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
    <=> ( v_s____ @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_s) ).

thf(5022,plain,
    ! [A: $i] :
      ( ( ( v_s____ @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ? [B: $i] :
            ( ( B @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
            & ? [C: $i] :
                ( ( ( C @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
                  = ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) )
                & ( v_r @ ( C @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
      & ( ? [B: $i] :
            ( ( B @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
            & ? [C: $i] :
                ( ( ( C @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
                  = ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) )
                & ( v_r @ ( C @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
       => ( v_s____ @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).

thf(934,axiom,
    tc_RealDef_Oreal @ class_Groups_Ocancel__comm__monoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add) ).

thf(4485,plain,
    tc_RealDef_Oreal @ class_Groups_Ocancel__comm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).

thf(717,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__trans) ).

thf(3773,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).

thf(776,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ c_Int_OBit0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I7_J) ).

thf(3964,plain,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ c_Int_OBit0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).

thf(832,axiom,
    tc_RealDef_Oreal @ class_Groups_Ocomm__monoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).

thf(4112,plain,
    tc_RealDef_Oreal @ class_Groups_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).

thf(110,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oring )
     => ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__commute) ).

thf(1635,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oring )
     => ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(913,axiom,
    ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ c_Transcendental_Otan )
    = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tan__45) ).

thf(4413,plain,
    ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ c_Transcendental_Otan )
    = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).

thf(595,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Int_Onumber__ring )
     => ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Int_Onumber__class_Onumber__of ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__number__of__eq) ).

thf(3340,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Int_Onumber__ring )
     => ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Int_Onumber__class_Onumber__of ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(533,axiom,
    tc_Int_Oint @ class_Rings_Ocomm__semiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).

thf(3123,plain,
    tc_Int_Oint @ class_Rings_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(628,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).

thf(3436,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(222,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
          = ( C @ c_Groups_Ozero__class_Ozero ) )
       => ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__unique) ).

thf(2055,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
          = ( C @ c_Groups_Ozero__class_Ozero ) )
       => ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(695,axiom,
    tc_Int_Oint @ class_Rings_Oring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).

thf(3700,plain,
    tc_Int_Oint @ class_Rings_Oring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(870,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__vector )
     => ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__not__less__zero) ).

thf(4273,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__vector )
     => ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).

thf(582,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__cancel2) ).

thf(3304,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(523,axiom,
    tc_Int_Oint @ class_Rings_Oring__1__no__zero__divisors,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).

thf(3091,plain,
    tc_Int_Oint @ class_Rings_Oring__1__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(111,axiom,
    tc_Int_Oint @ class_Rings_Ocomm__semiring__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).

thf(1638,plain,
    tc_Int_Oint @ class_Rings_Ocomm__semiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(250,axiom,
    ! [A: $i] :
      ( ( A @ class_Groups_Ocancel__comm__monoid__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ocancel__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).

thf(2161,plain,
    ! [A: $i] :
      ( ( A @ class_Groups_Ocancel__comm__monoid__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ocancel__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(862,axiom,
    ! [A: $i] :
      ( ? [B: $i] :
          ( ( A @ ( B @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
          & ( v_r @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
    <=> ( A @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096_B_By_O_A_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_A_N_A_I_N_Acmod_A_Ipoly_Ap_Az_J_J_A_060_Ay_J_A_061_A_I_N_As_A_060_Ay_J_096) ).

thf(4251,plain,
    ! [A: $i] :
      ( ( ( A @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ? [B: $i] :
            ( ( A @ ( B @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
            & ( v_r @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
      & ( ? [B: $i] :
            ( ( A @ ( B @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
            & ( v_r @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
       => ( A @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).

thf(952,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__vector )
     => ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_RealVector_Onorm__class_Onorm ) )
        = ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__minus__cancel) ).

thf(4526,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__vector )
     => ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_RealVector_Onorm__class_Onorm ) )
        = ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).

thf(725,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
        = ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult) ).

thf(3796,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
        = ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).

thf(80,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__ring__strict )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
        <=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).

thf(1503,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__ring__strict )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
          & ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(1151,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__def) ).

thf(5185,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).

thf(503,axiom,
    ! [A: $i] :
      ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__less0) ).

thf(3023,plain,
    ! [A: $i] :
      ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(1102,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I14_J) ).

thf(5039,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).

thf(961,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( B != A )
       => ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).

thf(4558,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( B != A )
       => ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).

thf(122,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add )
     => ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).

thf(1669,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add )
     => ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(1200,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Int_Onumber )
        & ( D @ class_Fields_Olinordered__field__inverse__zero ) )
     => ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
               => ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
              & ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
               => ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
          & ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( B @ ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__divide__eq__number__of) ).

thf(5363,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Int_Onumber )
        & ( D @ class_Fields_Olinordered__field__inverse__zero ) )
     => ( ( ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
                & ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
            & ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) )
         => ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
                & ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
            & ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( A @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).

thf(293,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).

thf(2293,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(1034,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__less__half__sum) ).

thf(4796,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).

thf(466,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ class_Rings_Oordered__ring )
     => ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( A @ ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__iff1) ).

thf(2891,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ class_Rings_Oordered__ring )
     => ( ( ( A @ ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(40,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Fields_Olinordered__field )
     => ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( C @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__less2) ).

thf(1371,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Fields_Olinordered__field )
     => ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( C @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(1046,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
        & ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of1) ).

thf(4837,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
        & ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).

thf(693,axiom,
    ! [A: $i] :
      ( ( A @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oabs__class_Oabs ) )
        = ( A @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__zero) ).

thf(3695,plain,
    ! [A: $i] :
      ( ( A @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oabs__class_Oabs ) )
        = ( A @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).

thf(827,axiom,
    ! [A: $i] :
      ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ c_Nat_OSuc @ c_Nat_OSuc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__2__eq__Suc_H) ).

thf(4099,plain,
    ! [A: $i] :
      ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ c_Nat_OSuc @ c_Nat_OSuc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).

thf(590,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add2) ).

thf(3330,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(421,axiom,
    tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add__imp__le,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).

thf(2738,plain,
    tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add__imp__le,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(557,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
        = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
    <=> ( ( A
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
        & ( B
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).

thf(3208,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
          & ( B
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) )
       => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) )
      & ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
       => ( ( A
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
          & ( B
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(1189,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ class_Rings_Oordered__ring )
     => ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__iff2) ).

thf(5331,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ class_Rings_Oordered__ring )
     => ( ( ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).

thf(179,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Fields_Ofield )
     => ( ( D
         != ( E @ c_Groups_Ozero__class_Ozero ) )
       => ( ( C
           != ( E @ c_Groups_Ozero__class_Ozero ) )
         => ( ( ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide ) ) )
              = ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide ) ) ) )
          <=> ( ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) )
              = ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__eq__eq) ).

thf(1897,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Fields_Ofield )
     => ( ( D
         != ( E @ c_Groups_Ozero__class_Ozero ) )
       => ( ( C
           != ( E @ c_Groups_Ozero__class_Ozero ) )
         => ( ( ( ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) )
                = ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes ) ) ) )
             => ( ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide ) ) )
                = ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide ) ) ) ) )
            & ( ( ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide ) ) )
                = ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide ) ) ) )
             => ( ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) )
                = ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(681,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Int_Onumber )
        & ( D @ class_Fields_Olinordered__field__inverse__zero ) )
     => ( ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( ( ~ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
               => ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
              & ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
               => ( C @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
          & ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__le__eq__number__of1) ).

thf(3641,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Int_Onumber )
        & ( D @ class_Fields_Olinordered__field__inverse__zero ) )
     => ( ( ( ( ~ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
                & ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( C @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
            & ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
         => ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( ~ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
                & ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( C @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
            & ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).

thf(698,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Ofield__inverse__zero )
     => ( ( C
         != ( D @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
          = ( C @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__frac__num) ).

thf(3719,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Ofield__inverse__zero )
     => ( ( C
         != ( D @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
          = ( C @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(309,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Oidom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).

thf(2358,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Oidom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(36,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
        = ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add) ).

thf(1356,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
        = ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(689,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oring )
     => ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__minus) ).

thf(3678,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oring )
     => ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).

thf(242,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).

thf(2119,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(406,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).

thf(2679,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(1244,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__0__number__of) ).

thf(5520,plain,
    ! [A: $i] :
      ( ( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).

thf(879,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__gt__half__sum) ).

thf(4305,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).

thf(1235,axiom,
    tc_RealDef_Oreal @ class_Groups_Oab__semigroup__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).

thf(5491,plain,
    tc_RealDef_Oreal @ class_Groups_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).

thf(138,axiom,
    tc_Int_Oint @ class_Rings_Olinordered__ring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).

thf(1722,plain,
    tc_Int_Oint @ class_Rings_Olinordered__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(1203,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).

thf(5381,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).

thf(902,axiom,
    ! [A: $i] : ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__mod__minus__le__complex__mod) ).

thf(4388,plain,
    ! [A: $i] : ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).

thf(677,axiom,
    tc_Int_Oint @ class_Rings_Olinordered__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).

thf(3631,plain,
    tc_Int_Oint @ class_Rings_Olinordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(364,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Ominus) ).

thf(2538,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(15,axiom,
    ! [A: $i] :
      ( A
     != ( A @ c_Nat_OSuc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).

thf(1282,plain,
    ! [A: $i] :
      ( A
     != ( A @ c_Nat_OSuc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(350,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ogroup__add )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__right) ).

thf(2478,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ogroup__add )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(249,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ c_Nat_OSuc )
        = ( A @ c_Nat_OSuc ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).

thf(2151,plain,
    ! [A: $i,B: $i] :
      ( ( ( B = A )
       => ( ( B @ c_Nat_OSuc )
          = ( A @ c_Nat_OSuc ) ) )
      & ( ( ( B @ c_Nat_OSuc )
          = ( A @ c_Nat_OSuc ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(398,axiom,
    ! [A: $i] : ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__ge__zero) ).

thf(2642,plain,
    ! [A: $i] : ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(272,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
        = ( B @ ( A @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

thf(2229,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
        = ( B @ ( A @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(730,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring__strict )
     => ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).

thf(3815,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring__strict )
     => ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).

thf(1241,axiom,
    tc_RealDef_Oreal @ class_Groups_Oab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).

thf(5506,plain,
    tc_RealDef_Oreal @ class_Groups_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).

thf(232,axiom,
    ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_Transcendental_Otan )
    = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tan__zero) ).

thf(2084,plain,
    ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_Transcendental_Otan )
    = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(576,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Odiff__right) ).

thf(3287,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(1042,axiom,
    tc_RealDef_Oreal @ class_Rings_Osemiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__1) ).

thf(4828,plain,
    tc_RealDef_Oreal @ class_Rings_Osemiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).

thf(720,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semiring__strict )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).

thf(3779,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semiring__strict )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).

thf(621,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono2) ).

thf(3419,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(1071,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
          | ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
          | ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__0__le__divide__iff) ).

thf(4914,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
            | ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
          & ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
            | ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
       => ( A @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
            | ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
          & ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
            | ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).

thf(572,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).

thf(3270,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(277,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oabs__class_Oabs ) )
        = ( A @ c_Groups_Oone__class_Oone ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__one) ).

thf(2246,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Oabs__class_Oabs ) )
        = ( A @ c_Groups_Oone__class_Oone ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(76,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
        = ( B @ c_Nat_OSuc @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq1) ).

thf(1492,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
        = ( B @ c_Nat_OSuc @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(241,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__leD2) ).

thf(2116,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(452,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
       != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
     => ( ( ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
          = ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__right__cancel) ).

thf(2839,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
       != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
     => ( ( ( B = A )
         => ( ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
            = ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) ) )
        & ( ( ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
            = ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(156,axiom,
    ! [A: $i] :
      ( ( A @ class_RealVector_Oreal__normed__vector )
     => ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Osgn__class_Osgn ) )
        = ( A @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__zero) ).

thf(1771,plain,
    ! [A: $i] :
      ( ( A @ class_RealVector_Oreal__normed__vector )
     => ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Osgn__class_Osgn ) )
        = ( A @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(1081,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Oordered__ab__group__add__abs )
     => ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__diff__triangle__ineq) ).

thf(4958,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Oordered__ab__group__add__abs )
     => ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).

thf(852,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__div__algebra )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) )
        = ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__mult) ).

thf(4213,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__div__algebra )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) )
        = ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).

thf(165,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ogroup__add )
     => ( ( ( B @ c_Groups_Ozero__class_Ozero )
          = ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
      <=> ( ( B @ c_Groups_Ozero__class_Ozero )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).

thf(1801,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ogroup__add )
     => ( ( ( ( B @ c_Groups_Ozero__class_Ozero )
            = A )
         => ( ( B @ c_Groups_Ozero__class_Ozero )
            = ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) )
        & ( ( ( B @ c_Groups_Ozero__class_Ozero )
            = ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
         => ( ( B @ c_Groups_Ozero__class_Ozero )
            = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(841,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
        = ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) )
    <=> ( ( C @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__2__times__iff) ).

thf(4154,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( C @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
          = ( A @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) )
       => ( C
          = ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ) )
      & ( ( C
          = ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) )
       => ( ( C @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
          = ( A @ ( B @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).

thf(43,axiom,
    tc_Int_Oint @ class_Rings_Oordered__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).

thf(1376,plain,
    tc_Int_Oint @ class_Rings_Oordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(943,axiom,
    tc_Complex_Ocomplex @ class_Groups_Oab__group__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).

thf(4509,plain,
    tc_Complex_Ocomplex @ class_Groups_Oab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).

thf(59,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
      = ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__mult) ).

thf(1439,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
      = ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(121,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
     => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__less__mono) ).

thf(1667,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
     => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(849,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Ofield__inverse__zero )
     => ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__divide__divide) ).

thf(4203,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Ofield__inverse__zero )
     => ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).

thf(908,axiom,
    v_d____ @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_d_I1_J) ).

thf(4401,plain,
    v_d____ @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).

thf(216,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( B @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).

thf(2025,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( B @ ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(387,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oring )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__left) ).

thf(2610,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oring )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(392,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).

thf(2625,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(518,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
        = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
     => ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).

thf(3073,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
        = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
     => ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(812,axiom,
    ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
    = ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Numeral1__eq1__nat) ).

thf(4064,plain,
    ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
    = ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).

thf(1190,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ c_Int_OBit1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit0__Bit1) ).

thf(5335,plain,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ c_Int_OBit1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).

thf(554,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
        = ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).

thf(3192,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
        = ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(639,axiom,
    tc_Int_Oint @ class_Rings_Olinordered__ring__strict,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).

thf(3483,plain,
    tc_Int_Oint @ class_Rings_Olinordered__ring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(67,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
    <=> ? [B: $i] :
          ( A
          = ( B @ c_Nat_OSuc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).

thf(1460,plain,
    ! [A: $i] :
      ( ( ? [B: $i] :
            ( A
            = ( B @ c_Nat_OSuc ) )
       => ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ? [B: $i] :
            ( A
            = ( B @ c_Nat_OSuc ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(476,axiom,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc )
      = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).

thf(2928,plain,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc )
      = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(1226,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( A @ ( c_Int_OPls @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__numeral__0) ).

thf(5459,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( A @ ( c_Int_OPls @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).

thf(960,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add )
     => ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__less__iff) ).

thf(4554,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add )
     => ( ( ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).

thf(69,axiom,
    ( c_Transcendental_Opi
   != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pi__neq__zero) ).

thf(1471,plain,
    ( c_Transcendental_Opi
   != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(708,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__idom )
     => ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
          = ( B @ c_Groups_Ozero__class_Ozero ) )
      <=> ( A
          = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__0__0) ).

thf(3747,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__idom )
     => ( ( ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
            = ( B @ c_Groups_Ozero__class_Ozero ) ) )
        & ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
            = ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(955,axiom,
    tc_RealDef_Oreal @ class_Groups_Ocancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).

thf(4541,plain,
    tc_RealDef_Oreal @ class_Groups_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).

thf(423,axiom,
    ! [A: $i] :
      ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__0__right) ).

thf(2742,plain,
    ! [A: $i] :
      ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(1062,axiom,
    tc_RealDef_Oreal @ class_Groups_Oordered__ab__semigroup__add__imp__le,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).

