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

View TPTP
Problem Process solution in
SystemOnTSTP Download .tgz
%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SWW237+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n005.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 09:09:43 AM UTC 2026

% Result   : Theorem 243.31s 69.69s
% Output   : Refutation 249.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   42
%            Number of leaves      : 1266
% Syntax   : Number of formulae    : 3439 ( 921 unt;   0 typ;   5 def)
%            Number of atoms       : 9608 (3086 equ;   0 cnn)
%            Maximal formula atoms :   17 (   2 avg)
%            Number of connectives : 46096 (2057   ~;1356   |; 699   &;38319   @)
%                                         ( 251 <=>;3414  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   4   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  119 ( 116 usr;  14 con; 0-4 aty)
%            Number of variables   : 6943 (   7   ^;6858   !;  73   ?;6943   :)
%                                         (   0  !>;   0  ?*;   0  @-;   5  @+)

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

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

thf(v_da_____decl,type,
    v_da____: $i ).

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

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

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

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

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

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

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

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

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

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

thf(v_cs_____decl,type,
    v_cs____: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(class_Rings_Osemiring__0_decl,type,
    class_Rings_Osemiring__0: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(sk2_decl,type,
    sk2: $i > $i > $i > $i > $i ).

thf(sk8_decl,type,
    sk8: $i > $i ).

thf(sk16_decl,type,
    sk16: $i > $i ).

thf(sk22_decl,type,
    sk22: $i > $i ).

thf(sk26_decl,type,
    sk26: $i > $i > $i ).

thf(sk2_def,definition,
    ( sk2
    = ( ^ [A: $i,B: $i,C: $i,D: $i] :
        @+[E: $i] :
          ~ ( E @ ( D @ hAPP ) @ ( E @ ( C @ hAPP ) @ ( A @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ).

thf(sk8_def,definition,
    ( sk8
    = ( @+[A: $i > $i] :
        ! [B: $i] :
          ( ( B @ c_Nat_OSuc @ A )
          = B ) ) ) ).

thf(sk16_def,definition,
    ( sk16
    = ( @+[A: $i > $i] :
        ! [B: $i] :
          ( ( B @ c_Nat_OSuc @ A )
          = B ) ) ) ).

thf(sk22_def,definition,
    ( sk22
    = ( ^ [A: $i] :
        @+[B: $i] :
          ( A
          = ( B @ c_Nat_OSuc ) ) ) ) ).

thf(sk26_def,definition,
    ( sk26
    = ( ^ [A: $i,B: $i] :
        @+[C: $i] :
          ( ! [D: $i] :
              ( ( A @ ( D @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
             => ( C @ ( D @ ( B @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ 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 ) ) ) ) ) ) ).

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

thf(5437,plain,
    tc_RealDef_Oreal @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).

thf(812,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/sandbox2/benchmark/theBenchmark.p',fact_divide__nonpos__pos) ).

thf(4188,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)],[812]) ).

thf(714,axiom,
    tc_Nat_Onat @ class_Orderings_Oorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).

thf(3883,plain,
    tc_Nat_Onat @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

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

thf(1469,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Rings_Odvd )
        & ( D @ class_Rings_Ocomm__ring ) )
     => ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
       => ! [E: $i,F: $i] :
            ( ( ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
             => ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) )
            & ( ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
             => ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(100,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__num) ).

thf(1633,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(804,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/sandbox2/benchmark/theBenchmark.p',fact_le__minus__iff) ).

thf(4169,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)],[804]) ).

thf(1193,axiom,
    tc_RealDef_Oreal @ class_Groups_Ocancel__comm__monoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add) ).

thf(5320,plain,
    tc_RealDef_Oreal @ class_Groups_Ocancel__comm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).

thf(846,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/sandbox2/benchmark/theBenchmark.p',fact_divide__neg__neg) ).

thf(4290,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)],[846]) ).

thf(181,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).

thf(1982,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(1032,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/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).

thf(4877,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)],[1032]) ).

thf(62,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
      = ( A @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).

thf(1501,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
      = ( A @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(308,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 @ hAPP ) @ hAPP ) )
          = ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__pos) ).

thf(2452,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 @ hAPP ) @ hAPP ) )
          = ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

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

thf(4294,plain,
    v_c____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).

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

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

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

thf(559,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/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).

thf(3403,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)],[559]) ).

thf(3404,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(miniscope,[status(thm)],[3403]) ).

thf(3405,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
      | ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(cnf,[status(esa)],[3404]) ).

thf(3406,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
      | ( A
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(lifteq,[status(thm)],[3405]) ).

thf(3407,plain,
    ! [A: $i] :
      ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    inference(simp,[status(thm)],[3406]) ).

thf(5601,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
      | ~ ( v_cs____ @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,3407]) ).

thf(5602,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
       != tc_Nat_Onat )
      | ~ ( v_cs____ @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[5601]) ).

thf(15110,plain,
    ! [A: $i] :
      ( ( ( v_cs____ @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       != ( v_c____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
      | ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
       != tc_Nat_Onat )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4294,5602]) ).

thf(15111,plain,
    ! [A: $i] :
      ( ( ( v_cs____ @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       != ( v_c____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
      | ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
       != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[15110]) ).

thf(15149,plain,
    ! [A: $i] :
      ( ( ( v_c____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
       != v_cs____ )
      | ( A
       != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
      | ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
       != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[15111]) ).

thf(15170,plain,
    ( ( ( v_c____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
     != v_cs____ )
    | ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[15149]) ).

thf(934,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/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).

thf(4560,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)],[934]) ).

thf(160,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 @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
          = ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) )
      <=> ( C
          = ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff2) ).

thf(1879,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 @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) )
         => ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
            = ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) )
        & ( ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
            = ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) )
         => ( C
            = ( A @ ( D @ ( E @ ( B @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(1240,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/sandbox2/benchmark/theBenchmark.p',fact_real__add__left__mono) ).

thf(5422,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)],[1240]) ).

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

thf(1337,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_Oone__class_Oone ) )
         => ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
        & ( ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
         => ( A
            = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(378,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ozero__neq__one )
     => ( ( A @ c_Groups_Oone__class_Oone )
       != ( A @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).

thf(2744,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)],[378]) ).

thf(1022,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ocomm__monoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).

thf(4835,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)],[1022]) ).

thf(898,axiom,
    tc_Int_Oint @ class_Rings_Osemiring__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).

thf(4450,plain,
    tc_Int_Oint @ class_Rings_Osemiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).

thf(279,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__add__eq__iff) ).

thf(2341,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

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

thf(3008,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

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

thf(4239,plain,
    tc_Int_Oint @ class_Groups_Ozero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ( A @ class_Groups_Ozero )
     => ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Polynomial_OpCons ) ) )
        = ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__0__0) ).