thf(4882,plain,
    tc_RealDef_Oreal @ class_Groups_Oordered__ab__semigroup__add__imp__le,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).

thf(513,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__0 )
     => ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes ) ) )
        = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__poly__0__right) ).

thf(3055,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__0 )
     => ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes ) ) )
        = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(1219,axiom,
    tc_RealDef_Oreal @ class_Groups_Oab__group__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).

thf(5439,plain,
    tc_RealDef_Oreal @ class_Groups_Oab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).

thf(142,axiom,
    ! [A: $i,B: $i] :
      ( ( c_Transcendental_Opi @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_Transcendental_Otan )
      = ( B @ c_Transcendental_Otan ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tan__periodic__nat) ).

thf(1731,plain,
    ! [A: $i,B: $i] :
      ( ( c_Transcendental_Opi @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_Transcendental_Otan )
      = ( B @ c_Transcendental_Otan ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(865,axiom,
    tc_Complex_Ocomplex @ class_Int_Onumber,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Onumber) ).

thf(4264,plain,
    tc_Complex_Ocomplex @ class_Int_Onumber,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).

thf(661,axiom,
    ! [A: $i] : ( A @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__refl) ).

thf(3572,plain,
    ! [A: $i] : ( A @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(183,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).

thf(1909,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(1090,axiom,
    ! [A: $i] :
      ( ? [B: $i] :
          ( ( A @ ( B @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
          & ( v_r @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
    <=> ( A @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_s1) ).

thf(4985,plain,
    ! [A: $i] :
      ( ( ( A @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ? [B: $i] :
            ( ( A @ ( B @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
            & ( v_r @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
      & ( ? [B: $i] :
            ( ( A @ ( B @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
            & ( v_r @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
       => ( A @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).

thf(329,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__left) ).

thf(2410,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(29,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonneg__pos) ).

thf(1325,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(382,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
     => ( ( B
          = ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) )
      <=> ( A
          = ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).

thf(2593,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
     => ( ( ( A
            = ( C @ c_Groups_Ozero__class_Ozero ) )
         => ( B
            = ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) )
        & ( ( B
            = ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) )
         => ( A
            = ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(499,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ c_RComplete_Onatceiling @ ( B @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__mono) ).

thf(3006,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ c_RComplete_Onatceiling @ ( B @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(1186,axiom,
    tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).

thf(5318,plain,
    tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).

thf(581,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__mono) ).

thf(3298,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(279,axiom,
    tc_Nat_Onat @ class_Rings_Osemiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).

thf(2252,plain,
    tc_Nat_Onat @ class_Rings_Osemiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(404,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
               => ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
              & ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
               => ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
          & ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__divide__eq) ).

thf(2664,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
                & ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
            & ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
         => ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
                & ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
            & ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(1091,axiom,
    ! [A: $i,B: $i] :
      ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__add__less__0__iff) ).

thf(4993,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).

thf(367,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Odiff) ).

thf(2553,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(376,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).

thf(2578,plain,
    ! [A: $i] :
      ( ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(130,axiom,
    ! [A: $i] :
      ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1__right) ).

thf(1688,plain,
    ! [A: $i] :
      ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(638,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).

thf(3480,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(545,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__ring__strict )
     => ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
        <=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).

thf(3159,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__ring__strict )
     => ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
          & ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(477,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
        = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).

thf(2931,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
        = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(428,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Odivision__ring )
     => ( ( C
         != ( D @ c_Groups_Ozero__class_Ozero ) )
       => ( ( ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
            = A )
        <=> ( B
            = ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__divide__eq__eq) ).

thf(2752,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Odivision__ring )
     => ( ( C
         != ( D @ c_Groups_Ozero__class_Ozero ) )
       => ( ( ( B
              = ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) )
           => ( ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
              = A ) )
          & ( ( ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
              = A )
           => ( B
              = ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(71,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oprod__diff__prod) ).

thf(1477,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(1006,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__int__code_I14_J) ).

thf(4703,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).

thf(1122,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ c_Transcendental_Otan @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tan__gt__zero) ).

thf(5089,plain,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ c_Transcendental_Otan @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).

thf(94,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).

thf(1562,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(650,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__0 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).

thf(3539,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__0 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(1074,axiom,
    tc_Complex_Ocomplex @ class_Rings_Omult__zero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).

thf(4933,plain,
    tc_Complex_Ocomplex @ class_Rings_Omult__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).

thf(1049,axiom,
    ! [A: $i,B: $i] : ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__minus__mult__self__le) ).

thf(4844,plain,
    ! [A: $i,B: $i] : ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).

thf(486,axiom,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc )
     != A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).

thf(2962,plain,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(312,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__1) ).

thf(2365,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(70,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ c_RComplete_Onatceiling )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__real__of__nat) ).

thf(1474,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ c_RComplete_Onatceiling )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(858,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( ~ ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
              = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ) )
          & ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
              = ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ) ) ) )
      & ( ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
          = ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nat__number__of) ).

thf(4232,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( ~ ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
              = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ) )
          & ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
              = ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ) ) ) )
      & ( ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
          = ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).

thf(306,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__assoc) ).

thf(2350,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(1221,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone @ ( B @ c_Polynomial_Opoly ) @ hAPP ) )
        = ( B @ c_Groups_Oone__class_Oone ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__1) ).

thf(5442,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone @ ( B @ c_Polynomial_Opoly ) @ hAPP ) )
        = ( B @ c_Groups_Oone__class_Oone ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).

thf(674,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono1) ).

thf(3627,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(1159,axiom,
    ( ( c_Int_OPls @ c_Int_OBit0 )
    = c_Int_OPls ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__Pls) ).

thf(5216,plain,
    ( ( c_Int_OPls @ c_Int_OBit0 )
    = c_Int_OPls ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).

thf(712,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Suc) ).

thf(3759,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).

thf(737,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).

thf(3838,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).

thf(1202,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Int_Oring__char__0 )
        & ( B @ class_Int_Onumber__ring ) )
     => ( ( A @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Int_Oiszero ) )
      <=> ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Int_Oiszero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__number__of__Bit0) ).

thf(5377,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Int_Oring__char__0 )
        & ( B @ class_Int_Onumber__ring ) )
     => ( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Int_Oiszero ) )
         => ( A @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Int_Oiszero ) ) )
        & ( ( A @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Int_Oiszero ) )
         => ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Int_Oiszero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).

thf(623,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
        <=> ( A @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__less__divide__eq) ).

thf(3423,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( ( A @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
          & ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( A @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(351,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
        <=> ( B @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__divide__le__eq) ).

thf(2481,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( ( B @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
          & ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( B @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(1160,axiom,
    ! [A: $i] :
      ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__add__one__not__less__self) ).

thf(5218,plain,
    ! [A: $i] :
      ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).

thf(233,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Ofield )
     => ( ( C
         != ( D @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
          = ( C @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__add__eq__iff) ).

thf(2086,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Ofield )
     => ( ( C
         != ( D @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
          = ( C @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(1231,axiom,
    ( ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
   => ? [A: $i] :
      ! [B: $i] :
        ( ( v_r @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_calculation) ).

thf(5482,plain,
    ( ~ ( v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
   => ? [A: $i] :
      ! [B: $i] :
        ( ( v_r @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).

thf(246,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
        & ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).

thf(2139,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
          & ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
       => ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
          & ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(691,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).

thf(3687,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).

thf(873,axiom,
    tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__strict,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).

thf(4282,plain,
    tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).

thf(979,axiom,
    tc_RealDef_Oreal @ class_Groups_Oordered__ab__group__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).

thf(4626,plain,
    tc_RealDef_Oreal @ class_Groups_Oordered__ab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).

thf(814,axiom,
    c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).

thf(4067,plain,
    c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).

thf(1141,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ class_RealVector_Oreal__field )
     => ( ( A @ ( B @ ( C @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( B @ ( A @ ( C @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Rings_Oinverse__class_Odivide ) ) @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DERIV__mult__lemma) ).

thf(5139,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ class_RealVector_Oreal__field )
     => ( ( A @ ( B @ ( C @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( B @ ( A @ ( C @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Rings_Oinverse__class_Odivide ) ) @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).

thf(1066,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ( ( B @ c_Transcendental_Otan )
        = A )
      & ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
      & ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lemma__tan__total1) ).

thf(4890,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ( ( B @ c_Transcendental_Otan )
        = A )
      & ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
      & ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).

thf(761,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__mono2) ).

thf(3908,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).

thf(747,axiom,
    ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_Transcendental_Oarctan )
    = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arctan__zero__zero) ).

thf(3876,plain,
    ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_Transcendental_Oarctan )
    = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).

thf(132,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc) ).

thf(1694,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(210,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring__strict )
     => ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).

thf(2005,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring__strict )
     => ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(1252,axiom,
    tc_Complex_Ocomplex @ class_Rings_Osemiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).

thf(5548,plain,
    tc_Complex_Ocomplex @ class_Rings_Osemiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).

thf(624,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).

thf(3427,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(1247,axiom,
    ! [A: $i,B: $i] : ( B @ c_Nat_OSuc @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__Suc) ).

thf(5528,plain,
    ! [A: $i,B: $i] : ( B @ c_Nat_OSuc @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).

thf(965,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
      = ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__numeral__code_I5_J) ).

thf(4580,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
      = ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).

thf(401,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ozero__left) ).

thf(2652,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(181,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).

thf(1905,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(953,axiom,
    ? [A: $i] :
    ! [B: $i] :
      ( ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( A @ hAPP ) @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
      & ( v_r @ ( B @ ( A @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096EX_Af_O_AALL_Ax_O_Acmod_A_If_Ax_J_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A_If_Ax_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_Ax_J_096) ).

thf(4529,plain,
    ? [A: $i] :
    ! [B: $i] :
      ( ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( A @ hAPP ) @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
      & ( v_r @ ( B @ ( A @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).

thf(263,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__assoc) ).

thf(2202,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(33,axiom,
    ! [A: $i,B: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
        = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
    <=> ( ( A
          = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
        & ( B
          = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).

thf(1340,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A
            = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
          & ( B
            = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) )
       => ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
          = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) ) )
      & ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
          = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
       => ( ( A
            = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
          & ( B
            = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(895,axiom,
    ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pi__not__less__zero) ).

thf(4355,plain,
    ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).

thf(469,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__ring__strict )
     => ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
        <=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).

thf(2899,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__ring__strict )
     => ( ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
          & ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(1197,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Odivision__ring__inverse__zero )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__zero) ).

thf(5358,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Odivision__ring__inverse__zero )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).

thf(910,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Rings_Olinordered__idom )
        & ( B @ class_Int_Onumber__ring ) )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I3_J) ).

thf(4405,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Rings_Olinordered__idom )
        & ( B @ class_Int_Onumber__ring ) )
     => ( ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).

thf(507,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
    <=> ( ( C
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
        | ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__cancel1) ).

thf(3031,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( C
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
          | ( B = A ) )
       => ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
          = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) ) )
      & ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
          = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
       => ( ( C
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
          | ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(443,axiom,
    tc_Int_Oint @ class_Rings_Olinordered__comm__semiring__strict,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).

thf(2816,plain,
    tc_Int_Oint @ class_Rings_Olinordered__comm__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(1003,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
        & ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__interval__iff) ).

thf(4690,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
          & ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
       => ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
          & ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).

thf(119,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Oab__group__add )
     => ( ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Deriv_Oadd__diff__add) ).

thf(1662,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Oab__group__add )
     => ( ( A @ ( B @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(906,axiom,
    tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__0) ).

thf(4394,plain,
    tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).

thf(150,axiom,
    tc_Int_Oint @ class_Groups_Ocomm__monoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).

thf(1758,plain,
    tc_Int_Oint @ class_Groups_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(237,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Odivision__ring )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__zero__left) ).

thf(2107,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Odivision__ring )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(434,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__ring__strict )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).

thf(2784,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__ring__strict )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(285,axiom,
    tc_Int_Oint @ class_Groups_Oab__group__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).

thf(2271,plain,
    tc_Int_Oint @ class_Groups_Oab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(13,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Rings_Olinordered__idom )
        & ( B @ class_Int_Onumber__ring ) )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__special_I3_J) ).

thf(1277,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Rings_Olinordered__idom )
        & ( B @ class_Int_Onumber__ring ) )
     => ( ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(809,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).

thf(4052,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).

thf(453,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( A @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Bit0) ).

thf(2846,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( A @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(281,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Olinordered__ab__group__add )
     => ( ( A
          = ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
      <=> ( A
          = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equal__neg__zero) ).

thf(2256,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Olinordered__ab__group__add )
     => ( ( ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( A
            = ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) )
        & ( ( A
            = ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
         => ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(833,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__idom )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Oabs__class_Oabs ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
          & ( C @ ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__diff__less__iff) ).

thf(4113,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__idom )
     => ( ( ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
            & ( C @ ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
         => ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Oabs__class_Oabs ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Oabs__class_Oabs ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
            & ( C @ ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).

thf(372,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
        = ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
    <=> ( C = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).

thf(2564,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C = A )
       => ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
          = ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
      & ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
          = ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
       => ( C = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(1039,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__vector )
     => ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( A
          = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__le__zero__iff) ).

thf(4812,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__vector )
     => ( ( ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).

thf(92,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).

thf(1551,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(1094,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( c_Int_OPls @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__numeral__0__right) ).

thf(5003,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( c_Int_OPls @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).

thf(805,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less) ).

thf(4045,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).

thf(1017,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I33_J) ).

thf(4749,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).

thf(103,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Int_Onumber )
        & ( D @ class_Fields_Ofield__inverse__zero ) )
     => ( ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
          = A )
      <=> ( ( ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) )
              = ( D @ c_Groups_Ozero__class_Ozero ) )
           => ( A
              = ( D @ c_Groups_Ozero__class_Ozero ) ) )
          & ( ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) )
             != ( D @ c_Groups_Ozero__class_Ozero ) )
           => ( C
              = ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__eq__number__of1) ).

thf(1598,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Int_Onumber )
        & ( D @ class_Fields_Ofield__inverse__zero ) )
     => ( ( ( ( ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) )
                = ( D @ c_Groups_Ozero__class_Ozero ) )
             => ( A
                = ( D @ c_Groups_Ozero__class_Ozero ) ) )
            & ( ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) )
               != ( D @ c_Groups_Ozero__class_Ozero ) )
             => ( C
                = ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ) )
         => ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
            = A ) )
        & ( ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
            = A )
         => ( ( ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) )
                = ( D @ c_Groups_Ozero__class_Ozero ) )
             => ( A
                = ( D @ c_Groups_Ozero__class_Ozero ) ) )
            & ( ( ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) )
               != ( D @ c_Groups_Ozero__class_Ozero ) )
             => ( C
                = ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(1055,axiom,
    tc_RealDef_Oreal @ class_Rings_Ocomm__ring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).

thf(4864,plain,
    tc_RealDef_Oreal @ class_Rings_Ocomm__ring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).

thf(709,axiom,
    ! [A: $i] : ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__natceiling__ge) ).

thf(3754,plain,
    ! [A: $i] : ( A @ c_RComplete_Onatceiling @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).

thf(773,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oring__no__zero__divisors )
     => ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
          = ( C @ c_Groups_Ozero__class_Ozero ) )
      <=> ( ( A
            = ( C @ c_Groups_Ozero__class_Ozero ) )
          | ( B
            = ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).

thf(3949,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oring__no__zero__divisors )
     => ( ( ( ( A
              = ( C @ c_Groups_Ozero__class_Ozero ) )
            | ( B
              = ( C @ c_Groups_Ozero__class_Ozero ) ) )
         => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
            = ( C @ c_Groups_Ozero__class_Ozero ) ) )
        & ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
            = ( C @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A
              = ( C @ c_Groups_Ozero__class_Ozero ) )
            | ( B
              = ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).

thf(514,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Olinordered__ab__group__add )
     => ( ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
          = ( B @ c_Groups_Ozero__class_Ozero ) )
      <=> ( A
          = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).

thf(3058,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Olinordered__ab__group__add )
     => ( ( ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
            = ( B @ c_Groups_Ozero__class_Ozero ) ) )
        & ( ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
            = ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(465,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__commute) ).

thf(2888,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(1223,axiom,
    tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__1__strict,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).

thf(5452,plain,
    tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__1__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).

thf(149,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
        = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
    <=> ( ( A
          = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
        & ( B
          = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).

thf(1748,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A
            = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
          & ( B
            = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) )
       => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
          = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) )
      & ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
          = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
       => ( ( A
            = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
          & ( B
            = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(164,axiom,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
        | ( A
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).

thf(1798,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
        | ( A
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(614,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).

thf(3391,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B = A )
       => ( ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
          = ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) ) )
      & ( ( ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
          = ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(1171,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__commute) ).

thf(5250,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).

thf(936,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ c_Int_OBit1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit1__Bit0) ).

thf(4490,plain,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ c_Int_OBit1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).

thf(490,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).

thf(2977,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(316,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Oordered__semiring )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__mono) ).

thf(2375,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Oordered__semiring )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(869,axiom,
    tc_RealDef_Oreal @ class_Groups_Oone,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).

thf(4272,plain,
    tc_RealDef_Oreal @ class_Groups_Oone,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).

thf(898,axiom,
    c_Transcendental_Opi @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pi__ge__two) ).

thf(4366,plain,
    c_Transcendental_Opi @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).

thf(194,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__ring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).

thf(1941,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__ring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(1232,axiom,
    ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
    = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__2__eq__2) ).

thf(5484,plain,
    ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
    = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).

thf(635,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Osemiring__1 )
     => ( ( A @ ( B @ c_Int_Oiszero ) )
      <=> ( A
          = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__def) ).

thf(3462,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Osemiring__1 )
     => ( ( ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( A @ ( B @ c_Int_Oiszero ) ) )
        & ( ( A @ ( B @ c_Int_Oiszero ) )
         => ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(848,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ c_Int_OBit0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I10_J) ).

thf(4200,plain,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ c_Int_OBit0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).

thf(39,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__commute) ).

thf(1368,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(948,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__right__mono__neg) ).

thf(4517,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).

thf(562,axiom,
    tc_Nat_Onat @ class_Rings_Oordered__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).

thf(3228,plain,
    tc_Nat_Onat @ class_Rings_Oordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(930,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I17_J) ).

thf(4469,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).

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

thf(2821,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(1117,axiom,
    tc_RealDef_Oreal @ class_Fields_Olinordered__field,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).

thf(5079,plain,
    tc_RealDef_Oreal @ class_Fields_Olinordered__field,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).

thf(887,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).

thf(4324,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add )
     => ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).

thf(520,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__int__code_I13_J) ).

thf(3080,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(1175,axiom,
    tc_Complex_Ocomplex @ class_Groups_Omonoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).

thf(5262,plain,
    tc_Complex_Ocomplex @ class_Groups_Omonoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).

thf(1166,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__special_I1_J) ).

thf(5235,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).

thf(962,axiom,
    ! [A: $i,B: $i] :
      ( ( B != A )
    <=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
        | ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__neq__iff) ).

thf(4561,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
          | ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
       => ( B != A ) )
      & ( ( B != A )
       => ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
          | ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).

thf(656,axiom,
    tc_Int_Oint @ class_Groups_Oab__semigroup__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).

thf(3554,plain,
    tc_Int_Oint @ class_Groups_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(504,axiom,
    ! [A: $i] : ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ c_Transcendental_Ocos @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__le__one) ).

thf(3026,plain,
    ! [A: $i] : ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ c_Transcendental_Ocos @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(1144,axiom,
    c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pi__half__gt__zero) ).

thf(5154,plain,
    c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).

thf(734,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__linear) ).

thf(3828,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).

thf(715,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).

thf(3769,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).

thf(911,axiom,
    tc_RealDef_Oreal @ class_Rings_Oordered__cancel__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).

thf(4409,plain,
    tc_RealDef_Oreal @ class_Rings_Oordered__cancel__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).

thf(921,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ? [B: $i] :
          ( ( B @ c_Transcendental_Otan @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
          & ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
          & ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lemma__tan__total) ).

thf(4437,plain,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ? [B: $i] :
          ( ( B @ c_Transcendental_Otan @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
          & ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
          & ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).

thf(235,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__idom )
     => ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__sgn__abs) ).

thf(2092,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__idom )
     => ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(824,axiom,
    ! [A: $i] : ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ c_Transcendental_Oarctan @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arctan__ubound) ).

thf(4092,plain,
    ! [A: $i] : ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ c_Transcendental_Oarctan @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).

thf(56,axiom,
    ! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).

thf(1432,plain,
    ! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(732,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Olinordered__ab__group__add )
     => ( ( ( B @ c_Groups_Ozero__class_Ozero )
          = ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) )
      <=> ( A
          = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__zero__sym) ).

thf(3818,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Olinordered__ab__group__add )
     => ( ( ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( ( B @ c_Groups_Ozero__class_Ozero )
            = ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) ) )
        & ( ( ( B @ c_Groups_Ozero__class_Ozero )
            = ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) )
         => ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).

thf(751,axiom,
    tc_Int_Oint @ class_Groups_Oordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).

thf(3885,plain,
    tc_Int_Oint @ class_Groups_Oordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).

thf(20,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__0 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).

thf(1300,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__0 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(63,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).

thf(1452,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(531,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).

thf(3114,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(573,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
          | ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__divide__iff) ).

thf(3273,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
              & ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
            | ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
              & ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
         => ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
              & ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
            | ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
              & ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(592,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Omonoid__mult )
     => ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__right) ).

thf(3334,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Omonoid__mult )
     => ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(699,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).

thf(3722,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).

thf(793,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add )
     => ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__minus__iff) ).

thf(4020,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add )
     => ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).

thf(1183,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__numeral__1__right) ).

thf(5309,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).

thf(152,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oring )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__mult__right) ).

thf(1763,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oring )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(536,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__idom )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__less) ).

thf(3127,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__idom )
     => ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(87,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__0 )
     => ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__poly__add__left) ).

thf(1538,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__0 )
     => ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(470,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).

thf(2903,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(1028,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
      | ( B = A )
      | ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__linear) ).

thf(4781,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
      | ( B = A )
      | ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).

thf(602,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).

thf(3359,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(525,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Olinordered__semiring__strict )
     => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
             => ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).

thf(3095,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Olinordered__semiring__strict )
     => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
             => ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(1129,axiom,
    tc_RealDef_Oreal @ class_Rings_Ono__zero__divisors,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).

thf(5106,plain,
    tc_RealDef_Oreal @ class_Rings_Ono__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).

thf(1187,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ class_Rings_Oordered__ring )
     => ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( A @ ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__iff1) ).

thf(5319,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ class_Rings_Oordered__ring )
     => ( ( ( A @ ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).

thf(318,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonpos__pos) ).

thf(2379,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(860,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__leI) ).

thf(4246,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).

thf(489,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__div__pos__less) ).

thf(2975,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(775,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Int_Onumber__ring )
        & ( B @ class_Fields_Ofield__inverse__zero ) )
     => ( ( c_Int_OPls @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__Numeral0) ).

thf(3961,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Int_Onumber__ring )
        & ( B @ class_Fields_Ofield__inverse__zero ) )
     => ( ( c_Int_OPls @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).

thf(283,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).

thf(2266,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(1040,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__int__code_I15_J) ).

thf(4819,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).

thf(191,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).

thf(1934,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(482,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add__diff) ).

thf(2948,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( C @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(89,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Odiff) ).

thf(1543,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(153,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).

thf(1766,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(778,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_RealVector_Oreal__normed__field )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide_Odiff) ).

thf(3970,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_RealVector_Oreal__normed__field )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).

thf(239,axiom,
    tc_Int_Oint @ class_Rings_Ocomm__ring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).

thf(2113,plain,
    tc_Int_Oint @ class_Rings_Ocomm__ring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(534,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__nonneg__neg) ).

thf(3124,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(86,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__ab__semigroup__add )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__mono) ).

thf(1536,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__ab__semigroup__add )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(204,axiom,
    v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rp) ).

thf(1981,plain,
    v_r @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(290,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_RealVector_Oreal__normed__vector )
     => ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( D @ c_RealVector_Onorm__class_Onorm ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B
            = ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__ratiotest__lemma) ).

thf(2279,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_RealVector_Oreal__normed__vector )
     => ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( D @ c_RealVector_Onorm__class_Onorm ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B
            = ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(944,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__neg__pos) ).

thf(4510,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).

thf(202,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).

thf(1972,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(413,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oab__semigroup__mult )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).

thf(2711,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oab__semigroup__mult )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(830,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Odivision__ring )
     => ( ( B
         != ( C @ c_Groups_Ozero__class_Ozero ) )
       => ( ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
          = ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__minus__divide__right) ).

thf(4106,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Odivision__ring )
     => ( ( B
         != ( C @ c_Groups_Ozero__class_Ozero ) )
       => ( ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
          = ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).

thf(1224,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono2) ).

thf(5453,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).

thf(560,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
          = ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__eq__less) ).

thf(3224,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
          = ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(54,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Fields_Olinordered__field )
     => ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
             => ( B @ ( C @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_frac__less) ).

thf(1427,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Fields_Olinordered__field )
     => ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
             => ( B @ ( C @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(612,axiom,
    ! [A: $i] :
      ( ( A @ class_Groups_Ocomm__monoid__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).

thf(3388,plain,
    ! [A: $i] :
      ( ( A @ class_Groups_Ocomm__monoid__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(920,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I16_J) ).

thf(4431,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).

thf(100,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( B @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
          = ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__pos) ).

thf(1585,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( B @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
          = ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(359,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).

thf(2511,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(983,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__ring__1 )
     => ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).

thf(4634,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__ring__1 )
     => ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).

thf(532,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
          = ( B @ c_Groups_Ozero__class_Ozero ) )
      <=> ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Int_Oiszero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__special_I3_J) ).

thf(3117,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Int_Oiszero ) )
         => ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
            = ( B @ c_Groups_Ozero__class_Ozero ) ) )
        & ( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
            = ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Int_Oiszero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(417,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__ring__strict )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
          | ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).

thf(2722,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__ring__strict )
     => ( ( ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
              & ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
            | ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
              & ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
              & ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
            | ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
              & ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(893,axiom,
    tc_RealDef_Oreal @ class_Rings_Olinordered__comm__semiring__strict,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).

thf(4342,plain,
    tc_RealDef_Oreal @ class_Rings_Olinordered__comm__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).

thf(136,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oabs__if ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oabs__if) ).

thf(1717,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oabs__if ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(218,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ class_Rings_Olinordered__semiring__1 )
     => ( ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
             => ( ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
                  = ( F @ c_Groups_Oone__class_Oone ) )
               => ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_convex__bound__le) ).

thf(2030,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ class_Rings_Olinordered__semiring__1 )
     => ( ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
             => ( ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
                  = ( F @ c_Groups_Oone__class_Oone ) )
               => ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(440,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( B @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).

thf(2807,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( C @ c_Groups_Oone__class_Oone @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( B @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(10,axiom,
    tc_Nat_Onat @ class_Groups_Ocancel__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).

thf(1272,plain,
    tc_Nat_Onat @ class_Groups_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(544,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).

thf(3156,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(763,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
     => ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).

thf(3914,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
     => ( ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).

thf(379,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).

thf(2584,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(995,axiom,
    ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) )
   != ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pi__half__neq__two) ).

thf(4671,plain,
    ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) )
   != ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).

thf(854,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( ( B = A )
        | ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__real__def) ).

thf(4217,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B = A )
          | ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
       => ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( B = A )
          | ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).

thf(104,axiom,
    tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add__imp__le,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).

thf(1617,plain,
    tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add__imp__le,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(475,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
        = B )
     => ( A
        = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).

thf(2924,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
        = B )
     => ( A
        = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(711,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__semidom )
     => ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__add__one) ).

thf(3757,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__semidom )
     => ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).

thf(524,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__antisym) ).

thf(3092,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( B @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(516,axiom,
    ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
   != ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0__neq__1) ).

thf(3067,plain,
    ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
   != ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(128,axiom,
    tc_Nat_Onat @ class_Groups_Oab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).

thf(1685,plain,
    tc_Nat_Onat @ class_Groups_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(1205,axiom,
    tc_RealDef_Oreal @ class_Rings_Oidom,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).

thf(5386,plain,
    tc_RealDef_Oreal @ class_Rings_Oidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).

thf(83,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__ring__strict )
     => ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
            & ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
          | ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
            & ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).

thf(1517,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__ring__strict )
     => ( ( ( ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
              & ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
            | ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
              & ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) )
         => ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
              & ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
            | ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
              & ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(846,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
               => ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
              & ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
               => ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
          & ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__divide__eq) ).

thf(4185,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
                & ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
            & ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) )
         => ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
                & ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) )
            & ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).

thf(270,axiom,
    tc_Nat_Onat @ class_Rings_Ocomm__semiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).

thf(2226,plain,
    tc_Nat_Onat @ class_Rings_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(1012,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__D2) ).

thf(4730,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).

thf(667,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__ring__strict )
     => ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
            & ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
          | ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
            & ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).

thf(3593,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__ring__strict )
     => ( ( ( ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
              & ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
            | ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
              & ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) )
         => ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
              & ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
            | ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
              & ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(336,axiom,
    tc_Int_Oint @ class_Groups_Ozero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).

thf(2435,plain,
    tc_Int_Oint @ class_Groups_Ozero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(575,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__numeral__code_I9_J) ).

thf(3284,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(429,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Olinordered__semiring__strict )
     => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
             => ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__strict__mono) ).

thf(2760,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Olinordered__semiring__strict )
     => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
             => ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(626,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).

thf(3433,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(772,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Ocancel__semigroup__add )
     => ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
          = ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).

thf(3946,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Ocancel__semigroup__add )
     => ( ( ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
          = ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).

thf(539,axiom,
    tc_Int_Oint @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).

thf(3139,plain,
    tc_Int_Oint @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(987,axiom,
    ! [A: $i] :
      ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bin__less__0__simps_I3_J) ).

thf(4651,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).

thf(918,axiom,
    tc_Complex_Ocomplex @ class_Fields_Ofield,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).

thf(4424,plain,
    tc_Complex_Ocomplex @ class_Fields_Ofield,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).

thf(838,axiom,
    ! [A: $i] :
      ( ( A @ c_Int_OBit1 )
     != c_Int_OPls ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I46_J) ).

thf(4138,plain,
    ! [A: $i] :
      ( ( A @ c_Int_OBit1 )
     != c_Int_OPls ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).

thf(459,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Ofield__inverse__zero )
     => ( ( C
         != ( D @ c_Groups_Ozero__class_Ozero ) )
       => ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
          = ( C @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__num__frac) ).

thf(2870,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Ofield__inverse__zero )
     => ( ( C
         != ( D @ c_Groups_Ozero__class_Ozero ) )
       => ( ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
          = ( C @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(448,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Int_Oring__char__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).

thf(2828,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Int_Oring__char__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(304,axiom,
    tc_Int_Oint @ class_Rings_Osemiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).

thf(2347,plain,
    tc_Int_Oint @ class_Rings_Osemiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(116,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
        = ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
     => ( ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
        = ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__zmult__eq__1) ).

thf(1654,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
        = ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
     => ( ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
        = ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(51,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__comm__monoid__add )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).

thf(1412,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__comm__monoid__add )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(828,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ class_RealVector_Oreal__normed__field )
        & ( C @ class_Fields_Ofield__inverse__zero ) )
     => ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) )
        = ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__divide) ).

thf(4102,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ class_RealVector_Oreal__normed__field )
        & ( C @ class_Fields_Ofield__inverse__zero ) )
     => ( ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) )
        = ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).

thf(598,axiom,
    c_Int_OPls @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I19_J) ).

thf(3346,plain,
    c_Int_OPls @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(238,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oab__group__add )
     => ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__left__minus) ).

thf(2110,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oab__group__add )
     => ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(587,axiom,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__1) ).