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

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

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

thf(5591,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ class_Groups_Ozero )
       != ( A @ class_Groups_Ozero ) )
      | ~ $true
      | ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Polynomial_OpCons ) ) )
        = ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(paramod_ordered,[status(thm)],[4239,1272]) ).

thf(5592,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ class_Groups_Ozero )
       != ( A @ class_Groups_Ozero ) )
      | ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Polynomial_OpCons ) ) )
        = ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(simp,[status(thm)],[5591]) ).

thf(5593,plain,
    ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Polynomial_OpCons ) ) )
    = ( tc_Int_Oint @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ),
    inference(pattern_uni,[status(thm)],[5592:[bind(A,$thf( tc_Int_Oint ))]]) ).

thf(220,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 @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DERIV__mult__lemma) ).

thf(2131,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 @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Rings_Oinverse__class_Odivide ) ) @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(1045,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/sandbox2/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).

thf(4909,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)],[1045]) ).

thf(835,axiom,
    tc_Complex_Ocomplex @ class_Rings_Osemiring__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).

thf(4262,plain,
    tc_Complex_Ocomplex @ class_Rings_Osemiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).

thf(204,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ c_Nat_OSuc )
        = ( A @ c_Nat_OSuc ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).

thf(2072,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)],[204]) ).

thf(1165,axiom,
    tc_RealDef_Oreal @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

thf(5260,plain,
    tc_RealDef_Oreal @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).

thf(1041,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ? [C: $i] :
          ( ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ 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__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ononneg__bounded) ).

thf(4899,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ? [C: $i] :
          ( ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ 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__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).

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

thf(1559,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

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

thf(3312,plain,
    ! [A: $i] : ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(3313,plain,
    ! [A: $i] : ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ),
    inference(cnf,[status(esa)],[3312]) ).

thf(1166,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/sandbox2/benchmark/theBenchmark.p',fact_less__eq__real__def) ).

thf(5261,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)],[1166]) ).

thf(5262,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: $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 ) ) ) ) ) ),
    inference(miniscope,[status(thm)],[5261]) ).

thf(5263,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( D @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
        | ( D != C ) )
      & ( ( C @ ( D @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
        | ~ ( C @ ( D @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( B = A )
        | ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
        | ~ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(cnf,[status(esa)],[5262]) ).

thf(5266,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ( B != A ) ),
    inference(cnfConj,[status(thm)],[5263]) ).

thf(5269,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ( B != A ) ),
    inference(lifteq,[status(thm)],[5266]) ).

thf(5270,plain,
    ! [A: $i] : ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(simp,[status(thm)],[5269]) ).

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

thf(1358,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B != A )
          & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
       => ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) )
      & ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
       => ( ( B != A )
          & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(1359,plain,
    ( ! [A: $i,B: $i] :
        ( ( ( B != A )
          & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
       => ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) )
    & ! [A: $i,B: $i] :
        ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
       => ( ( B != A )
          & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(miniscope,[status(thm)],[1358]) ).

thf(1360,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ~ ( D @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        | ( D = C )
        | ~ ( C @ ( D @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      & ( ( C @ ( D @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        | ( D = C )
        | ~ ( C @ ( D @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      & ( ( B != A )
        | ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        | ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      & ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        | ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        | ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(cnf,[status(esa)],[1359]) ).

thf(1364,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ( B = A )
      | ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(cnfConj,[status(thm)],[1360]) ).

thf(1369,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ( B = A ) ),
    inference(lifteq,[status(thm)],[1364]) ).

thf(1370,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ( B = A ) ),
    inference(simp,[status(thm)],[1369]) ).

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

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

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

thf(10697,plain,
    ! [B: $i,A: $i] :
      ( ( B != v_da____ )
      | ~ ( v_mazh @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1370,1263]) ).

thf(10698,plain,
    ! [A: $i] :
      ( ~ ( v_mazh @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( v_da____ @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(pattern_uni,[status(thm)],[10697:[bind(A,$thf( A )),bind(B,$thf( v_da____ ))]]) ).

thf(17858,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       != ( v_mazh @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      | ~ $true
      | ~ ( v_da____ @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( B @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5270,10698]) ).

thf(17859,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       != ( v_mazh @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      | ~ ( v_da____ @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( B @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[17858]) ).

thf(17860,plain,
    ( ~ ( v_da____ @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
    | ~ ( v_mazh @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(pattern_uni,[status(thm)],[17859:[bind(A,$thf( v_mazh )),bind(B,$thf( v_mazh ))]]) ).

thf(19180,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_da____ @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ $true
      | ~ ( v_mazh @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3313,17860]) ).

thf(19181,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_da____ @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ ( v_mazh @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[19180]) ).

thf(19249,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != v_da____ )
      | ( A != v_mazh )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ~ ( v_mazh @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[19181]) ).

thf(19269,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != v_da____ )
    | ~ ( v_mazh @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[19249]) ).

thf(21157,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_mazh @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != v_da____ )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3313,19269]) ).

thf(21158,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_mazh @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != v_da____ ) ),
    inference(simp,[status(thm)],[21157]) ).

thf(21215,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != v_mazh )
      | ( A != v_da____ )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != v_da____ ) ),
    inference(simp,[status(thm)],[21158]) ).

thf(21237,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != v_mazh )
    | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != v_da____ ) ),
    inference(simp,[status(thm)],[21215]) ).

thf(21434,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
    | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != v_mazh )
    | ( v_cs____ != v_da____ ) ),
    inference(paramod_ordered,[status(thm)],[1280,21237]) ).

thf(21439,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Nat_Onat )
    | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != v_mazh )
    | ( v_cs____ != v_da____ ) ),
    inference(simp,[status(thm)],[21434]) ).

thf(649,axiom,
    tc_Int_Oint @ class_Rings_Olinordered__semiring__1__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).

thf(3666,plain,
    tc_Int_Oint @ class_Rings_Olinordered__semiring__1__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(122,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__idom )
     => ( ( ( A
           != ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
         => ( ( ~ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Osgn__class_Osgn ) )
                = ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) ) ) )
            & ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Osgn__class_Osgn ) )
                = ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone ) ) ) ) )
        & ( ( A
            = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Osgn__class_Osgn ) )
            = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__poly__def) ).

thf(1729,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__idom )
     => ( ( ( A
           != ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
         => ( ( ~ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Osgn__class_Osgn ) )
                = ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) ) ) )
            & ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ tc_Polynomial_Opoly @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Osgn__class_Osgn ) )
                = ( B @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone ) ) ) ) )
        & ( ( A
            = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Osgn__class_Osgn ) )
            = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(17,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone )
        = ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Polynomial_OpCons ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__poly__def) ).

thf(1316,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone )
        = ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Polynomial_OpCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(1317,plain,
    ! [A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone )
        = ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Polynomial_OpCons ) ) ) )
      | ~ ( A @ class_Rings_Ocomm__semiring__1 ) ),
    inference(cnf,[status(esa)],[1316]) ).

thf(1318,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Rings_Ocomm__semiring__1 )
      | ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Polynomial_OpCons ) ) )
        = ( A @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone ) ) ),
    inference(lifteq,[status(thm)],[1317]) ).

thf(7,axiom,
    ( ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) )
   != ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons_Oprems) ).

thf(1276,plain,
    ( ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) )
   != ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(1277,plain,
    ( ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) )
   != ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ),
    inference(polarity_switch,[status(thm)],[1276]) ).

thf(1278,plain,
    ( ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) )
   != ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ),
    inference(lifteq,[status(thm)],[1277]) ).

thf(5516,plain,
    ( ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) )
   != v_cs____ ),
    inference(rewrite,[status(thm)],[1278,1280]) ).

thf(5741,plain,
    ! [A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Polynomial_OpCons ) ) )
       != ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) ) )
      | ( ( A @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone )
       != v_cs____ )
      | ~ ( A @ class_Rings_Ocomm__semiring__1 ) ),
    inference(paramod_ordered,[status(thm)],[1318,5516]) ).

thf(5784,plain,
    ! [A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
       != v_cs____ )
      | ( ( A @ c_Groups_Oone__class_Oone )
       != v_c____ )
      | ( A != tc_Complex_Ocomplex )
      | ( ( A @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone )
       != v_cs____ )
      | ~ ( A @ class_Rings_Ocomm__semiring__1 ) ),
    inference(simp,[status(thm)],[5741]) ).

thf(5801,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != v_cs____ )
    | ( ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone )
     != v_c____ )
    | ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone )
     != v_cs____ )
    | ~ ( tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__1 ) ),
    inference(simp,[status(thm)],[5784]) ).