thf(3320,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(49,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Int_Onumber )
        & ( D @ class_Fields_Ofield__inverse__zero ) )
     => ( ( ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
          = ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) ) )
      <=> ( ( ( B
              = ( D @ c_Groups_Ozero__class_Ozero ) )
           => ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) )
              = ( D @ c_Groups_Ozero__class_Ozero ) ) )
          & ( ( B
             != ( D @ c_Groups_Ozero__class_Ozero ) )
           => ( C
              = ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__eq__eq__number__of) ).

thf(1390,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Int_Onumber )
        & ( D @ class_Fields_Ofield__inverse__zero ) )
     => ( ( ( ( ( B
                = ( D @ c_Groups_Ozero__class_Ozero ) )
             => ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) )
                = ( D @ c_Groups_Ozero__class_Ozero ) ) )
            & ( ( B
               != ( D @ c_Groups_Ozero__class_Ozero ) )
             => ( C
                = ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ) )
         => ( ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
            = ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) ) ) )
        & ( ( ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
            = ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) ) )
         => ( ( ( B
                = ( D @ c_Groups_Ozero__class_Ozero ) )
             => ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) )
                = ( D @ c_Groups_Ozero__class_Ozero ) ) )
            & ( ( B
               != ( D @ c_Groups_Ozero__class_Ozero ) )
             => ( C
                = ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(1137,axiom,
    ! [A: $i] :
      ( ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
      = ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ c_Int_OBit0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Bit0) ).

thf(5124,plain,
    ! [A: $i] :
      ( ( A @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
      = ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ c_Int_OBit0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).

thf(1207,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
        & ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__nat__number__of) ).

thf(5389,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
          & ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
           => ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) )
       => ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
          & ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
           => ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).

thf(228,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).

thf(2071,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(403,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).

thf(2658,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(768,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__trans) ).

thf(3929,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).

thf(143,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__idom )
     => ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
        = ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__sgn) ).

thf(1734,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__idom )
     => ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
        = ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(882,axiom,
    tc_RealDef_Oreal @ class_Rings_Ozero__neq__one,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).

thf(4310,plain,
    tc_RealDef_Oreal @ class_Rings_Ozero__neq__one,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).

thf(287,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__semidom )
     => ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__one) ).

thf(2273,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__semidom )
     => ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(640,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
       != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
     => ( ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
          = ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__left__cancel) ).

thf(3484,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
       != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
     => ( ( ( B = A )
         => ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
            = ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) ) )
        & ( ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
            = ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(999,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__0 )
     => ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__add) ).

thf(4683,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__0 )
     => ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).

thf(1217,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ c_Int_OBit0 )
        = ( A @ c_Int_OBit0 ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I48_J) ).

thf(5426,plain,
    ! [A: $i,B: $i] :
      ( ( ( B = A )
       => ( ( B @ c_Int_OBit0 )
          = ( A @ c_Int_OBit0 ) ) )
      & ( ( ( B @ c_Int_OBit0 )
          = ( A @ c_Int_OBit0 ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).

thf(1032,axiom,
    c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pi__half__less__two) ).

thf(4791,plain,
    c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).

thf(147,axiom,
    tc_Int_Oint @ class_Groups_Ocancel__comm__monoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).

thf(1745,plain,
    tc_Int_Oint @ class_Groups_Ocancel__comm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(891,axiom,
    c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pi__less__4) ).

thf(4338,plain,
    c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).

thf(334,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).

thf(2431,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(244,axiom,
    ! [A: $i] :
      ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( A
        = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__le__zero__cancel__iff) ).

thf(2130,plain,
    ! [A: $i] :
      ( ( ( A
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
       => ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(604,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Oordered__ring )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).

thf(3368,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Oordered__ring )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(925,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Oabs__class_Oabs ) )
        = ( A @ ( B @ c_Groups_Oabs__class_Oabs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__idempotent) ).

thf(4451,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Oabs__class_Oabs ) )
        = ( A @ ( B @ c_Groups_Oabs__class_Oabs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).

thf(1174,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl2) ).

thf(5258,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).

thf(102,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
        | ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__gr__0) ).

thf(1590,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
          | ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
          | ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(1185,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_RealVector_Oreal__normed__algebra__1 )
        & ( B @ class_Int_Onumber__ring ) )
     => ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_RealVector_Onorm__class_Onorm ) )
        = ( A @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__number__of) ).

thf(5315,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_RealVector_Oreal__normed__algebra__1 )
        & ( B @ class_Int_Onumber__ring ) )
     => ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_RealVector_Onorm__class_Onorm ) )
        = ( A @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).

thf(338,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__comm__monoid__add )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).

thf(2443,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__comm__monoid__add )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(671,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
        = ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__inject) ).

thf(3613,plain,
    ! [A: $i,B: $i] :
      ( ( ( B = A )
       => ( ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
          = ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) ) ) )
      & ( ( ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
          = ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(1,conjecture,
    c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( v_wa____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( v_wa____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(1253,plain,
    ~ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( v_s____ @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( v_z____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( v_wa____ @ ( v_p @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(1070,axiom,
    tc_RealDef_Oreal @ class_Rings_Oring__1__no__zero__divisors,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).

thf(4913,plain,
    tc_RealDef_Oreal @ class_Rings_Oring__1__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).

thf(254,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__zminus) ).

thf(2174,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(1038,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I15_J) ).

thf(4806,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).

thf(724,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ogroup__add )
     => ( ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
          = ( B @ c_Groups_Ozero__class_Ozero ) )
      <=> ( A
          = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).

thf(3789,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ogroup__add )
     => ( ( ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
            = ( B @ c_Groups_Ozero__class_Ozero ) ) )
        & ( ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
            = ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).

thf(456,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Rings_Olinordered__idom )
        & ( B @ class_Int_Onumber__ring ) )
     => ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__special_I1_J) ).

thf(2855,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Rings_Olinordered__idom )
        & ( B @ class_Int_Onumber__ring ) )
     => ( ( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(112,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).

thf(1639,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(455,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ c_Transcendental_Oarctan @ ( B @ c_Transcendental_Oarctan @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arctan__monotone_H) ).

thf(2853,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ c_Transcendental_Oarctan @ ( B @ c_Transcendental_Oarctan @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(292,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Fields_Ofield )
     => ( ( D
         != ( E @ c_Groups_Ozero__class_Ozero ) )
       => ( ( C
           != ( E @ c_Groups_Ozero__class_Ozero ) )
         => ( ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
            = ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__frac__eq) ).

thf(2290,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Fields_Ofield )
     => ( ( D
         != ( E @ c_Groups_Ozero__class_Ozero ) )
       => ( ( C
           != ( E @ c_Groups_Ozero__class_Ozero ) )
         => ( ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
            = ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(733,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( B @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
        = ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__diff__le) ).

thf(3825,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( B @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
        = ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).

thf(180,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__le__self) ).

thf(1903,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(993,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__2) ).

thf(4666,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).

thf(1096,axiom,
    ( ( c_Int_OPls @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
    = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__Pls) ).

thf(5008,plain,
    ( ( c_Int_OPls @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
    = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).

thf(823,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
        = ( B @ ( A @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__commute) ).

thf(4089,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
        = ( B @ ( A @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).

thf(1204,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Int_Onumber__ring )
        & ( B @ class_Fields_Olinordered__field__inverse__zero ) )
     => ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_half__gt__zero__iff) ).

thf(5382,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Int_Onumber__ring )
        & ( B @ class_Fields_Olinordered__field__inverse__zero ) )
     => ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).

thf(446,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__leI) ).

thf(2823,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(803,axiom,
    tc_RealDef_Oreal @ class_Rings_Oordered__ring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).

thf(4042,plain,
    tc_RealDef_Oreal @ class_Rings_Oordered__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).

thf(956,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Int_Onumber__ring )
     => ( ( A @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__number__of__mult) ).

thf(4542,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Int_Onumber__ring )
     => ( ( A @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).

thf(1163,axiom,
    ! [A: $i] :
      ( c_Int_OPls
     != ( A @ c_Int_OBit1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I39_J) ).

thf(5228,plain,
    ! [A: $i] :
      ( c_Int_OPls
     != ( A @ c_Int_OBit1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).

thf(676,axiom,
    tc_Nat_Onat @ class_Rings_Osemiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).

thf(3630,plain,
    tc_Nat_Onat @ class_Rings_Osemiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).

thf(497,axiom,
    tc_Int_Oint @ class_Groups_Oone,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).

thf(3003,plain,
    tc_Int_Oint @ class_Groups_Oone,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(169,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rabs__ratiotest__lemma) ).

thf(1822,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(1097,axiom,
    ! [A: $i] :
    ? [B: $i] :
      ( ! [C: $i] :
          ( ( ( ( C @ c_Transcendental_Otan )
              = A )
            & ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
            & ( C @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
         => ( C = B ) )
      & ( ( B @ c_Transcendental_Otan )
        = A )
      & ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
      & ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tan__total) ).

thf(5010,plain,
    ! [A: $i] :
    ? [B: $i] :
      ( ! [C: $i] :
          ( ( ( ( C @ c_Transcendental_Otan )
              = A )
            & ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
            & ( C @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
         => ( C = B ) )
      & ( ( B @ c_Transcendental_Otan )
        = A )
      & ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
      & ( B @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).

thf(431,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
          = ( C @ c_Groups_Ozero__class_Ozero ) )
      <=> ( A
          = ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__eq__0__iff) ).

thf(2764,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( ( A
            = ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
         => ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
            = ( C @ c_Groups_Ozero__class_Ozero ) ) )
        & ( ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
            = ( C @ c_Groups_Ozero__class_Ozero ) )
         => ( A
            = ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(569,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ocomm__monoid__mult )
     => ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).

thf(3252,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ocomm__monoid__mult )
     => ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(1240,axiom,
    v_d____ @ ( v_z____ @ ( v_wa____ @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_w) ).

thf(5505,plain,
    v_d____ @ ( v_z____ @ ( v_wa____ @ ( tc_Complex_Ocomplex @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240]) ).

thf(684,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
            = ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) )
        <=> ( B = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__diff__iff) ).

thf(3662,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( ( B = A )
           => ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
              = ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) )
          & ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
              = ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) )
           => ( B = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).

thf(363,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( A @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
               => ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
              & ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
               => ( C @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
          & ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__le__eq) ).

thf(2526,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
                & ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( C @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
            & ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
         => ( A @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
                & ( ( D @ c_Groups_Ozero__class_Ozero @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( C @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
            & ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(1068,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( ( B != A )
        & ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__less__def) ).

thf(4900,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B != A )
          & ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
       => ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( B != A )
          & ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).

thf(478,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Int_Onumber__ring )
     => ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__mult) ).

thf(2934,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Int_Onumber__ring )
     => ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(231,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ocomm__monoid__add )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).

thf(2081,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ocomm__monoid__add )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(847,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ c_RComplete_Onatceiling )
      = ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_natceiling__number__of__eq) ).

thf(4197,plain,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ c_RComplete_Onatceiling )
      = ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).

thf(1210,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
      = ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__commute) ).

thf(5408,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
      = ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).

thf(625,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).

thf(3430,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(645,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring__1__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).

thf(3529,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring__1__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(258,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Opi @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ c_Transcendental_Otan )
      = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tan__npi) ).

thf(2183,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Opi @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ c_Transcendental_Otan )
      = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(1143,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ c_Int_OBit1 )
        = ( A @ c_Int_OBit1 ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I51_J) ).

thf(5144,plain,
    ! [A: $i,B: $i] :
      ( ( ( B = A )
       => ( ( B @ c_Int_OBit1 )
          = ( A @ c_Int_OBit1 ) ) )
      & ( ( ( B @ c_Int_OBit1 )
          = ( A @ c_Int_OBit1 ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).

thf(1135,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__0 )
     => ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__mult) ).

thf(5119,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__0 )
     => ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).

thf(1058,axiom,
    c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pi__gt__zero) ).

thf(4869,plain,
    c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).

thf(320,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Olinordered__ab__group__add )
     => ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).

thf(2384,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Olinordered__ab__group__add )
     => ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(348,axiom,
    tc_Nat_Onat @ class_Groups_Omonoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).

thf(2475,plain,
    tc_Nat_Onat @ class_Groups_Omonoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(435,axiom,
    tc_Int_Oint @ class_Int_Onumber,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber) ).

thf(2786,plain,
    tc_Int_Oint @ class_Int_Onumber,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(972,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oab__group__add )
     => ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ab__diff__minus) ).

thf(4602,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oab__group__add )
     => ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).

thf(473,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add )
     => ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__minus__iff) ).

thf(2912,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add )
     => ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(886,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arith__simps_I30_J) ).

thf(4321,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).

thf(18,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
     => ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).

thf(1294,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
     => ( ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(1132,axiom,
    tc_Complex_Ocomplex @ class_Groups_Ocancel__comm__monoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add) ).

thf(5109,plain,
    tc_Complex_Ocomplex @ class_Groups_Ocancel__comm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).

thf(343,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__comm__semiring__strict )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).

thf(2462,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__comm__semiring__strict )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(22,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Omult__zero )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__zero__right) ).

thf(1308,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Omult__zero )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(757,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oadd__left) ).

thf(3896,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).

thf(261,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__lessD) ).

thf(2198,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(375,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__SucI) ).

thf(2576,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(932,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__0__less__add__iff) ).

thf(4478,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).

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

thf(2066,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
     => ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(236,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Int_Onumber )
        & ( D @ class_Fields_Olinordered__field__inverse__zero ) )
     => ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( ( ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
               => ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
              & ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
               => ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
          & ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__divide__eq__number__of1) ).

thf(2095,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Int_Onumber )
        & ( D @ class_Fields_Olinordered__field__inverse__zero ) )
     => ( ( ( ( ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
                & ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
            & ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
         => ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( ~ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( ~ ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( D @ c_Groups_Ozero__class_Ozero @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
                & ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
                 => ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) )
            & ( ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
             => ( B @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(818,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( C @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__less__mono) ).

thf(4074,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( C @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).

thf(422,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__idom )
     => ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__mult__self) ).

thf(2739,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__idom )
     => ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(355,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq2) ).

thf(2494,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(61,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__add1) ).

thf(1444,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(1153,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__half__sum) ).

thf(5196,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).

thf(60,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Olinordered__semiring__strict )
     => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
             => ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).

thf(1442,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Olinordered__semiring__strict )
     => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( D @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless ) ) )
             => ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(655,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( B @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__strict__left__mono__neg) ).

thf(3552,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( B @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(1072,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__vector )
     => ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) )
        = ( B @ ( A @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__minus__commute) ).

thf(4927,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__vector )
     => ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) )
        = ( B @ ( A @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_RealVector_Onorm__class_Onorm ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).

thf(795,axiom,
    tc_RealDef_Oreal @ class_Groups_Oabs__if,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oabs__if) ).

thf(4025,plain,
    tc_RealDef_Oreal @ class_Groups_Oabs__if,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).

thf(215,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__le__iff) ).

thf(2019,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(975,axiom,
    ! [A: $i] :
      ( ( ( A @ class_Int_Onumber__ring )
        & ( A @ class_Fields_Olinordered__field__inverse__zero ) )
     => ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_half) ).

thf(4619,plain,
    ! [A: $i] :
      ( ( ( A @ class_Int_Onumber__ring )
        & ( A @ class_Fields_Olinordered__field__inverse__zero ) )
     => ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( A @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).

thf(609,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oab__group__add )
     => ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add__distrib) ).

thf(3379,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oab__group__add )
     => ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(1061,axiom,
    ! [A: $i] : ( v_r @ ( A @ v_g____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_g_I1_J) ).

thf(4880,plain,
    ! [A: $i] : ( v_r @ ( A @ v_g____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).

thf(113,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
          | ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__le__0__iff) ).

thf(1642,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
              & ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
            | ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
              & ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
              & ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
            | ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
              & ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(157,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__0 )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__semigroup__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).

thf(1774,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__0 )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__semigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(140,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
     => ( ( B
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
        | ( A
          = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).

thf(1725,plain,
    ! [A: $i,B: $i] :
      ( ( B
        = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ) )
     => ( ( B
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
        | ( A
          = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(564,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
     => ( ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
          = ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) )
      <=> ( ( C = A )
          | ( D = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_crossproduct__eq) ).

thf(3232,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
     => ( ( ( ( C = A )
            | ( D = B ) )
         => ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
            = ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) )
        & ( ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
            = ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) )
         => ( ( C = A )
            | ( D = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(704,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

thf(3733,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).

thf(969,axiom,
    c_Transcendental_Opi @ ( c_Transcendental_Opi @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_m2pi__less__pi) ).

thf(4596,plain,
    c_Transcendental_Opi @ ( c_Transcendental_Opi @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).

thf(90,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).

thf(1546,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(528,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
        = ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).

thf(3100,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
        = ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(951,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Int_Onumber__ring )
     => ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__diff) ).

thf(4523,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Int_Onumber__ring )
     => ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).

thf(643,axiom,
    ! [A: $i,B: $i] :
      ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).

thf(3521,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(896,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__vector )
     => ( ( ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) )
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
      <=> ( A
          = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__eq__zero) ).

thf(4357,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__vector )
     => ( ( ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) )
            = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
        & ( ( ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) )
            = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
         => ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).

thf(197,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__right__mono) ).

thf(1957,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(1001,axiom,
    ! [A: $i,B: $i] : ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complex__mod__triangle__sub) ).

thf(4687,plain,
    ! [A: $i,B: $i] : ( A @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).

thf(744,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Int_Onumber__ring )
     => ( ( ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) )
          = ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
      <=> ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Int_Oiszero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of__eq) ).

thf(3860,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Int_Onumber__ring )
     => ( ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Int_Oiszero ) )
         => ( ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) )
            = ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) ) )
        & ( ( ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) )
            = ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
         => ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_Int_Oiszero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).

thf(125,axiom,
    ! [A: $i] :
      ( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
      = c_Int_OPls ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Pls) ).

thf(1678,plain,
    ! [A: $i] :
      ( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
      = c_Int_OPls ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(723,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Olinordered__ab__group__add )
     => ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).

thf(3785,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Olinordered__ab__group__add )
     => ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( A @ ( B @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).

thf(642,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oidom )
     => ( ( ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
          = ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) )
      <=> ( ( B
            = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
          | ( B = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_square__eq__iff) ).

thf(3511,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oidom )
     => ( ( ( ( B
              = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
            | ( B = A ) )
         => ( ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
            = ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) )
        & ( ( ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
            = ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) )
         => ( ( B
              = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
            | ( B = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(578,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oordered__ring )
     => ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
          | ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
       => ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).

thf(3291,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oordered__ring )
     => ( ( ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
          | ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
       => ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(786,axiom,
    tc_RealDef_Oreal @ class_Rings_Ocomm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).

thf(3997,plain,
    tc_RealDef_Oreal @ class_Rings_Ocomm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).

thf(493,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__mono1) ).

thf(2983,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(416,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__idom )
     => ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Osgn__class_Osgn ) )
        = ( A @ ( B @ c_Groups_Osgn__class_Osgn ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__sgn) ).

thf(2719,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__idom )
     => ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Osgn__class_Osgn ) )
        = ( A @ ( B @ c_Groups_Osgn__class_Osgn ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(1178,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
          & ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__le__iff) ).

thf(5268,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).

thf(668,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).

thf(3601,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).

thf(750,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).

thf(3882,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).

thf(1164,axiom,
    tc_Complex_Ocomplex @ class_Rings_Osemiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__1) ).

thf(5232,plain,
    tc_Complex_Ocomplex @ class_Rings_Osemiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).

thf(607,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
        <=> ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__divide__le__eq) ).

thf(3373,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
          & ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(385,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oab__group__add )
     => ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__poly__code_I2_J) ).

thf(2604,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oab__group__add )
     => ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(420,axiom,
    ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_Transcendental_Ocos )
    = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__zero) ).

thf(2736,plain,
    ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_Transcendental_Ocos )
    = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(212,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__trans__Suc) ).

thf(2008,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(1047,axiom,
    tc_RealDef_Oreal @ class_Rings_Odivision__ring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).

thf(4841,plain,
    tc_RealDef_Oreal @ class_Rings_Odivision__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).

thf(593,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Omonoid__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).

thf(3337,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(123,axiom,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc )
      = ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).

thf(1673,plain,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc )
      = ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(538,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).

thf(3132,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( ( A = B )
         => ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( B @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(1246,axiom,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__field,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__field) ).

thf(5527,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__field,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246]) ).

thf(1064,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__less__iff1) ).

thf(4885,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).

thf(72,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__div__algebra )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Osgn__class_Osgn ) )
        = ( A @ ( C @ c_Groups_Osgn__class_Osgn ) @ ( B @ ( C @ c_Groups_Osgn__class_Osgn ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__mult) ).

thf(1480,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__div__algebra )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Osgn__class_Osgn ) )
        = ( A @ ( C @ c_Groups_Osgn__class_Osgn ) @ ( B @ ( C @ c_Groups_Osgn__class_Osgn ) @ ( C @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(970,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__numeral__1) ).

thf(4597,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).

thf(1170,axiom,
    ! [A: $i] :
      ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
        | ( A
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__2__cases) ).

thf(5247,plain,
    ! [A: $i] :
      ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
        | ( A
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).

thf(1208,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__pos__pos) ).

thf(5398,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).

thf(899,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__assoc) ).

thf(4367,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).

thf(636,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).

thf(3469,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(547,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__ring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Onumber) ).

thf(3164,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__ring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(1182,axiom,
    ! [A: $i] :
      ( ( ( A @ c_Transcendental_Oarctan @ c_Transcendental_Otan )
        = A )
      & ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ c_Transcendental_Oarctan @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
      & ( A @ c_Transcendental_Oarctan @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arctan) ).

thf(5300,plain,
    ! [A: $i] :
      ( ( ( A @ c_Transcendental_Oarctan @ c_Transcendental_Otan )
        = A )
      & ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ c_Transcendental_Oarctan @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
      & ( A @ c_Transcendental_Oarctan @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).

thf(425,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).

thf(2746,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(332,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( ( B = A )
        | ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).

thf(2417,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B = A )
          | ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( B = A )
          | ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(414,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
     != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__nonzero) ).

thf(2714,plain,
    ! [A: $i] :
      ( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
     != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(509,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Oordered__semiring )
     => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
             => ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__mono) ).

thf(3045,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Oordered__semiring )
     => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( C @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( ( B @ ( E @ c_Groups_Ozero__class_Ozero @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) )
             => ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(781,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
        = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_expand__Suc) ).

thf(3982,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) )
        = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ c_Nat_OSuc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).

thf(395,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ c_Int_OBit0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Bit0__Bit0) ).

thf(2636,plain,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ c_Int_OBit0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(58,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ogroup__add )
     => ( ( A @ ( A @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self) ).

thf(1436,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ogroup__add )
     => ( ( A @ ( A @ ( B @ c_Groups_Ominus__class_Ominus ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(840,axiom,
    ! [A: $i] :
      ( ( ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
          = A ) )
      & ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
          = ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__real__def) ).

thf(4146,plain,
    ! [A: $i] :
      ( ( ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
          = A ) )
      & ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
          = ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).

thf(878,axiom,
    ! [A: $i] : ( A @ c_Transcendental_Oarctan @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arctan__lbound) ).

thf(4303,plain,
    ! [A: $i] : ( A @ c_Transcendental_Oarctan @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).

thf(808,axiom,
    tc_RealDef_Oreal @ class_Groups_Ocomm__monoid__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).

thf(4051,plain,
    tc_RealDef_Oreal @ class_Groups_Ocomm__monoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).

thf(1146,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Rings_Olinordered__idom )
        & ( B @ class_Int_Onumber__ring ) )
     => ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I2_J) ).

thf(5159,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Rings_Olinordered__idom )
        & ( B @ class_Int_Onumber__ring ) )
     => ( ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).

thf(77,axiom,
    ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
    = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__1) ).

thf(1495,plain,
    ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
    = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(1018,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add__abs )
     => ( B @ ( A @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__triangle__ineq2__sym) ).

thf(4755,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add__abs )
     => ( B @ ( A @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).

thf(1089,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add )
     => ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).

thf(4981,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add )
     => ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).

thf(117,axiom,
    ! [A: $i] :
      ( ( A @ c_Int_OBit0 )
      = ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__def) ).

thf(1657,plain,
    ! [A: $i] :
      ( ( A @ c_Int_OBit0 )
      = ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

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

thf(5092,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
           => ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
          & ( ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
           => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).

thf(599,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Odivision__ring )
     => ( ( B
         != ( C @ c_Groups_Ozero__class_Ozero ) )
       => ( ( ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide ) ) )
            = ( C @ c_Groups_Oone__class_Oone ) )
        <=> ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_right__inverse__eq) ).

thf(3347,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Odivision__ring )
     => ( ( B
         != ( C @ c_Groups_Ozero__class_Ozero ) )
       => ( ( ( A = B )
           => ( ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide ) ) )
              = ( C @ c_Groups_Oone__class_Oone ) ) )
          & ( ( ( B @ ( A @ ( C @ c_Rings_Oinverse__class_Odivide ) ) )
              = ( C @ c_Groups_Oone__class_Oone ) )
           => ( A = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(875,axiom,
    ! [A: $i] :
      ( ( c_Int_OPls
        = ( A @ c_Int_OBit0 ) )
    <=> ( c_Int_OPls = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I38_J) ).

thf(4286,plain,
    ! [A: $i] :
      ( ( ( c_Int_OPls = A )
       => ( c_Int_OPls
          = ( A @ c_Int_OBit0 ) ) )
      & ( ( c_Int_OPls
          = ( A @ c_Int_OBit0 ) )
       => ( c_Int_OPls = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).

thf(259,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
     => ( ( ( B != A )
          & ( D != C ) )
      <=> ( ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
         != ( B @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).

thf(2186,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct )
     => ( ( ( ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
           != ( B @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) )
         => ( ( B != A )
            & ( D != C ) ) )
        & ( ( ( B != A )
            & ( D != C ) )
         => ( ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
           != ( B @ ( C @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(872,axiom,
    tc_RealDef_Oreal @ class_Groups_Olinordered__ab__group__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).

thf(4281,plain,
    tc_RealDef_Oreal @ class_Groups_Olinordered__ab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).

thf(982,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
        = ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__of__nat__diff) ).

thf(4631,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_RealDef_Oreal ) )
        = ( B @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( A @ ( tc_Nat_Onat @ c_RealDef_Oreal ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).

thf(551,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oab__group__add )
     => ( ( B = A )
      <=> ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
          = ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).

thf(3177,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oab__group__add )
     => ( ( ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
            = ( C @ c_Groups_Ozero__class_Ozero ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
            = ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(1098,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
          = ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__nonpos) ).

thf(5019,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
          = ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).

thf(822,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__bin__lemma) ).

thf(4083,plain,
    ! [A: $i,B: $i] :
      ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).

thf(794,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__field,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__field) ).

thf(4024,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__field,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).

thf(373,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Oidom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Ono__zero__divisors ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).

thf(2572,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Oidom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Ono__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(1212,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) )
      = ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__average__minus__second) ).

thf(5413,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) )
      = ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212]) ).

thf(1227,axiom,
    ! [A: $i] :
      ( ~ ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A
        = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__real__square__gt__zero) ).

thf(5462,plain,
    ! [A: $i] :
      ( ( ( A
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
       => ~ ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ~ ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( A
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).

thf(740,axiom,
    ! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__square) ).

thf(3850,plain,
    ! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).

thf(412,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ class_Rings_Oring )
     => ( ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
          = ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) )
      <=> ( ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
          = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__add__iff1) ).

thf(2704,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( F @ class_Rings_Oring )
     => ( ( ( ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
            = A )
         => ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
            = ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) )
        & ( ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
            = ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) )
         => ( ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes ) ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
            = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(485,axiom,
    tc_Int_Oint @ class_Rings_Oring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).

thf(2961,plain,
    tc_Int_Oint @ class_Rings_Oring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(17,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__0__le__add__iff) ).

thf(1288,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(135,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__vector )
     => ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
          = ( B @ c_Groups_Ozero__class_Ozero ) )
      <=> ( A
          = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__zero__iff) ).

thf(1710,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__vector )
     => ( ( ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
            = ( B @ c_Groups_Ozero__class_Ozero ) ) )
        & ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
            = ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(326,axiom,
    tc_Int_Oint @ class_Int_Onumber__ring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).

thf(2404,plain,
    tc_Int_Oint @ class_Int_Onumber__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(588,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add )
     => ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__le__iff) ).

thf(3323,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oordered__ab__group__add )
     => ( ( ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(1056,axiom,
    tc_RealDef_Oreal @ class_Int_Onumber__ring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).

thf(4865,plain,
    tc_RealDef_Oreal @ class_Int_Onumber__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).

thf(506,axiom,
    tc_Int_Oint @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

thf(3030,plain,
    tc_Int_Oint @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(922,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( ( B @ c_Groups_Oone__class_Oone )
          = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
      <=> ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Int_Oiszero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__special_I2_J) ).

thf(4442,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Int_Onumber__ring )
     => ( ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Int_Oiszero ) )
         => ( ( B @ c_Groups_Oone__class_Oone )
            = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) ) )
        & ( ( ( B @ c_Groups_Oone__class_Oone )
            = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
         => ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( c_Int_OPls @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Int_Oiszero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).

thf(269,axiom,
    ! [A: $i] :
      ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls__right) ).

thf(2223,plain,
    ! [A: $i] :
      ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(1158,axiom,
    tc_RealDef_Oreal @ class_Groups_Oordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).

thf(5215,plain,
    tc_RealDef_Oreal @ class_Groups_Oordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).

thf(225,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ominus__right) ).

thf(2063,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(687,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Oordered__ring )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).

thf(3673,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Oordered__ring )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).

thf(1181,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ hAPP ) @ hBOOL )
    <=> ~ ( ? [D: $i] :
              ( ~ ( D @ ( C @ hAPP ) @ hBOOL )
              & ( B
                = ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
          | ( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL )
            & ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).

thf(5283,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( ? [D: $i] :
                ( ~ ( D @ ( C @ hAPP ) @ hBOOL )
                & ( B
                  = ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
            | ( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL )
              & ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ hAPP ) @ hBOOL ) )
      & ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ hAPP ) @ hBOOL )
       => ~ ( ? [D: $i] :
                ( ~ ( D @ ( C @ hAPP ) @ hBOOL )
                & ( B
                  = ( D @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
            | ( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( C @ hAPP ) @ hBOOL )
              & ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).

thf(1133,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I32_J) ).

thf(5110,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ c_Int_OBit1 @ ( B @ c_Int_OBit0 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).

thf(728,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ? [C: $i] :
          ( A
          = ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).

thf(3805,plain,
    ! [A: $i,B: $i] :
      ( ( ? [C: $i] :
            ( A
            = ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ? [C: $i] :
            ( A
            = ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).

thf(1220,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).

thf(5440,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( B @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).

thf(400,axiom,
    tc_Nat_Onat @ class_Rings_Olinordered__semidom,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).

thf(2651,plain,
    tc_Nat_Onat @ class_Rings_Olinordered__semidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(146,axiom,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).

thf(1742,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(366,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Odivision__ring )
     => ( ( C
         != ( D @ c_Groups_Ozero__class_Ozero ) )
       => ( ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
            = A )
         => ( B
            = ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__divide__imp) ).

thf(2549,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Odivision__ring )
     => ( ( C
         != ( D @ c_Groups_Ozero__class_Ozero ) )
       => ( ( ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
            = A )
         => ( B
            = ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(307,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Osemiring )
     => ( ( A @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_combine__common__factor) ).

thf(2353,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Osemiring )
     => ( ( A @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(171,axiom,
    tc_Int_Oint @ class_Groups_Olinordered__ab__group__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).

thf(1827,plain,
    tc_Int_Oint @ class_Groups_Olinordered__ab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(834,axiom,
    tc_RealDef_Oreal @ class_Rings_Olinordered__idom,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).

thf(4118,plain,
    tc_RealDef_Oreal @ class_Rings_Olinordered__idom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).

thf(357,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__right__mono__neg) ).

thf(2507,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field__inverse__zero )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( D @ c_Groups_Ozero__class_Ozero @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(856,axiom,
    tc_RealDef_Oreal @ class_Int_Oring__char__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).