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

thf(4958,plain,
    tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).

thf(6284,plain,
    ( ( v_cs____ != v_cs____ )
    | ( ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone )
     != v_c____ )
    | ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone )
     != v_cs____ )
    | ~ $true ),
    inference(rewrite,[status(thm)],[5801,1280,4958]) ).

thf(6285,plain,
    ( ( ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone )
     != v_c____ )
    | ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone )
     != v_cs____ ) ),
    inference(simp,[status(thm)],[6284]) ).

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

thf(2463,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
           => ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
          & ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(163,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_abs__zmult__eq__1) ).

thf(1899,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[163]) ).

thf(149,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__right) ).

thf(1840,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(1021,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/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).

thf(4834,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)],[1021]) ).

thf(14551,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 ) ) )
     != ( v_mazh @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4834,1263]) ).

thf(14552,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 ) ) )
   != ( v_mazh @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(simp,[status(thm)],[14551]) ).

thf(14585,plain,
    ( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
     != v_mazh )
    | ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
     != v_da____ )
    | ( tc_Int_Oint != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[14552]) ).

thf(16,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Ocomm__monoid__add )
     => ( ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) @ ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Polynomial_OpCons ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pCons) ).

thf(1313,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Ocomm__monoid__add )
     => ( ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) @ ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Polynomial_OpCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(1314,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) @ ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Polynomial_OpCons ) ) ) )
      | ~ ( E @ class_Groups_Ocomm__monoid__add ) ),
    inference(cnf,[status(esa)],[1313]) ).

thf(1315,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ class_Groups_Ocomm__monoid__add )
      | ( ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) @ ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( E @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Polynomial_OpCons ) ) ) ) ),
    inference(lifteq,[status(thm)],[1314]) ).

thf(318,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).

thf(2499,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(1077,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/sandbox2/benchmark/theBenchmark.p',fact_minus__equation__iff) ).

thf(4992,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)],[1077]) ).

thf(1114,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Oidom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oring__no__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).

thf(5131,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)],[1114]) ).

thf(265,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power) ).

thf(2280,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(1043,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( A != B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).

thf(4904,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( A != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).

thf(493,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( A @ ( B @ c_Complex_Orcis ) @ ( C @ ( D @ c_Complex_Orcis ) @ ( tc_Complex_Ocomplex @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Complex_Orcis ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rcis__mult) ).

thf(3172,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( A @ ( B @ c_Complex_Orcis ) @ ( C @ ( D @ c_Complex_Orcis ) @ ( tc_Complex_Ocomplex @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( D @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ c_Complex_Orcis ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

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

thf(4166,plain,
    ( v_c____
   != ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).

thf(253,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__div__algebra )
     => ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_RealVector_Onorm__class_Onorm ) )
        = ( A @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__power) ).

thf(2250,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__div__algebra )
     => ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_RealVector_Onorm__class_Onorm ) )
        = ( A @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(651,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/sandbox2/benchmark/theBenchmark.p',fact_real__add__eq__0__iff) ).

thf(3674,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)],[651]) ).

thf(3675,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: $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 ) ) ) ) ),
    inference(miniscope,[status(thm)],[3674]) ).

thf(3676,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( ( C @ ( D @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
        | ( C
         != ( D @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ) )
      & ( ( 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 ) ) ) ),
    inference(cnf,[status(esa)],[3675]) ).

thf(3678,plain,
    ! [B: $i,A: $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 ) ) ) ),
    inference(cnfConj,[status(thm)],[3676]) ).

thf(3680,plain,
    ! [B: $i,A: $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 ) ) ) ),
    inference(lifteq,[status(thm)],[3678]) ).

thf(3681,plain,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
      = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
    inference(simp,[status(thm)],[3680]) ).

thf(873,axiom,
    tc_Nat_Onat @ class_Rings_Olinordered__semidom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).

thf(4376,plain,
    tc_Nat_Onat @ class_Rings_Olinordered__semidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).

thf(1151,axiom,
    tc_RealDef_Oreal @ class_Groups_Osgn__if,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Osgn__if) ).

thf(5242,plain,
    tc_RealDef_Oreal @ class_Groups_Osgn__if,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).

thf(722,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/sandbox2/benchmark/theBenchmark.p',fact_ab__left__minus) ).

thf(3910,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)],[722]) ).

thf(1065,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/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__zero) ).

thf(4960,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)],[1065]) ).

thf(952,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/sandbox2/benchmark/theBenchmark.p',fact_zero__reorient) ).

thf(4603,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)],[952]) ).

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

thf(3498,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
     => ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( 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)],[600]) ).

thf(73,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oord) ).

thf(1533,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

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

thf(1541,plain,
    ! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(1542,plain,
    ! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ),
    inference(cnf,[status(esa)],[1541]) ).

thf(19178,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_mazh @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ ( v_da____ @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3313,17860]) ).

thf(19179,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_mazh @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ ( v_da____ @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[19178]) ).

thf(19253,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != v_mazh )
      | ( A != v_da____ )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ~ ( v_da____ @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[19179]) ).

thf(19272,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != v_mazh )
    | ~ ( v_da____ @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[19253]) ).

thf(21546,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_da____ @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != v_mazh )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1542,19272]) ).

thf(21547,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_da____ @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != v_mazh ) ),
    inference(simp,[status(thm)],[21546]) ).

thf(21558,plain,
    ! [A: $i] :
      ( ( A != v_da____ )
      | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
       != v_mazh )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != v_mazh ) ),
    inference(simp,[status(thm)],[21547]) ).

thf(21570,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_mazh )
    | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != v_mazh ) ),
    inference(simp,[status(thm)],[21558]) ).

thf(13,axiom,
    ! [A: $i,B: $i] :
      ( ( v_cs____
       != ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
     => ? [C: $i] :
        ! [D: $i] :
          ( ( D @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( D @ ( v_cs____ @ ( A @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons_Ohyps) ).

thf(1305,plain,
    ! [A: $i,B: $i] :
      ( ( v_cs____
       != ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
     => ? [C: $i] :
        ! [D: $i] :
          ( ( D @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( D @ ( v_cs____ @ ( A @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(552,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/sandbox2/benchmark/theBenchmark.p',fact_abs__norm__cancel) ).

thf(3382,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)],[552]) ).

thf(58,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C = B )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       => ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__eq__le__trans) ).

thf(1486,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C = B )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       => ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(1252,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/sandbox2/benchmark/theBenchmark.p',fact_zle__linear) ).

thf(5444,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)],[1252]) ).

thf(762,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 @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_divide__left__mono) ).

thf(4043,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 @ hAPP ) @ hAPP ) @ ( 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)],[762]) ).

thf(608,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).

thf(3532,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(3533,plain,
    ~ ? [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    inference(miniscope,[status(thm)],[3532]) ).

thf(3534,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    inference(cnf,[status(esa)],[3533]) ).

thf(217,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( 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 ) )
        | ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).

thf(2117,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
          | ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( 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 ) )
          | ( 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)],[217]) ).

thf(92,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
     => ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incr__lemma) ).

thf(1596,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
     => ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(1117,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0) ).

thf(5139,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)],[1117]) ).

thf(5140,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    inference(cnf,[status(esa)],[5139]) ).

thf(5141,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    inference(lifteq,[status(thm)],[5140]) ).

thf(391,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_decr__lemma) ).

thf(2808,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
     => ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[391]) ).

thf(68,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 @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__less__div__pos) ).

thf(1522,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 @ hAPP ) @ hAPP ) @ ( 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)],[68]) ).

thf(677,axiom,
    tc_Int_Oint @ class_Groups_Ocomm__monoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).

thf(3762,plain,
    tc_Int_Oint @ class_Groups_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(352,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( A @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( C @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
           => ( D @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).

thf(2644,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( A @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( C @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
           => ( D @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(692,axiom,
    tc_Nat_Onat @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).

thf(3813,plain,
    tc_Nat_Onat @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).

thf(510,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 @ hAPP ) @ hAPP ) )
      = ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).

thf(3230,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 @ hAPP ) @ hAPP ) )
      = ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(830,axiom,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).

thf(4254,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)],[830]) ).

thf(4255,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    inference(cnf,[status(esa)],[4254]) ).

thf(4256,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    inference(lifteq,[status(thm)],[4255]) ).