thf(4229,plain,
    tc_RealDef_Oreal @ class_Int_Oring__char__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).

thf(752,axiom,
    tc_Nat_Onat @ class_Groups_Oordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).

thf(3886,plain,
    tc_Nat_Onat @ class_Groups_Oordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).

thf(907,axiom,
    ! [A: $i] :
      ( ( c_Int_OPls @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I29_J) ).

thf(4395,plain,
    ! [A: $i] :
      ( ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( c_Int_OPls @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( c_Int_OPls @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).

thf(409,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Int_Onumber__ring )
     => ( ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__number__of__left) ).

thf(2687,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Int_Onumber__ring )
     => ( ( A @ ( B @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(792,axiom,
    tc_Complex_Ocomplex @ class_Groups_Oone,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).

thf(4019,plain,
    tc_Complex_Ocomplex @ class_Groups_Oone,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).

thf(940,axiom,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc )
      = ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc3__eq__add__3) ).

thf(4501,plain,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc @ c_Nat_OSuc @ c_Nat_OSuc )
      = ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit1 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).

thf(1229,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Opi @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_Transcendental_Otan )
      = ( A @ c_Transcendental_Otan ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tan__periodic) ).

thf(5473,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Opi @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_Transcendental_Otan )
      = ( A @ c_Transcendental_Otan ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).

thf(487,axiom,
    ! [A: $i] :
      ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__less__0) ).

thf(2966,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(8,axiom,
    ( ( c_Transcendental_Opi @ c_Transcendental_Otan )
    = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tan__pi) ).

thf(1268,plain,
    ( ( c_Transcendental_Opi @ c_Transcendental_Otan )
    = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(696,axiom,
    tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0__less__1) ).

thf(3701,plain,
    tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).

thf(383,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ozero__neq__one )
     => ( ( A @ c_Groups_Ozero__class_Ozero )
       != ( A @ c_Groups_Oone__class_Oone ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__neq__one) ).

thf(2600,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ozero__neq__one )
     => ( ( A @ c_Groups_Ozero__class_Ozero )
       != ( A @ c_Groups_Oone__class_Oone ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(47,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).

thf(1384,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(352,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
     => ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).

thf(2485,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oordered__ab__semigroup__add__imp__le )
     => ( ( ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( B @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(716,axiom,
    tc_Nat_Onat @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

thf(3772,plain,
    tc_Nat_Onat @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(1111,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__ring )
     => ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
        = ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_poly__minus) ).

thf(5061,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__ring )
     => ( ( A @ ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
        = ( A @ ( B @ ( C @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).

thf(378,axiom,
    tc_Nat_Onat @ class_Groups_Ocomm__monoid__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).

thf(2583,plain,
    tc_Nat_Onat @ class_Groups_Ocomm__monoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(813,axiom,
    tc_RealDef_Oreal @ class_Rings_Oordered__comm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).

thf(4066,plain,
    tc_RealDef_Oreal @ class_Rings_Oordered__comm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).

thf(933,axiom,
    tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).

thf(4484,plain,
    tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).

thf(1180,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__is__id) ).

thf(5280,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).

thf(731,axiom,
    tc_Int_Oint @ class_Groups_Ocancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).

thf(3817,plain,
    tc_Int_Oint @ class_Groups_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).

thf(79,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Odivision__ring )
     => ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__1) ).

thf(1500,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Odivision__ring )
     => ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Rings_Oinverse__class_Odivide ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(566,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).

thf(3245,plain,
    ! [A: $i,B: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(912,axiom,
    ! [A: $i,B: $i] :
      ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ c_Transcendental_Oarctan @ ( B @ c_Transcendental_Oarctan @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
          = ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ c_Transcendental_Oarctan ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_arctan__add) ).

thf(4410,plain,
    ! [A: $i,B: $i] :
      ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ c_Transcendental_Oarctan @ ( B @ c_Transcendental_Oarctan @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
          = ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ c_Transcendental_Oarctan ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).

thf(1104,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ c_Transcendental_Otan )
      = ( A @ c_Transcendental_Otan @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tan__minus) ).

thf(5046,plain,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ c_Transcendental_Otan )
      = ( A @ c_Transcendental_Otan @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).

thf(850,axiom,
    ! [A: $i] :
      ( ( c_Int_OPls @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I12_J) ).

thf(4206,plain,
    ! [A: $i] :
      ( ( ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( c_Int_OPls @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( c_Int_OPls @ ( A @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( c_Int_OPls @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).

thf(989,axiom,
    tc_Complex_Ocomplex @ class_Groups_Ocomm__monoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).

thf(4659,plain,
    tc_Complex_Ocomplex @ class_Groups_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).

thf(649,axiom,
    c_Int_OPls @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of2) ).

thf(3538,plain,
    c_Int_OPls @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(890,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
          = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ) )
      & ( ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nat__number__of) ).

thf(4330,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
          = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ) )
      & ( ( c_Int_OPls @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).

thf(1195,axiom,
    tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).

thf(5354,plain,
    tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).

thf(519,axiom,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != ( A @ c_Nat_OSuc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).

thf(3076,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != ( A @ c_Nat_OSuc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(817,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Ofield )
     => ( ( C
         != ( D @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) )
          = ( C @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__diff__eq__iff) ).

thf(4071,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Ofield )
     => ( ( C
         != ( D @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) )
          = ( C @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).

thf(764,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__ring__strict )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__neg__neg) ).

thf(3918,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__ring__strict )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).

thf(106,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__ring )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).

thf(1621,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__ring )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(245,axiom,
    tc_Nat_Onat @ class_Rings_Omult__zero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).

thf(2138,plain,
    tc_Nat_Onat @ class_Rings_Omult__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(996,axiom,
    tc_Complex_Ocomplex @ class_Groups_Ogroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).

thf(4674,plain,
    tc_Complex_Ocomplex @ class_Groups_Ogroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).

thf(31,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).

thf(1331,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(950,axiom,
    ! [A: $i] :
      ( ( A @ class_Int_Onumber__ring )
     => ( ( A @ c_Groups_Ozero__class_Ozero )
        = ( c_Int_OPls @ ( A @ c_Int_Onumber__class_Onumber__of ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I112_J) ).

thf(4520,plain,
    ! [A: $i] :
      ( ( A @ class_Int_Onumber__ring )
     => ( ( A @ c_Groups_Ozero__class_Ozero )
        = ( c_Int_OPls @ ( A @ c_Int_Onumber__class_Onumber__of ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).

thf(410,axiom,
    tc_Int_Oint @ class_Groups_Omonoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).

thf(2690,plain,
    tc_Int_Oint @ class_Groups_Omonoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(845,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
     => ( ( ( C = B )
         => ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
       => ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
           => ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
         => ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__less__cases) ).

thf(4174,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
     => ( ( ( C = B )
         => ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
       => ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
           => ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
         => ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).

thf(580,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__mono) ).

thf(3296,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(463,axiom,
    tc_Int_Oint @ class_Int_Oring__char__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).

thf(2879,plain,
    tc_Int_Oint @ class_Int_Oring__char__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(397,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__le__mono1) ).

thf(2640,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(1145,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Rings_Olinordered__idom )
        & ( B @ class_Int_Onumber__ring ) )
     => ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__special_I1_J) ).

thf(5155,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Rings_Olinordered__idom )
        & ( B @ class_Int_Onumber__ring ) )
     => ( ( ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( c_Int_OPls @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).

thf(1027,axiom,
    ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc )
    = ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I115_J) ).

thf(4779,plain,
    ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc )
    = ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).

thf(664,axiom,
    tc_Nat_Onat @ class_Rings_Ocomm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).

thf(3580,plain,
    tc_Nat_Onat @ class_Rings_Ocomm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(27,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).

thf(1320,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(985,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_RealVector_Oreal__normed__algebra )
     => ( ( C @ ( D @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__mult__less) ).

thf(4642,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_RealVector_Oreal__normed__algebra )
     => ( ( C @ ( D @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes ) ) @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).

thf(115,axiom,
    tc_Int_Oint @ class_Rings_Olinordered__semiring__1__strict,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).

thf(1653,plain,
    tc_Int_Oint @ class_Rings_Olinordered__semiring__1__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(561,axiom,
    tc_Nat_Onat @ class_Groups_Oone,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).

thf(3227,plain,
    tc_Nat_Onat @ class_Groups_Oone,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(980,axiom,
    ! [A: $i] :
      ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ c_Transcendental_Ocos @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cos__gt__zero__pi) ).

thf(4627,plain,
    ! [A: $i] :
      ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ c_Transcendental_Ocos @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).

thf(199,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring )
     => ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).

thf(1962,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring )
     => ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(371,axiom,
    tc_Nat_Onat @ class_Rings_Oordered__comm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).

thf(2563,plain,
    tc_Nat_Onat @ class_Rings_Oordered__comm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(1184,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__diff__inverse) ).

thf(5312,plain,
    ! [A: $i,B: $i] :
      ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).

thf(1029,axiom,
    ! [A: $i] :
      ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ c_Transcendental_Otan @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tan__less__zero) ).

thf(4784,plain,
    ! [A: $i] :
      ( ( A @ ( c_Int_OPls @ c_Int_OBit1 @ c_Int_OBit0 @ ( tc_RealDef_Oreal @ c_Int_Onumber__class_Onumber__of ) @ ( c_Transcendental_Opi @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ c_Transcendental_Otan @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).

thf(144,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).

thf(1737,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(126,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__imp__0__less) ).

thf(1681,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(1079,axiom,
    ! [A: $i] :
      ( ( ~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
          = A ) )
      & ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
          = ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zabs__def) ).

thf(4949,plain,
    ! [A: $i] :
      ( ( ~ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
          = A ) )
      & ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
          = ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).

thf(229,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).

thf(2074,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(1218,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Oabs__class_Oabs ) )
        = ( A @ ( B @ c_Groups_Oabs__class_Oabs ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__cancel) ).

thf(5436,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Oabs__class_Oabs ) )
        = ( A @ ( B @ c_Groups_Oabs__class_Oabs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).

thf(337,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
          = ( B @ c_Groups_Ozero__class_Ozero ) )
      <=> ( A
          = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__eq__0) ).

thf(2436,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( ( ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
            = ( B @ c_Groups_Ozero__class_Ozero ) ) )
        & ( ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) )
            = ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(275,axiom,
    ! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__add1) ).

thf(2238,plain,
    ! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(75,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
     => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__strict__mono) ).

thf(1490,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Oordered__cancel__ab__semigroup__add )
     => ( ( C @ ( D @ ( E @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( E @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(295,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__ring__strict )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( ( A
            = ( C @ c_Groups_Ozero__class_Ozero ) )
          & ( B
            = ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).

thf(2297,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__ring__strict )
     => ( ( ( ( A
              = ( C @ c_Groups_Ozero__class_Ozero ) )
            & ( B
              = ( C @ c_Groups_Ozero__class_Ozero ) ) )
         => ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( A
              = ( C @ c_Groups_Ozero__class_Ozero ) )
            & ( B
              = ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(631,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ocomm__monoid__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).

thf(3443,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(1222,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ class_Int_Oring__char__0 )
        & ( C @ class_Int_Onumber__ring ) )
     => ( ( ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) )
          = ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of) ).

thf(5445,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ class_Int_Oring__char__0 )
        & ( C @ class_Int_Onumber__ring ) )
     => ( ( ( B = A )
         => ( ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) )
            = ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) ) )
        & ( ( ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) )
            = ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).

thf(389,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__ring )
     => ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).

thf(2615,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__ring )
     => ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(155,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oordered__ring )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).

thf(1769,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oordered__ring )
     => ( ( C @ c_Groups_Ozero__class_Ozero @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(1087,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__minus__le__zero) ).

thf(4977,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Oordered__ab__group__add__abs )
     => ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).

thf(186,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
      = ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).

thf(1917,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
      = ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(811,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Int_Onumber )
     => ( ( ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) )
          = A )
      <=> ( A
          = ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__reorient) ).

thf(4056,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Int_Onumber )
     => ( ( ( A
            = ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
         => ( ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) )
            = A ) )
        & ( ( ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) )
            = A )
         => ( A
            = ( B @ ( C @ c_Int_Onumber__class_Onumber__of ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).

thf(512,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).

thf(3052,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes ) ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(585,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__imp__le__div__pos) ).

thf(3316,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Olinordered__field )
     => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(252,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring__strict )
     => ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).

thf(2170,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring__strict )
     => ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes ) ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(1052,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ c_Int_OBit1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I9_J) ).

thf(4858,plain,
    ! [A: $i,B: $i] :
      ( ( A @ c_Int_OBit0 @ ( B @ c_Int_OBit1 @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ c_Int_OBit1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).

thf(68,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_times__numeral__code_I5_J) ).

thf(1468,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( B @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) @ ( tc_Int_Oint @ c_Int_Onumber__class_Onumber__of ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(510,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Suc__right) ).

thf(3047,plain,
    ! [A: $i,B: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(346,axiom,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).

thf(2470,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(1076,axiom,
    tc_Complex_Ocomplex @ class_Fields_Ofield__inverse__zero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).

thf(4940,plain,
    tc_Complex_Ocomplex @ class_Fields_Ofield__inverse__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).

thf(184,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__add__cancel) ).

thf(1912,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ogroup__add )
     => ( ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(959,axiom,
    ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
    = ( c_Int_OPls @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I113_J) ).

thf(4552,plain,
    ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
    = ( c_Int_OPls @ ( tc_Nat_Onat @ c_Int_Onumber__class_Onumber__of ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).

thf(255,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__0 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Omult__zero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).

thf(2177,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__0 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Omult__zero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(402,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).

thf(2655,plain,
    ! [A: $i,B: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(53,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
        = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
    <=> ( ( A
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
        & ( B
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__0) ).

thf(1417,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
          & ( B
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
       => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
      & ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
          & ( B
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(175,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__le__linear) ).

thf(1870,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(685,axiom,
    tc_Int_Oint @ class_Groups_Ocancel__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).

thf(3669,plain,
    tc_Int_Oint @ class_Groups_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(432,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
        = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
    <=> ( ( A
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
        | ( B
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__is__0) ).