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

thf(5323,plain,
    v_ma @ ( v_mazh @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( v_mzh @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).

thf(15368,plain,
    ( ( ( v_ma @ ( v_mazh @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( v_mzh @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     != ( v_mazh @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[5323,1263]) ).

thf(15369,plain,
    ( ( v_ma @ ( v_mazh @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( v_mzh @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
   != ( v_mazh @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(simp,[status(thm)],[15368]) ).

thf(15409,plain,
    ( ( ( v_ma @ ( v_mazh @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
     != v_mazh )
    | ( v_mzh != v_da____ )
    | ( tc_RealDef_Oreal != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[15369]) ).

thf(15428,plain,
    ( ( ( v_ma @ ( v_mazh @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
     != v_mazh )
    | ( v_mzh != v_da____ ) ),
    inference(simp,[status(thm)],[15409]) ).

thf(25165,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
       != ( v_ma @ ( v_mazh @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) )
      | ( A != v_mazh )
      | ( v_mzh != v_da____ ) ),
    inference(paramod_ordered,[status(thm)],[4256,15428]) ).

thf(25193,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != v_ma )
    | ( v_mazh != v_mazh )
    | ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( v_mzh != v_da____ ) ),
    inference(simp,[status(thm)],[25165]) ).

thf(25212,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != v_ma )
    | ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( v_mzh != v_da____ ) ),
    inference(simp,[status(thm)],[25193]) ).

thf(25301,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
    | ( v_ma != v_cs____ )
    | ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( v_mzh != v_da____ ) ),
    inference(paramod_ordered,[status(thm)],[1280,25212]) ).

thf(25304,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Nat_Onat )
    | ( v_ma != v_cs____ )
    | ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( v_mzh != v_da____ ) ),
    inference(simp,[status(thm)],[25301]) ).

thf(1101,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/sandbox2/benchmark/theBenchmark.p',fact_right__minus__eq) ).

thf(5069,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)],[1101]) ).

thf(293,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ozero__neq__one )
     => ( ( A @ c_Groups_Ozero__class_Ozero )
       != ( A @ c_Groups_Oone__class_Oone ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__neq__one) ).

thf(2393,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)],[293]) ).

thf(2394,plain,
    ! [A: $i] :
      ( ( ( A @ c_Groups_Ozero__class_Ozero )
       != ( A @ c_Groups_Oone__class_Oone ) )
      | ~ ( A @ class_Rings_Ozero__neq__one ) ),
    inference(cnf,[status(esa)],[2393]) ).

thf(2395,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Rings_Ozero__neq__one )
      | ( ( A @ c_Groups_Oone__class_Oone )
       != ( A @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(lifteq,[status(thm)],[2394]) ).

thf(613,axiom,
    tc_Int_Oint @ class_Groups_Ouminus,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).

thf(3549,plain,
    tc_Int_Oint @ class_Groups_Ouminus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(48,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 @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).

thf(1443,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 @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(1078,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/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__right__mono) ).

thf(5000,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)],[1078]) ).

thf(567,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/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).

thf(3417,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)],[567]) ).

thf(583,axiom,
    ! [A: $i] :
      ( ( A @ class_Groups_Oab__group__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ominus) ).

thf(3460,plain,
    ! [A: $i] :
      ( ( A @ class_Groups_Oab__group__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ominus ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(41,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Odvd )
     => ( ( C
          = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
       => ( C @ ( B @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvdI) ).

thf(1422,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Odvd )
     => ( ( C
          = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
       => ( C @ ( B @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(252,axiom,
    ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
    = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__nat__def) ).

thf(2248,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)],[252]) ).

thf(1142,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/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).

thf(5224,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)],[1142]) ).

thf(266,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 @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__lt) ).

thf(2282,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 @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(90,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__ring )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).

thf(1591,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__ring )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(216,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__minus) ).

thf(2114,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(1230,axiom,
    tc_RealDef_Oreal @ class_RealVector_Oreal__field,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__field) ).

thf(5405,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__field,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).

thf(398,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( 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__eq ) ) )
       => ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
         => ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__neg__lemma) ).

thf(2837,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( 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__eq ) ) )
       => ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
         => ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

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

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

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

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

thf(45,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 @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).

thf(1435,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 @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(1436,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
    inference(cnf,[status(esa)],[1435]) ).

thf(1437,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
    inference(lifteq,[status(thm)],[1436]) ).

thf(910,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__le) ).

thf(4487,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).

thf(948,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/sandbox2/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).

thf(4592,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)],[948]) ).

thf(880,axiom,
    tc_Int_Oint @ class_Rings_Oordered__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).

thf(4403,plain,
    tc_Int_Oint @ class_Rings_Oordered__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).

thf(571,axiom,
    tc_Complex_Ocomplex @ class_Groups_Oone,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).

thf(3429,plain,
    tc_Complex_Ocomplex @ class_Groups_Oone,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(887,axiom,
    ! [A: $i] :
      ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0__right) ).

thf(4418,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)],[887]) ).

thf(362,axiom,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc )
     != A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).

thf(2686,plain,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(643,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/sandbox2/benchmark/theBenchmark.p',fact_sgn__greater) ).

thf(3648,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)],[643]) ).

thf(753,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/sandbox2/benchmark/theBenchmark.p',fact_diff__add__cancel) ).

thf(4011,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)],[753]) ).

thf(547,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__eq) ).

thf(3365,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)],[547]) ).

thf(578,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/sandbox2/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).

thf(3446,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)],[578]) ).

thf(540,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_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1) ).

thf(3338,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_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(841,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/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).

thf(4279,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)],[841]) ).

thf(684,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/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).

thf(3776,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)],[684]) ).

thf(3777,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
        | ( B != A ) )
      & ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
        | ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(cnf,[status(esa)],[3776]) ).

thf(3779,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ( B != A ) ),
    inference(cnfConj,[status(thm)],[3777]) ).

thf(3780,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ( B != A ) ),
    inference(lifteq,[status(thm)],[3779]) ).

thf(3781,plain,
    ! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(simp,[status(thm)],[3780]) ).

thf(961,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/sandbox2/benchmark/theBenchmark.p',fact_abs__diff__triangle__ineq) ).

thf(4650,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)],[961]) ).

thf(424,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ c_Nat_OSuc )
        = ( A @ c_Nat_OSuc ) )
     => ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).

thf(2930,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ c_Nat_OSuc )
        = ( A @ c_Nat_OSuc ) )
     => ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(2931,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( ( B @ c_Nat_OSuc )
       != ( A @ c_Nat_OSuc ) ) ),
    inference(cnf,[status(esa)],[2930]) ).

thf(2932,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( ( B @ c_Nat_OSuc )
       != ( A @ c_Nat_OSuc ) ) ),
    inference(lifteq,[status(thm)],[2931]) ).

thf(2933,plain,
    ? [A: $i > $i] :
    ! [B: $i] :
      ( ( B @ c_Nat_OSuc @ A )
      = B ),
    inference(detectInverse,[status(thm)],[2932]) ).

thf(2934,plain,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc @ sk16 )
      = A ),
    inference(cnf,[status(esa)],[2933]) ).

thf(19653,plain,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc @ sk16 )
      = A ),
    inference(lifteq,[status(thm)],[2934]) ).

thf(647,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).

thf(3660,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)],[647]) ).

thf(3661,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    inference(cnf,[status(esa)],[3660]) ).

thf(3662,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    inference(lifteq,[status(thm)],[3661]) ).

thf(25064,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
       != ( v_ma @ ( v_mazh @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) )
      | ( A != v_mazh )
      | ( v_mzh != v_da____ ) ),
    inference(paramod_ordered,[status(thm)],[3662,15428]) ).

thf(25078,plain,
    ( ( v_ma != v_mazh )
    | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != v_mazh )
    | ( tc_Nat_Onat != tc_RealDef_Oreal )
    | ( v_mzh != v_da____ ) ),
    inference(simp,[status(thm)],[25064]) ).

thf(26,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
        = ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__power__minus) ).

thf(1352,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
        = ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(1353,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
        = ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) ) )
      | ~ ( C @ class_Rings_Olinordered__idom ) ),
    inference(cnf,[status(esa)],[1352]) ).

thf(1354,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ class_Rings_Olinordered__idom )
      | ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
        = ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) ) ) ),
    inference(lifteq,[status(thm)],[1353]) ).

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

thf(5412,plain,
    tc_RealDef_Oreal @ class_Rings_Oring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).

thf(60,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
    <=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__reduce) ).

thf(1492,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       => ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      & ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(1493,plain,
    ( ! [A: $i,B: $i] :
        ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       => ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
    & ! [A: $i,B: $i] :
        ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(miniscope,[status(thm)],[1492]) ).

thf(1494,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        | ~ ( C @ ( D @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      & ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        | ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(cnf,[status(esa)],[1493]) ).

thf(1496,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(cnfConj,[status(thm)],[1494]) ).

thf(1497,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[1496]) ).

thf(115,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( C @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        & ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
     => ( ( B = A )
       => ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__less__eq__trans) ).

thf(1705,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( C @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        & ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
     => ( ( B = A )
       => ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(448,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 @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__left__mono__neg) ).

thf(3017,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 @ hAPP ) @ hAPP ) @ ( 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)],[448]) ).

thf(927,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/sandbox2/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).

thf(4543,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)],[927]) ).

thf(1242,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/sandbox2/benchmark/theBenchmark.p',fact_real__le__antisym) ).

thf(5425,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)],[1242]) ).

thf(42,axiom,
    ! [A: $i] :
      ( ( A @ class_Groups_Oab__group__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).

thf(1426,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)],[42]) ).

thf(505,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/sandbox2/benchmark/theBenchmark.p',fact_poly__1) ).

thf(3217,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)],[505]) ).

thf(607,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/sandbox2/benchmark/theBenchmark.p',fact_abs__sum__triangle__ineq) ).

thf(3530,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)],[607]) ).

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

thf(5438,plain,
    tc_RealDef_Oreal @ class_Groups_Oab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).

thf(1427,plain,
    ! [A: $i] :
      ( ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ ( A @ class_Groups_Oab__group__add ) ),
    inference(cnf,[status(esa)],[1426]) ).

thf(21249,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[5438,1427]) ).

thf(21250,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[21249]) ).

thf(21251,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[21250:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(21323,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[21251,1427]) ).

thf(21324,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[21323]) ).

thf(21325,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[21324:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(21489,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[21325,1427]) ).

thf(21490,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[21489]) ).

thf(21491,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[21490:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(21802,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[21491,1427]) ).

thf(21803,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[21802]) ).

thf(21804,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[21803:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(22329,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[21804,1427]) ).

thf(22330,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[22329]) ).

thf(22331,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[22330:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(22544,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22331,1427]) ).

thf(22545,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[22544]) ).

thf(22546,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[22545:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(23057,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22546,1427]) ).

thf(23058,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[23057]) ).

thf(23059,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[23058:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(23436,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[23059,1427]) ).

thf(23437,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[23436]) ).

thf(23438,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[23437:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(777,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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__eq) ).

thf(4090,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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).

thf(105,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__ring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).

thf(1655,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)],[105]) ).

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

thf(5361,plain,
    tc_RealDef_Oreal @ class_Rings_Omult__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).

thf(129,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
       => ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power__same) ).

thf(1756,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
       => ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

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

thf(4079,plain,
    tc_Complex_Ocomplex @ class_Groups_Oab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).

thf(21241,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4079,1427]) ).

thf(21242,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[21241]) ).

thf(21243,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[21242:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(21294,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[21243,1427]) ).

thf(21295,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[21294]) ).

thf(21296,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[21295:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly ))]]) ).

thf(21389,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[21296,1427]) ).

thf(21390,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[21389]) ).

thf(21391,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[21390:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(21749,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[21391,1427]) ).

thf(21750,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[21749]) ).

thf(21751,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[21750:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(22050,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[21751,1427]) ).

thf(22051,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[22050]) ).

thf(22052,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[22051:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(22467,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22052,1427]) ).

thf(22468,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[22467]) ).

thf(22469,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[22468:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(22968,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22469,1427]) ).

thf(22969,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[22968]) ).

thf(22970,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[22969:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(758,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/sandbox2/benchmark/theBenchmark.p',fact_minus__le__iff) ).

thf(4026,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)],[758]) ).

thf(454,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( C @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        & ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       => ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__le__trans) ).

thf(3044,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( C @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        & ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       => ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(1177,axiom,
    tc_RealDef_Oreal @ class_Rings_Ozero__neq__one,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).

thf(5288,plain,
    tc_RealDef_Oreal @ class_Rings_Ozero__neq__one,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).

thf(924,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/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).

thf(4528,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)],[924]) ).

thf(494,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 @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).

thf(3175,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 @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

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

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

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

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

thf(1189,axiom,
    tc_RealDef_Oreal @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).

thf(5316,plain,
    tc_RealDef_Oreal @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).

thf(1162,axiom,
    tc_RealDef_Oreal @ class_Groups_Ocomm__monoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).

thf(5257,plain,
    tc_RealDef_Oreal @ class_Groups_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).

thf(958,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).

thf(4638,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)],[958]) ).

thf(1119,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/sandbox2/benchmark/theBenchmark.p',fact_zless__add1__eq) ).

thf(5146,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)],[1119]) ).

thf(158,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__1) ).

thf(1872,plain,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

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

thf(1325,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__ring__1 )
     => ( ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ ( A @ ( C @ c_Polynomial_Osynthetic__div ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(1326,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ ( A @ ( C @ c_Polynomial_Osynthetic__div ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
        = A )
      | ~ ( C @ class_Rings_Ocomm__ring__1 ) ),
    inference(cnf,[status(esa)],[1325]) ).

thf(1327,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ class_Rings_Ocomm__ring__1 )
      | ( ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ ( A @ ( C @ c_Polynomial_Opoly ) @ hAPP ) @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ ( A @ ( C @ c_Polynomial_Osynthetic__div ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
        = A ) ),
    inference(lifteq,[status(thm)],[1326]) ).

thf(654,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/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).

thf(3693,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)],[654]) ).

thf(699,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/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).

thf(3826,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)],[699]) ).