thf(2771,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
          | ( B
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
       => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
      & ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
          | ( B
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(14009,plain,
    $false,
    inference(e,[status(thm)],[2163,1665,3873,5116,4094,5088,5136,4262,3167,2876,2559,2331,1818,1554,5422,1337,2306,3345,4464,2341,3008,1454,3399,2263,3698,3979,3581,4852,1315,3830,2787,2427,1982,1686,4166,4037,2210,2940,4500,4339,1618,2953,2282,2114,4623,5348,3382,2363,2077,4043,3534,3681,3990,4311,3762,2644,3813,2381,5069,2908,2062,5000,1808,3417,3377,4391,3460,2947,1939,4697,3959,2676,3910,4960,1728,1793,3402,1486,4105,5037,3439,5361,2607,4026,2448,3781,1327,2459,4294,3577,4762,3848,1497,3017,5425,3745,4418,4739,3004,2035,3332,4097,3942,3365,4870,1867,3175,2434,1872,2476,5163,1354,2146,1507,2360,4047,4792,3994,5476,1359,3281,3140,2516,5342,4941,3370,1746,3103,3836,4343,3629,2348,5227,2972,4142,2491,5486,1782,2985,2227,3249,4371,4079,4266,3088,3777,2010,4803,1650,5056,2400,4760,4963,2825,4665,3880,3878,1265,4467,2405,1623,1254,4775,2869,1409,3221,3195,4070,3689,3574,5188,4778,5182,2897,4243,3891,4637,2603,2916,4866,4896,3131,1660,4415,2269,1907,5064,1264,2217,1323,3148,3653,4130,3542,1313,4275,5130,1577,2466,5108,4766,3855,2745,2356,4862,5127,4551,4265,5077,1922,2691,3099,5338,4119,3998,5355,1379,3385,5256,3638,1514,2373,4622,5323,4830,4317,5052,4675,3014,2520,2730,2989,1362,4390,5091,4507,3557,5493,4514,2388,3866,4967,4008,4669,1847,2007,2950,1302,4578,4297,3670,3163,2236,2880,4724,3357,3152,4329,3887,4583,2027,5526,3934,1373,3724,4454,4600,3295,2782,3527,3702,4050,2122,1828,3621,3973,1978,3923,3290,4798,4686,2335,2058,4842,5375,5101,4504,4825,2639,3327,2750,1943,1564,2762,5045,5059,4718,4660,4230,1377,4033,2833,5096,3421,4364,2979,5246,4307,2002,3756,2809,2804,4519,1697,3559,2392,3906,4588,2718,2205,3184,4475,2586,3435,4700,3899,3097,3229,3857,5530,1691,3852,5167,5142,5034,1915,5122,4216,3591,4589,4629,2473,2574,5411,3531,3635,2047,3318,5416,4076,4370,1311,2232,2296,4910,5519,4031,2621,1768,2905,3550,4172,4999,2249,2541,2277,4878,5266,5455,3989,4499,4661,3339,1274,5206,5049,2589,1387,1723,2733,4016,2560,1570,1676,3371,5470,2937,3154,4449,4493,5085,5507,5102,2414,4836,3307,5492,2628,1920,4053,3314,1296,2200,2179,4979,3931,3166,2445,2464,2873,1968,3198,4757,3065,5534,1457,3894,2068,1624,3546,4746,4402,2181,4740,3028,3926,3050,2345,2344,3763,3727,1281,1634,4461,4732,1573,3799,3445,4027,5066,3731,1350,4486,5502,2509,5362,1878,3632,4883,5081,3001,3782,1541,1983,4957,5053,5221,3413,1270,5098,1259,2377,2801,5238,4512,2685,5006,5345,2895,4248,3218,4789,4930,1719,4227,4109,5233,1567,1964,4772,3728,4513,1446,3555,4621,5387,4320,1683,3775,2877,5080,5496,5107,2830,4721,1739,4425,4421,3441,2312,4545,5253,5263,1414,2196,2240,5547,1700,5213,2613,1937,1810,4861,2172,3242,1825,4970,1932,2581,4717,1947,1984,2813,4259,4689,1759,1776,5273,4846,2450,1588,3126,2681,3541,2836,1456,1382,3354,4068,3390,4829,4934,2497,1429,3967,3247,3409,4416,3920,2272,2370,1525,4535,3802,4644,3563,2402,1895,5198,4572,5170,4163,3454,2634,2749,1434,1991,1318,1779,3624,2208,4081,4212,4889,4966,4765,3999,1286,2368,5419,4448,2408,2793,5209,2089,3190,2221,4036,3841,2617,2338,3675,4308,3660,2413,3042,3607,3890,1273,4657,3262,4393,3738,3111,1374,5400,5241,3343,1959,2556,2275,2033,2149,4613,2253,3491,1483,1548,3985,4269,4017,3070,2859,2981,3086,3900,3604,5535,3536,4786,4943,4283,1784,5488,3255,5065,2849,3472,2489,3736,1929,4677,2016,2514,4801,4122,4032,4709,4605,5050,1535,1795,2398,4328,3404,2817,1256,5022,4485,3773,3964,4112,1635,4413,3340,3123,3436,2055,3700,4273,3304,3091,1638,2161,4251,4526,3796,1503,5185,3023,5039,4558,1669,5363,2293,4796,2891,1371,4837,3695,4099,3330,2738,3208,5331,1897,3641,3719,2358,1356,3678,2119,2679,5520,4305,5491,1722,5381,4388,3631,2538,1282,2478,2151,2642,2229,3815,5506,2084,3287,4828,3779,3419,4914,3270,2246,1492,2116,2839,1771,4958,4213,1801,4154,1376,4509,1439,1667,4203,4401,2025,2610,2625,3073,4064,5335,3192,3483,1460,2928,5459,4554,1471,3747,4541,2742,4882,3055,5439,1731,4264,3572,1909,4985,2410,1325,2593,3006,5318,3298,2252,2664,4993,2553,2578,1688,3480,3159,2931,2752,1477,4703,5089,1562,3539,4933,4844,2962,2365,1474,4232,2350,5442,3627,5216,3759,3838,5377,3423,2481,5218,2086,5482,2139,3687,4282,4626,4067,5139,4890,3908,3876,1694,2005,5548,3427,5528,4580,2652,1905,4529,2202,1340,4355,2899,5358,4405,3031,2816,4690,1662,4394,1758,2107,2784,2271,1277,4052,2846,2256,4113,2564,4812,1551,5003,4045,4749,1598,4864,3754,3949,3058,2888,5452,1748,1798,3391,5250,4490,2977,2375,4272,4366,1941,5484,3462,4200,1368,4517,3228,4469,2821,5079,4324,3080,5262,5235,4561,3554,3026,5154,3828,3769,4409,4437,2092,4092,1432,3818,3885,1300,1452,3114,3273,3334,3722,4020,5309,1763,3127,1538,2903,4781,3359,3095,5106,5319,2379,4246,2975,3961,2266,4819,1934,2948,1543,1766,3970,2113,3124,1536,1981,2279,4510,1972,2711,4106,5453,3224,1427,3388,4431,1585,2511,4634,3117,2722,4342,1717,2030,2807,1272,3156,3914,2584,4671,4217,1617,2924,3757,3092,3067,1685,5386,1517,4185,2226,4730,3593,2435,3284,2760,3433,3946,3139,4651,4424,4138,2870,2828,2347,1654,1412,4102,3346,2110,3320,1390,5124,5389,2071,2658,3929,1734,4310,2273,3484,4683,5426,4791,1745,4338,2431,2130,3368,4451,5258,1590,5315,2443,3613,1253,4913,2174,4806,3789,2855,1639,2853,2290,3825,1903,4666,5008,4089,5382,2823,4042,4542,5228,3630,3003,1822,5010,2764,3252,5505,3662,2526,4900,2934,2081,4197,5408,3430,3529,2183,5144,5119,4869,2384,2475,2786,4602,2912,4321,1294,5109,2462,1308,3896,2198,2576,4478,2066,2095,4074,2739,2494,1444,5196,1442,3552,4927,4025,2019,4619,3379,4880,1642,1774,1725,3232,3733,4596,1546,3100,4523,3521,4357,1957,4687,3860,1678,3785,3511,3291,3997,2983,2719,5268,3601,3882,5232,3373,2604,2736,2008,4841,3337,1673,3132,5527,4885,1480,4597,5247,5398,4367,3469,3164,5300,2746,2417,2714,3045,3982,2636,1436,4146,4303,4051,5159,1495,4755,4981,1657,5092,3347,4286,2186,4281,4631,3177,5019,4083,4024,2572,5413,5462,3850,2704,2961,1288,1710,2404,3323,4865,3030,4442,2223,5215,2063,3673,5283,5110,3805,5440,2651,1742,2549,2353,1827,4118,2507,4229,3886,4395,2687,4019,4501,5473,2966,1268,3701,2600,1384,2485,3772,5061,2583,4066,4484,5280,3817,1500,3245,4410,5046,4206,4659,3538,4330,5354,3076,4071,3918,1621,2138,4674,1331,4520,2690,4174,3296,2879,2640,5155,4779,3580,1320,4642,1653,3227,4627,1962,2563,5312,4784,1737,1681,4949,2074,5436,2436,2238,1490,2297,3443,5445,2615,1769,4977,1917,4056,3052,3316,2170,4858,1468,3047,2470,4940,1912,4552,2177,2655,1417,1870,3669,2771]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SWW222+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.07  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.37  % Computer : n009.cluster.edu
% 0.10/0.37  % Model    : x86_64 x86_64
% 0.10/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37  % Memory   : 8046.5625MB
% 0.10/0.37  % OS       : Linux 6.8.0-71-generic
% 0.10/0.37  % CPULimit : 300
% 0.10/0.37  % WCLimit  : 300
% 0.10/0.37  % DateTime : Sat Sep 26 15:29:29 UTC 2026
% 0.10/0.37  % CPUTime  : 
% 0.10/0.37  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.59/0.67  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.57/0.97  % [INFO] 	 Parsing done (294ms). 
% 1.57/0.98  % [INFO] 	 Running in sequential loop mode. 
% 2.61/1.17  % [INFO] 	 eprover registered as external prover. 
% 2.61/1.18  % [INFO] 	 Scanning for conjecture ... 
% 3.26/1.32  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1250 axioms. Running axiom selection ... 
% 4.67/1.67  % [INFO] 	 Axiom selection finished. Selected 1250 axioms (removed 0 axioms). 
% 6.10/2.01  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 6.68/2.04  % [INFO] 	 Type checking passed. 
% 6.68/2.05  % [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 ... 
% 66.59/17.77  % External prover 'e' found a proof!
% 66.59/17.77  % [INFO] 	 Killing All external provers ... 
% 66.59/17.78  % Time passed: 17310ms (effective reasoning time: 16797ms)
% 66.59/17.78  % 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)>
% 66.59/17.78  % Axioms used in derivation (1250): fact_less__eq__int__code_I14_J, fact_le__SucI, arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra, fact_le__imp__diff__is__add, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_Numeral1__eq1__nat, fact_arctan__monotone, fact_minus__Bit0, fact_complex__diff__def, fact_zle__refl, fact_neg__le__0__iff__le, fact_add__le__less__mono, fact_mult__strict__left__mono__neg, fact_pos2, fact_zero__le__divide__iff, fact_Nat_Oadd__0__right, fact_right__inverse__eq, fact_real__squared__diff__one__factored, fact_tan__inverse, fact_numeral__2__eq__2, fact_abs__of__pos, fact_real__le__refl, fact_abs__le__D2, arity_Complex__Ocomplex__Rings_Oidom, fact_nat_Osimps_I3_J, fact_real__less__def, arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_number__of__diff, fact_mult__right__le__imp__le, arity_Nat__Onat__Groups_Ocancel__semigroup__add, fact_real__le__trans, fact_neg__le__divide__eq, arity_Complex__Ocomplex__Groups_Omonoid__add, arity_Int__Oint__Rings_Ocomm__semiring, fact_pos__add__strict, arity_Int__Oint__Rings_Osemiring, fact_mult__poly__0__right, fact_add__strict__right__mono, arity_Int__Oint__Orderings_Olinorder, fact__096_B_Bthesis_O_A_I_B_Bd_O_A_091_124_A0_A_060_Ad_059_AALL_Aw_O_A0_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_A_N_N_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_mult__1__left, fact_diff__0__eq__0, fact_minus__mult__left, fact_neg__divide__le__eq, fact_fz_I2_J, fact_semiring__norm_I112_J, fact_diff__add__inverse, fact_diff__bin__simps_I10_J, fact_abs__if, fact_bin__less__0__simps_I4_J, fact_le__eq__less__or__eq, arity_Polynomial__Opoly__Rings_Ocomm__semiring__0, arity_Polynomial__Opoly__Int_Onumber, arity_RealDef__Oreal__Groups_Ozero, fact_trans__less__add1, fact_mult__nonneg__nonpos, fact_one__is__num__one, fact_add__poly__code_I2_J, fact_abs__ge__self, arity_RealDef__Oreal__Rings_Oordered__comm__semiring, arity_Complex__Ocomplex__Groups_Oab__group__add, fact_diff__0__right, fact_mult__less__cancel__left__disj, fact_nat__add__left__commute, fact_real__mult__left__cancel, fact_mult__nonpos__nonpos, fact_tan__pi, fact_neg__equal__0__iff__equal, fact_arctan1__eq__pi4, fact_real__of__nat__zero, fact_mult__left_Ominus, fact_number__of__minus, arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors, fact_real__sgn__eq, fact_abs__minus__commute, fact_tan__npi, arity_Nat__Onat__Rings_Ono__zero__divisors, fact_nat__less__cases, fact_divide__nonpos__neg, fact_one__is__add, fact_diff__le__mono2, fact_mult__nat__number__of, arity_Int__Oint__Rings_Olinordered__semiring__strict, arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add, fact_minus__mult__right, fact_real__of__nat__diff, fact_norm__mult__less, fact_odd__nonzero, fact_tan__total__pi4, fact_add__nat__number__of, fact_zminus__zminus, fact_norm__diff__triangle__ineq, fact_less__int__code_I14_J, fact_mult__eq__0__iff, fact_less__imp__le__nat, fact_combine__common__factor, fact_le__imp__0__less, fact_add__leD1, fact_diff__number__of__eq, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_eq__divide__eq__number__of, fact_pi__half__neq__two, fact_abs__div__pos, arity_RealDef__Oreal__Rings_Olinordered__ring, arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le, fact_add__less__mono, fact_real__0__less__add__iff, fact_abs__triangle__ineq2__sym, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, fact__096_B_By_O_A_IEX_Az_Ax_O_Acmod_Az_A_060_061_Ar_A_G_A_N_A_I_N_Acmod_A_Ipoly_Ap_Az_J_J_A_060_Ay_J_A_061_A_I_N_As_A_060_Ay_J_096, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J, fact_mult__right__less__imp__less, fact_abs__eq__mult, fact_split__mult__neg__le, fact_real__gt__half__sum, fact_rel__simps_I49_J, fact_rel__simps_I27_J, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, arity_Int__Oint__Rings_Osemiring__1, fact_divide__numeral__1, fact_numeral__1__eq__Suc__0, fact_Suc__mono, 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, fact_mult__le__less__imp__less, fact_zadd__commute, arity_Nat__Onat__Groups_Omonoid__mult, fact_diff__Suc__less, fact_real__add__le__0__iff, fact_mult__0, fact_mult__poly__0__left, arity_Polynomial__Opoly__Rings_Olinordered__ring__strict, fact_add__right__imp__eq, fact_iszero__0, fact_diff__diff__cancel, fact_gr0__conv__Suc, fact_abs__diff__triangle__ineq, arity_Complex__Ocomplex__Int_Onumber__ring, fact_Suc__le__mono, fact_le__number__of__eq__not__less, fact_norm__add__less, arity_Nat__Onat__Rings_Ozero__neq__one, fact_poly__zero, fact_nat__number__of__Pls, fact_eq__neg__iff__add__eq__0, arity_Polynomial__Opoly__Groups_Oab__semigroup__mult, fact_iszero__def, arity_Complex__Ocomplex__Groups_Oab__semigroup__mult, arity_Polynomial__Opoly__Rings_Oidom, fact_zero__less__diff, fact_abs__poly__def, fact_mult__mono, fact_cos__gt__zero__pi, fact_nat__add__right__cancel, fact_neg__le__iff__le, arity_RealDef__Oreal__Groups_Omonoid__add, fact_neg__0__less__iff__less, fact_less__special_I4_J, arity_RealDef__Oreal__Rings_Oidom, fact_int__pos__lt__two__imp__zero__or__one, fact_mult__le__mono2, fact_Suc__diff__diff, fact_rel__simps_I31_J, fact_le__neq__implies__less, arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add, fact_not__iszero__Numeral1, fact_lemma__NBseq__def2, fact_zero__le__one, arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add, fact_poly__add, arity_RealDef__Oreal__Rings_Ocomm__ring__1, fact_diff__bin__simps_I7_J, fact_Bit1__def, fact_int__0__less__1, fact_le__minus__iff, fact_left__diff__distrib__number__of, fact_mult_Oadd__right, fact_mult_Ominus__right, fact_le__add__iff2, fact_mult__eq__self__implies__10, 