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

thf(4114,plain,
    tc_Int_Oint @ class_Groups_Oab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).

thf(21263,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4114,1427]) ).

thf(21264,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[21263]) ).

thf(21265,plain,
    tc_Int_Oint @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[21264:[bind(A,$thf( tc_Int_Oint ))]]) ).

thf(21352,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[21265,1427]) ).

thf(21353,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[21352]) ).

thf(21354,plain,
    tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[21353:[bind(A,$thf( tc_Int_Oint @ tc_Polynomial_Opoly ))]]) ).

thf(21700,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[21354,1427]) ).

thf(21701,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[21700]) ).

thf(21702,plain,
    tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[21701:[bind(A,$thf( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(21855,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[21702,1427]) ).

thf(21856,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[21855]) ).

thf(21857,plain,
    tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[21856:[bind(A,$thf( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(565,axiom,
    ! [A: $i] :
      ( ( A @ class_Groups_Ocomm__monoid__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Omonoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).

thf(3414,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)],[565]) ).

thf(892,axiom,
    tc_Complex_Ocomplex @ class_Rings_Odivision__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).

thf(4435,plain,
    tc_Complex_Ocomplex @ class_Rings_Odivision__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).

thf(620,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/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__add__cancel) ).

thf(3577,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)],[620]) ).

thf(659,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/sandbox2/benchmark/theBenchmark.p',fact_le__imp__0__less) ).

thf(3717,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)],[659]) ).

thf(1132,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/sandbox2/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).

thf(5190,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)],[1132]) ).

thf(5191,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(cnf,[status(esa)],[5190]) ).

thf(5192,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(lifteq,[status(thm)],[5191]) ).

thf(997,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/sandbox2/benchmark/theBenchmark.p',fact_norm__zero) ).

thf(4762,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)],[997]) ).

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

thf(1452,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 ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( 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
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(1453,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 ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
    & ! [A: $i,B: $i] :
        ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( 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
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(miniscope,[status(thm)],[1452]) ).

thf(1454,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( D @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
        | ~ ( D @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( C @ ( D @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
        | ( C
         != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
      & ( ( 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 ) )
        | ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(cnf,[status(esa)],[1453]) ).

thf(1455,plain,
    ! [B: $i,A: $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 ) )
      | ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(cnfConj,[status(thm)],[1454]) ).

thf(1458,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( 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 ) ) ),
    inference(lifteq,[status(thm)],[1455]) ).

thf(1054,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( A != B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).

thf(4941,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)],[1054]) ).

thf(147,axiom,
    ! [A: $i,B: $i] :
      ( ( B
        = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
     => ( ( B
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
        | ( A
          = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).

thf(1835,plain,
    ! [A: $i,B: $i] :
      ( ( B
        = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
     => ( ( 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)],[147]) ).

thf(1134,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/sandbox2/benchmark/theBenchmark.p',fact_zero__less__divide__iff) ).

thf(5195,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)],[1134]) ).

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

thf(3730,plain,
    tc_Int_Oint @ class_Rings_Olinordered__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(205,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).

thf(2082,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(304,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__is__0) ).

thf(2432,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 @ hAPP ) @ hAPP ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
      & ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
          = ( 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)],[304]) ).

thf(2433,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 @ hAPP ) @ hAPP ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
    & ! [A: $i,B: $i] :
        ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
          = ( 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(miniscope,[status(thm)],[2432]) ).

thf(2434,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
        | ( C
         != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
      & ( ( ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
        | ( D
         != ( 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 ) )
        | ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
         != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
    inference(cnf,[status(esa)],[2433]) ).

thf(2437,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
      | ( A
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(cnfConj,[status(thm)],[2434]) ).

thf(2441,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
      | ( A
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(lifteq,[status(thm)],[2437]) ).

thf(2442,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(simp,[status(thm)],[2441]) ).

thf(1456,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( 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 ) ) ),
    inference(cnfConj,[status(thm)],[1454]) ).

thf(1459,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( 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 ) ) ),
    inference(lifteq,[status(thm)],[1456]) ).

thf(1460,plain,
    ! [A: $i] : ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    inference(simp,[status(thm)],[1459]) ).

thf(32568,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1460,3407]) ).

thf(32569,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[32568]) ).

thf(32655,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
      | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != B )
      | ( tc_Nat_Onat != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[32569]) ).

thf(32682,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(simp,[status(thm)],[32655]) ).

thf(38905,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
      | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(paramod_ordered,[status(thm)],[2442,32682]) ).

thf(38906,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
    inference(simp,[status(thm)],[38905]) ).

thf(38972,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
      | ( ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) )
       != ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) ) ) ),
    inference(simp,[status(thm)],[38906]) ).

thf(39017,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) )
     != ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) ) ),
    inference(simp,[status(thm)],[38972]) ).

thf(799,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/sandbox2/benchmark/theBenchmark.p',fact_divide_Oadd) ).

thf(4156,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)],[799]) ).

thf(326,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( A @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( E @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( E @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
           => ( B @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).

thf(2531,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( A @ ( B @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( E @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( E @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
           => ( B @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(56,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Osgn__if )
     => ( ( ( A
           != ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( ( ~ ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
                = ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) )
            & ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
                = ( B @ c_Groups_Oone__class_Oone ) ) ) ) )
        & ( ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
            = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__if) ).

thf(1475,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Osgn__if )
     => ( ( ( A
           != ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( ( ~ ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
                = ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) )
            & ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
                = ( B @ c_Groups_Oone__class_Oone ) ) ) ) )
        & ( ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
            = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(1476,plain,
    ! [B: $i,A: $i] :
      ( ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
          = ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
        | ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
        | ( A
          = ( B @ c_Groups_Ozero__class_Ozero ) )
        | ~ ( B @ class_Groups_Osgn__if ) )
      & ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
          = ( B @ c_Groups_Oone__class_Oone ) )
        | ~ ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
        | ( A
          = ( B @ c_Groups_Ozero__class_Ozero ) )
        | ~ ( B @ class_Groups_Osgn__if ) )
      & ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
          = ( B @ c_Groups_Ozero__class_Ozero ) )
        | ( A
         != ( B @ c_Groups_Ozero__class_Ozero ) )
        | ~ ( B @ class_Groups_Osgn__if ) ) ),
    inference(cnf,[status(esa)],[1475]) ).

thf(1478,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
        = ( B @ c_Groups_Oone__class_Oone ) )
      | ~ ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
      | ( A
        = ( B @ c_Groups_Ozero__class_Ozero ) )
      | ~ ( B @ class_Groups_Osgn__if ) ),
    inference(cnfConj,[status(thm)],[1476]) ).

thf(1482,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
      | ~ ( B @ class_Groups_Osgn__if )
      | ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
        = ( B @ c_Groups_Oone__class_Oone ) )
      | ( A
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(lifteq,[status(thm)],[1478]) ).

thf(1082,axiom,
    tc_Int_Oint @ class_Groups_Oordered__ab__group__add__abs,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).

thf(5024,plain,
    tc_Int_Oint @ class_Groups_Oordered__ab__group__add__abs,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).

thf(700,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).

thf(3836,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).