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fact_iszero__number__of__Bit0, fact_le__divide__eq__number__of1, fact_mult__le__mono, arity_Nat__Onat__Orderings_Olinorder, fact_zminus__0, fact__096_B_Bn_O_AEX_Az_O_Acmod_Az_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_Az_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_An_J_096, fact_mult__le__0__iff, fact_le__iff__diff__le__0, fact_divide__self__if, fact_mult__is__0, fact_Suc__diff__1, fact_add__special_I3_J, fact_nat__add__left__cancel, fact_norm__triangle__ineq, fact_numeral__1__eq__1, fact_real__average__minus__second, arity_Int__Oint__Rings_Omult__zero, fact_minus__Pls, fact_real__le__antisym, arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs, fact_rel__simps_I14_J, fact_one__add__one__is__two, fact_n__not__Suc__n, fact_nat__le__linear, fact_mult__zero__right, fact_natceiling__eq, arity_Int__Oint__Rings_Oring, fact_divide__zero, arity_Nat__Onat__Rings_Omult__zero, fact_less__minus__self__iff, arity_Int__Oint__Groups_Oordered__comm__monoid__add, fact_le__divide__eq__number__of, fact_sum__squares__gt__zero__iff, fact_mult__less__cancel1, fact_nat__0__less__mult__iff, arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1, arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add, fact_rel__simps_I33_J, fact_abs__le__interval__iff, arity_Int__Oint__Groups_Oordered__ab__group__add__abs, arity_RealDef__Oreal__Groups_Ocomm__monoid__add, fact_pi__ge__two, fact_abs__mult, arity_RealDef__Oreal__Rings_Ocomm__semiring__1, fact_diff__eq__diff__less, arity_Polynomial__Opoly__Rings_Ozero__neq__one, fact_add__mult__distrib, fact_abs__number__of, fact_le__add__diff, fact_abs__real__of__nat__cancel, fact_diff__bin__simps_I1_J, arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict, fact_abs__divide, fact_iszero__number__of__Bit1, fact_add__strict__left__mono, fact_diff__poly__code_I1_J, fact_add__Suc, fact_diff__add__assoc, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_real__sum__of__halves, fact_real__of__nat__mult, fact_diff__divide__distrib, fact_less__2__cases, arity_RealDef__Oreal__Rings_Ono__zero__divisors, fact_add__gr__0, arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict, fact_zdiff__zmult__distrib2, fact_add__diff__assoc2, fact_mult__divide__mult__cancel__right, fact_minus__unique, fact_cos__le__one, fact_diff__less__mono2, fact_divide__zero__left, arity_Nat__Onat__Rings_Oordered__cancel__semiring, fact_int__0__neq__1, fact_real__divide__square__eq, arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le, fact_Suc__eq__plus1__left, fact_Zero__not__Suc, arity_RealDef__Oreal__Rings_Olinordered__semiring__1, arity_Complex__Ocomplex__Rings_Ono__zero__divisors, arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add, fact_mult__strict__mono, fact_not__real__of__nat__less__zero, fact_zero__less__one, fact_neg__equal__zero, fact_real__diff__def, fact_mult__2, fact_diff__mult__distrib, fact_tan__periodic__nat, fact_add__less__imp__less__right, fact_le__Suc__ex__iff, arity_RealDef__Oreal__Rings_Oring__no__zero__divisors, fact_zdiff__zmult__distrib, fact_subseq__def, arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le, fact_diff__less__mono, fact_Suc__leD, fact_add__number__of__eq, fact_add__minus__cancel, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, arity_RealDef__Oreal__Rings_Oordered__ring__abs, fact_zero__less__divide__iff, fact_real__of__nat__1, fact_add_Ocomm__neutral, fact_norm__ratiotest__lemma, arity_Int__Oint__Groups_Osgn__if, arity_Nat__Onat__Rings_Oordered__semiring, fact_mult__Suc, fact_Bit0__def, fact_arctan__minus, fact_le__minus__self__iff, fact_rel__simps_I50_J, fact_diff__frac__eq, arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors, fact_abs__mult__less, fact_le__special_I3_J, fact_rel__simps_I4_J, fact_arctan__monotone_H, fact_less__number__of, fact_pos__divide__less__eq, fact_s, fact_diff__bin__simps_I3_J, fact_mult__zero__left, fact_abs__sum__triangle__ineq, fact_less__trans__Suc, arity_Int__Oint__Groups_Oordered__ab__semigroup__add, fact_add__scale__eq__noteq, fact_Nat_Odiff__diff__eq, fact_le__refl, fact_nat__add__assoc, fact_eq__add__iff2, fact_zadd__zmult__distrib2, fact_abs__add__one__not__less__self, fact_norm__minus__cancel, fact_mult__imp__div__pos__le, fact_less__not__refl2, fact_mult__Bit0, fact_le__add1, fact_mult__cancel1, fact_trans__le__add2, fact_pi__ge__zero, fact_abs__le__zero__iff, fact_mult__right__le__one__le, arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, fact_Suc__mult__le__cancel1, fact_One__nat__def, fact_semiring__norm_I113_J, fact_divide__diff__eq__iff, fact_rel__simps_I46_J, fact_mult__diff__mult, fact_rel__simps_I16_J, fact_abs__triangle__ineq4, fact_divide_Oadd, fact_ab__diff__minus, fact_le__imp__less__Suc, fact_d_I1_J, arity_RealDef__Oreal__Groups_Oone, arity_Int__Oint__Rings_Olinordered__semiring, fact_nonzero__minus__divide__divide, 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arity_RealDef__Oreal__Rings_Olinordered__semidom, fact_neg__equal__iff__equal, arity_Polynomial__Opoly__Rings_Olinordered__semiring__1, arity_RealDef__Oreal__Groups_Ocomm__monoid__mult, fact_diff__add__0, fact_add__pos__pos, arity_Nat__Onat__Groups_Oab__semigroup__mult, fact_diff__cancel2, fact_add__nonneg__nonneg, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J, arity_RealDef__Oreal__Groups_Oab__group__add, fact_Suc__eq__plus1, fact_arctan__inverse, arity_Int__Oint__Rings_Olinordered__idom, arity_Int__Oint__Rings_Ocomm__semiring__1, fact_sgn__greater, fact_machin, fact_divide__le__eq__number__of1, fact_tan__monotone_H, arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1, fact_mult__nonpos__nonneg, fact_Suc__diff__le, arity_Polynomial__Opoly__Rings_Osemiring, fact_Zero__neq__Suc, fact_less__eq__int__code_I16_J, arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict, fact_less__special_I3_J, arity_Nat__Onat__Groups_Oab__semigroup__add, fact_zabs__def, fact_less__1__mult, arity_Int__Oint__Rings_Oordered__comm__semiring, fact_le0, fact__096_B_Bz_Ax_O_A_091_124_Acmod_Az_A_060_061_Ar_059_Acmod_A_Ipoly_Ap_Az_J_A_061_A_N_Ax_059_A_126_Ax_A_060_A1_A_124_093_A_061_061_062_AFalse_096, fact_square__eq__1__iff, fact_Suc__pred, arity_Int__Oint__Groups_Oab__semigroup__add, fact_divide__less__eq, arity_Int__Oint__Groups_Oone, arity_Nat__Onat__Rings_Olinordered__semidom, fact_add__le__cancel__right, arity_Complex__Ocomplex__Groups_Omonoid__mult, arity_Int__Oint__Groups_Ocomm__monoid__mult, fact_add__left__mono, fact_real__add__eq__0__iff, fact_nat__mult__eq__1__iff, fact_not__less__eq__eq, fact_mult__right_Ominus, fact_less__not__refl, fact_double__add__le__zero__iff__single__add__le__zero, fact_mult__less__cancel__left__neg, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_poly__diff, fact_le__diff__conv2, fact_mult__pos__pos, fact_minus__mult__minus, fact_right__distrib__number__of, fact_crossproduct__eq, fact_neg__less__divide__eq, fact_le__trans, arity_Int__Oint__Groups_Oabs__if, fact_add__Pls__right, fact_zmult__zless__mono2, fact_diff__Suc__diff__eq1, fact_comm__mult__left__mono, fact_divide__eq__eq__number__of1, fact_plus__numeral__code_I9_J, fact_gr__implies__not0, fact_mult__strict__right__mono__neg, fact_pi__neq__zero, fact_abs__triangle__ineq, fact_real__two__squares__add__zero__iff, fact_less__add__one, fact_int__one__le__iff__zero__less, fact_mult__less__imp__less__right, fact_zero__neq__one, fact_less__Suc__eq, fact_add__leE, fact_mult_Odiff__left, fact_diff__Suc__1, fact_add__less__le__mono, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, fact_real__of__nat__Suc__gt__zero, fact_wr, arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add, arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero, arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors, arity_Nat__Onat__Int_Onumber, fact_double__number__of__Bit0, arity_Nat__Onat__Rings_Olinordered__semiring__strict, fact_number__of1, fact_norm__mult__ineq, fact_nat__add__commute, arity_Int__Oint__Rings_Ono__zero__divisors, fact_add__poly__code_I1_J, fact_diff__eq__diff__less__eq, fact_less__int__code_I15_J, fact_divide__strict__left__mono, fact_arctan, arity_RealDef__Oreal__Rings_Ocomm__semiring__0, fact_Suc__less__eq, fact_mult__neg__neg, arity_Int__Oint__Rings_Oring__1, fact_right__minus__eq, arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add, fact_neg__0__le__iff__le, fact_cos__zero, arity_RealDef__Oreal__Rings_Osemiring__1, arity_Polynomial__Opoly__Groups_Ogroup__add, fact_zmult__zminus, fact_sgn__one, arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add, arity_RealDef__Oreal__Rings_Oring__1, fact_divide_Odiff, fact_zero__less__Suc, fact_iszero__Numeral0, fact_rel__simps_I2_J, arity_Complex__Ocomplex__Rings_Ocomm__ring, fact_less__divide__eq, fact_mult_Ocomm__neutral, arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_add__nonpos__neg, fact_number__of__Bit1, arity_RealDef__Oreal__Rings_Oordered__semiring, fact_le__SucE, fact_divide__Numeral1, fact_add1__zle__eq, fact__096cmod_A0_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A0_J_A_061_A_N_A_I_N_Acmod_A_Ipoly_Ap_A0_J_J_096, arity_Polynomial__Opoly__Rings_Olinordered__semiring, fact_eq__imp__le, fact_diff__add__inverse2, arity_Complex__Ocomplex__Int_Oring__char__0, arity_Int__Oint__Rings_Olinordered__semiring__1, fact_plus__nat_Oadd__0, fact_subseq__Suc__iff, arity_RealDef__Oreal__Int_Onumber, fact_neg__divide__less__eq, fact_diff__eq__diff__eq, fact_minus__le__self__iff, fact_pi__half__ge__zero, fact_real__add__left__mono, fact_less__int__code_I16_J, fact_add__strict__increasing, fact_tan__periodic__pi, fact__096EX_Af_O_AALL_Ax_O_Acmod_A_If_Ax_J_A_060_061_Ar_A_G_Acmod_A_Ipoly_Ap_A_If_Ax_J_J_A_060_A_N_As_A_L_A1_A_P_Areal_A_ISuc_Ax_J_096, fact_real__mult__order, fact_le__less__Suc__eq, fact_real__norm__def, fact_d_I2_J, fact_neq0__conv, fact_mult__left__mono__neg, fact_le__antisym, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, arity_Int__Oint__Rings_Olinordered__comm__semiring__strict, fact_abs__mult__pos, arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring, fact_mult__Suc__right, fact_le__special_I4_J, fact_nonzero__abs__divide, arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le, arity_Polynomial__Opoly__Rings_Ocomm__ring__1, fact_add__2__eq__Suc, fact_s1, fact_Suc__n__not__n, fact_nat__numeral__1__eq__1, fact_add__frac__num, fact_minus__equation__iff, fact_half, fact_real__of__nat__gt__zero__cancel__iff, fact_divide__strict__right__mono, fact_mult__0__right, fact_real__add__less__0__iff, fact_zless__linear, fact_mult__less__cancel__left__pos, fact_real__mult__le__cancel__iff2, fact_bin__less__0__simps_I1_J, fact_trans__le__add1, fact_zadd__0__right, fact_e2, fact_add__divide__distrib, fact_divide__less__eq__number__of, fact_lemma__MVT, fact_diff__le__mono, fact_zero__less__mult__pos, arity_Polynomial__Opoly__Rings_Ocomm__semiring, arity_Complex__Ocomplex__Rings_Omult__zero, fact_zmult__1__right, arity_Polynomial__Opoly__Rings_Ono__zero__divisors, fact_double__eq__0__iff, fact_le__0__eq, fact_real__0__le__add__iff, fact_mult__less__cancel2, fact_zle__add1__eq__le, fact_mult__1__right, fact_less__Suc0, fact_rel__simps_I32_J, fact_divide__nonneg__neg, arity_Nat__Onat__Rings_Osemiring, arity_Polynomial__Opoly__Groups_Oabs__if, fact_less__iff__Suc__add, fact_real__average__minus__first, fact_zero__less__two, fact_diff__is__0__eq, fact_number__of__Pls, fact_real__of__nat__one, arity_Polynomial__Opoly__Groups_Ozero, fact_rp, fact_add__le__imp__le__right, fact__096EX_Ad_0620_O_AALL_Aw_O_A0_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_A_N_N_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096, fact_real__of__nat__le__iff, fact_abs__mult__self, fact_real__mult__less__mono2, fact_sum__squares__eq__zero__iff, fact_abs__norm__cancel, fact_le__add__diff__inverse, fact_zabs__less__one__iff, arity_Int__Oint__Rings_Ocomm__ring__1, fact_add__le__mono, fact_add__diff__inverse, fact_convex__bound__le, arity_Int__Oint__Groups_Olinordered__ab__group__add, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_mult__less__imp__less__left, fact_le__diff__iff, arity_Nat__Onat__Groups_Oone, fact_diff__Suc__Suc, fact_add__imp__eq, arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_le__square, fact_less__iff__diff__less__0, fact_zadd__zmult__distrib, fact_real__le__linear, fact_zadd__zminus__inverse2, fact_nonzero__eq__divide__eq, fact_ab__semigroup__add__class_Oadd__ac_I1_J, arity_RealDef__Oreal__Groups_Oab__semigroup__mult, arity_Int__Oint__Rings_Ozero__neq__one, arity_RealDef__Oreal__Fields_Ofield, fact_half__gt__zero, arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_minus__poly__code_I1_J, fact_nat__less__le, arity_Complex__Ocomplex__RealVector_Oreal__normed__vector, fact_no__zero__divisors, fact_less__SucE, fact_gt__half__sum, fact_le__cube, fact_zless__add1__eq, fact_add__less__mono1, fact_add__le__cancel__left, fact_eq__divide__eq, fact_divisors__zero, arity_Polynomial__Opoly__Rings_Olinordered__ring, fact_nonzero__norm__divide, fact_mult__sgn__abs, arity_RealDef__Oreal__Groups_Ogroup__add, arity_Polynomial__Opoly__Groups_Ocomm__monoid__add, arity_Polynomial__Opoly__Groups_Oone, fact_poly__eq__iff, fact_double__add__less__zero__iff__single__add__less__zero, fact_minus__divide__left, fact_DERIV__mult__lemma, arity_RealDef__Oreal__Groups_Olinordered__ab__group__add, fact_arctan__bounded, fact_less__diff__iff, fact_odd__less__0, fact_tan__45, fact_pi__less__4, arity_Int__Oint__Groups_Omonoid__add, fact_add__Suc__shift, fact_real__of__nat__add, fact_mult__1, fact_rel__simps_I22_J, fact_less__special_I1_J, fact_le__special_I2_J, arity_Complex__Ocomplex__Int_Onumber, fact_divide__self, fact_diff__special_I2_J, fact_arctan__tan, fact_pi__half__less__two, fact_real__of__nat__inject, fact_norm__triangle__ineq2, fact_less__half__sum, arity_Int__Oint__Rings_Ocomm__semiring__0, fact_less__SucI, fact_Suc__not__Zero, arity_Complex__Ocomplex__Groups_Ozero, fact__0960_A_060_Acmod_A_Iw_A_N_Az_J_A_G_Acmod_A_Iw_A_N_Az_J_A_060_Ad_061_061_062_Acmod_A_Ipoly_Ap_Aw_A_N_Apoly_Ap_Az_J_A_060_Aabs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_A_P_A2_096, arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add, fact_add__2__eq__Suc_H, fact_not__square__less__zero, fact_Suc__lessI, fact_add__Suc__right, fact_less__bin__lemma, arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add, arity_Int__Oint__Rings_Olinordered__ring__strict, fact_mult_Odiff__right, arity_Complex__Ocomplex__Rings_Ocomm__semiring__0, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J
% 66.59/17.78  % No. of inferences in proof: 2504
% 66.59/17.78  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 17310 ms resp. 16797 ms w/o parsing
% 69.28/18.15  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 69.28/18.17  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------