thf(861,axiom,
    tc_Nat_Onat @ class_Groups_Ocomm__monoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).

thf(4343,plain,
    tc_Nat_Onat @ class_Groups_Ocomm__monoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).

thf(512,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/sandbox2/benchmark/theBenchmark.p',fact_add__Suc) ).

thf(3236,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)],[512]) ).

thf(637,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Oidom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oring__1__no__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).

thf(3629,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)],[637]) ).

thf(1143,axiom,
    tc_Complex_Ocomplex @ class_Rings_Osemiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).

thf(5227,plain,
    tc_Complex_Ocomplex @ class_Rings_Osemiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).

thf(370,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       => ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__trans) ).

thf(2723,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       => ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(435,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono) ).

thf(2972,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(1159,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/sandbox2/benchmark/theBenchmark.p',fact_add__left__mono) ).

thf(5252,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)],[1159]) ).

thf(680,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__0 )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__semigroup__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).

thf(3766,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)],[680]) ).

thf(1224,axiom,
    tc_RealDef_Oreal @ class_Rings_Olinordered__ring__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).

thf(5393,plain,
    tc_RealDef_Oreal @ class_Rings_Olinordered__ring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).

thf(382,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ocomm__monoid__mult )
     => ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1) ).

thf(2763,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ocomm__monoid__mult )
     => ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(246,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
     => ( ( B != A )
       => ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__neq__trans) ).

thf(2227,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
     => ( ( B != A )
       => ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(88,axiom,
    ! [A: $i,B: $i] :
      ( ( B = A )
    <=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oeq__iff) ).

thf(1576,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(2249,plain,
    ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
    = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ),
    inference(lifteq,[status(thm)],[2248]) ).

thf(438,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).

thf(2981,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)],[438]) ).

thf(2982,plain,
    ~ ? [A: $i] : ( A @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(miniscope,[status(thm)],[2981]) ).

thf(2983,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(cnf,[status(esa)],[2982]) ).

thf(13394,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
       != ( A @ c_Nat_OSuc ) )
      | ~ ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2249,2983]) ).

thf(13395,plain,
    ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(pattern_uni,[status(thm)],[13394:[bind(A,$thf( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ))]]) ).

thf(13908,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
    | ~ ( v_cs____ @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,13395]) ).

thf(13915,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Nat_Onat )
    | ~ ( v_cs____ @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(simp,[status(thm)],[13908]) ).

thf(47,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing) ).

thf(1441,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(837,axiom,
    tc_Complex_Ocomplex @ class_Rings_Oring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).

thf(4266,plain,
    tc_Complex_Ocomplex @ class_Rings_Oring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).

thf(954,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( B != A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).

thf(4618,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( B != A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).

thf(467,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__one__le__power) ).

thf(3088,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(94,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).

thf(1601,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)],[94]) ).

thf(33,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__semiring__1 )
     => ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__left) ).

thf(1386,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__semiring__1 )
     => ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

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

thf(4030,plain,
    tc_Nat_Onat @ class_Rings_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(120,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__decreasing) ).

thf(1724,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(295,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Omonoid__mult )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__add) ).

thf(2400,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Omonoid__mult )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(71,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).

thf(1529,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(5147,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 ) ) ) )
    & ! [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 ) ) ) ) ) ),
    inference(miniscope,[status(thm)],[5146]) ).

thf(5148,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
        | ( D != C ) )
      & ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
        | ~ ( C @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( 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 ) ) ) ) ),
    inference(cnf,[status(esa)],[5147]) ).

thf(5151,plain,
    ! [B: $i,A: $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 ) ),
    inference(cnfConj,[status(thm)],[5148]) ).

thf(5154,plain,
    ! [B: $i,A: $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 ) ),
    inference(lifteq,[status(thm)],[5151]) ).

thf(5155,plain,
    ! [A: $i] : ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
    inference(simp,[status(thm)],[5154]) ).

thf(48997,plain,
    ! [B: $i,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_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
      | ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5192,5155]) ).

thf(48998,plain,
    tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ),
    inference(pattern_uni,[status(thm)],[48997:[bind(A,$thf( tc_Int_Oint @ c_Groups_Oone__class_Oone )),bind(B,$thf( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ))]]) ).

thf(49301,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[48998,3407]) ).

thf(49302,plain,
    ! [A: $i] :
      ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[49301]) ).

thf(49365,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
      | ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
       != A )
      | ( tc_Int_Oint != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[49302]) ).

thf(49388,plain,
    ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
    | ( tc_Int_Oint != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[49365]) ).

thf(49854,plain,
    ( ( tc_Int_Oint != tc_Nat_Onat )
    | ( tc_Int_Oint != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[49388]) ).

thf(49907,plain,
    tc_Int_Oint != tc_Nat_Onat,
    inference(simp,[status(thm)],[49854]) ).

thf(49910,plain,
    ! [B: $i,A: $i] :
      ( ( B != tc_Int_Oint )
      | ( A != tc_Nat_Onat )
      | ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1370,49907]) ).

thf(49911,plain,
    ! [A: $i] :
      ( ( A != tc_Nat_Onat )
      | ~ ( tc_Int_Oint @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(pattern_uni,[status(thm)],[49910:[bind(A,$thf( A )),bind(B,$thf( tc_Int_Oint ))]]) ).

thf(49917,plain,
    ( ~ ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
    | ~ ( tc_Nat_Onat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[49911]) ).

thf(55513,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ $true
      | ~ ( tc_Nat_Onat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3313,49917]) ).

thf(55514,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( tc_Int_Oint @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ ( tc_Nat_Onat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[55513]) ).

thf(55617,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != tc_Int_Oint )
      | ( A != tc_Nat_Onat )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ~ ( tc_Nat_Onat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[55514]) ).

thf(55637,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != tc_Int_Oint )
    | ~ ( tc_Nat_Onat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[55617]) ).

thf(59240,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( tc_Nat_Onat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != tc_Int_Oint )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1542,55637]) ).

thf(59241,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( tc_Nat_Onat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[59240]) ).

thf(59268,plain,
    ! [A: $i] :
      ( ( A != tc_Nat_Onat )
      | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
       != tc_Int_Oint )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[59241]) ).

thf(59281,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != tc_Int_Oint )
    | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[59268]) ).

thf(4419,plain,
    ! [A: $i] :
      ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    inference(cnf,[status(esa)],[4418]) ).

thf(4420,plain,
    ! [A: $i] :
      ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = A ),
    inference(lifteq,[status(thm)],[4419]) ).

thf(25882,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
       != ( v_ma @ ( v_mazh @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) )
      | ( A != v_mazh )
      | ( v_mzh != v_da____ ) ),
    inference(paramod_ordered,[status(thm)],[4420,15428]) ).

thf(25915,plain,
    ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
     != v_ma )
    | ( v_mazh != v_mazh )
    | ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( v_mzh != v_da____ ) ),
    inference(simp,[status(thm)],[25882]) ).

thf(25940,plain,
    ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
     != v_ma )
    | ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( v_mzh != v_da____ ) ),
    inference(simp,[status(thm)],[25915]) ).

thf(431,axiom,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).

thf(2955,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(2956,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = A ),
    inference(cnf,[status(esa)],[2955]) ).

thf(2957,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = A ),
    inference(lifteq,[status(thm)],[2956]) ).

thf(696,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__ring )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).

thf(3820,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__ring )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).

thf(275,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__ring )
     => ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__square) ).

thf(2328,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__ring )
     => ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(196,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).

thf(2039,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( 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)],[196]) ).

thf(1175,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/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).

thf(5284,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)],[1175]) ).

thf(598,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).

thf(3495,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(461,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/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__eq) ).

thf(3061,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)],[461]) ).

thf(1130,axiom,
    tc_Int_Oint @ class_Groups_Oordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).

thf(5188,plain,
    tc_Int_Oint @ class_Groups_Oordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).

thf(671,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/sandbox2/benchmark/theBenchmark.p',fact_abs__leI) ).

thf(3744,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)],[671]) ).

thf(1178,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Lattices_Oboolean__algebra )
     => ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_compl__le__compl__iff) ).

thf(5289,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Lattices_Oboolean__algebra )
     => ( ( ( 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)],[1178]) ).

thf(284,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 @ hAPP ) @ hAPP ) )
      = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).

thf(2356,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 @ hAPP ) @ hAPP ) )
      = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(36,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
    <=> ( ( B = A )
        | ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__less) ).

thf(1398,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B = A )
          | ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
            & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      & ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       => ( ( B = A )
          | ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
            & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(1399,plain,
    ( ! [A: $i,B: $i] :
        ( ( ( B = A )
          | ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
            & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
    & ! [A: $i,B: $i] :
        ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       => ( ( B = A )
          | ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
            & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ) ),
    inference(miniscope,[status(thm)],[1398]) ).

thf(1400,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( D @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        | ( D != C ) )
      & ( ( C @ ( D @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        | ( D @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        | ~ ( C @ ( D @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      & ( ( B = A )
        | ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        | ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      & ( ( B = A )
        | ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        | ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(cnf,[status(esa)],[1399]) ).

thf(1404,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ( B != A ) ),
    inference(cnfConj,[status(thm)],[1400]) ).

thf(1408,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ( B != A ) ),
    inference(lifteq,[status(thm)],[1404]) ).

thf(1409,plain,
    ! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ),
    inference(simp,[status(thm)],[1408]) ).

thf(824,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/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).

thf(4238,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)],[824]) ).

thf(11,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Ozero )
     => ( ( ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) )
          = ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) ) )
      <=> ( ( C = A )
          & ( D = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__iff) ).

thf(1287,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Ozero )
     => ( ( ( ( C = A )
            & ( D = B ) )
         => ( ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) )
            = ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) ) ) )
        & ( ( ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) )
            = ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) ) )
         => ( ( C = A )
            & ( D = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(19234,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_mazh @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ ( v_da____ @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1542,17860]) ).

thf(19235,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_mazh @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ ( v_da____ @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[19234]) ).

thf(19247,plain,
    ! [A: $i] :
      ( ( A != v_mazh )
      | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
       != v_da____ )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ~ ( v_da____ @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[19235]) ).

thf(19267,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_da____ )
    | ~ ( v_da____ @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[19247]) ).

thf(929,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/sandbox2/benchmark/theBenchmark.p',fact_right__minus) ).

thf(4546,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)],[929]) ).

thf(730,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/sandbox2/benchmark/theBenchmark.p',fact_double__zero__sym) ).

thf(3938,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)],[730]) ).

thf(1152,axiom,
    tc_RealDef_Oreal @ class_Groups_Ozero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).

thf(5243,plain,
    tc_RealDef_Oreal @ class_Groups_Ozero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).

thf(7275,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Groups_Ozero )
       != ( A @ class_Groups_Ozero ) )
      | ~ $true
      | ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Polynomial_OpCons ) ) )
        = ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(paramod_ordered,[status(thm)],[5243,1272]) ).

thf(7276,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Groups_Ozero )
       != ( A @ class_Groups_Ozero ) )
      | ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Polynomial_OpCons ) ) )
        = ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(simp,[status(thm)],[7275]) ).

thf(7277,plain,
    ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Polynomial_OpCons ) ) )
    = ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ),
    inference(pattern_uni,[status(thm)],[7276:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(865,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/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).

thf(4348,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)],[865]) ).

thf(23243,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22970,1427]) ).

thf(23244,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[23243]) ).

thf(23245,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[23244:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(24297,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[23245,1427]) ).

thf(24298,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[24297]) ).

thf(24299,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[24298:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(25497,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[24299,1427]) ).

thf(25498,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[25497]) ).

thf(25499,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[25498:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(990,axiom,
    tc_Nat_Onat @ class_Groups_Oab__semigroup__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).

thf(4743,plain,
    tc_Nat_Onat @ class_Groups_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).

thf(1183,axiom,
    tc_RealDef_Oreal @ class_Groups_Ominus,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ominus) ).

thf(5306,plain,
    tc_RealDef_Oreal @ class_Groups_Ominus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).

thf(1030,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( ( B != A )
          & ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).

thf(4866,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( ( ( B != A )
            & ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
         => ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( B != A )
            & ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).

thf(375,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 @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).

thf(2735,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 @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(936,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/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).

thf(4563,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)],[936]) ).

thf(182,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 @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).

thf(1985,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 @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(889,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/sandbox2/benchmark/theBenchmark.p',fact_odd__nonzero) ).

thf(4422,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)],[889]) ).

thf(131,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).

thf(1760,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(1061,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_Complex_Orcis ) )
      = ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rcis__zero__mod) ).

thf(4954,plain,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_Complex_Orcis ) )
      = ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).

thf(4955,plain,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_Complex_Orcis ) )
      = ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) ),
    inference(cnf,[status(esa)],[4954]) ).

thf(4956,plain,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ c_Complex_Orcis ) )
      = ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) ),
    inference(lifteq,[status(thm)],[4955]) ).

thf(885,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).

thf(4415,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)],[885]) ).

thf(542,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 @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).

thf(3342,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 @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[542]) ).

thf(1169,axiom,
    tc_RealDef_Oreal @ class_Groups_Oone,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).

thf(5274,plain,
    tc_RealDef_Oreal @ class_Groups_Oone,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).

thf(1099,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/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).

thf(5064,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)],[1099]) ).

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

thf(2839,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(2840,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = A ),
    inference(cnf,[status(esa)],[2839]) ).

thf(2841,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = A ),
    inference(lifteq,[status(thm)],[2840]) ).

thf(49657,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) ) )
      | ( A
       != ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2841,39017]) ).

thf(49768,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) )
       != A )
      | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) )
       != ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ),
    inference(simp,[status(thm)],[49657]) ).

thf(49845,plain,
    ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) )
   != ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ),
    inference(simp,[status(thm)],[49768]) ).

thf(50665,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) ) )
      | ( A
       != ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ),
    inference(paramod_ordered,[status(thm)],[2957,49845]) ).

thf(50738,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
    | ( ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) )
     != ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ),
    inference(simp,[status(thm)],[50665]) ).

thf(50772,plain,
    ( ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) )
   != ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ),
    inference(simp,[status(thm)],[50738]) ).

thf(632,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/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).

thf(3617,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)],[632]) ).

thf(155,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( 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 @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      <=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel1) ).

thf(1860,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
         => ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
        & ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
         => ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__0 )
     => ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Osynthetic__div ) ) )
        = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__0) ).

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

thf(243,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 @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__div__pos__less) ).

thf(2217,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 @ hAPP ) @ hAPP ) @ ( 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)],[243]) ).

thf(18,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oidom )
     => ( ( B
         != ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
       => ( ~ ( B @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ c_Nat_OSuc @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) )
          & ( B @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order) ).

thf(1319,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oidom )
     => ( ( B
         != ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
       => ( ~ ( B @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ c_Nat_OSuc @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) )
          & ( B @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(1320,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ~ ( B @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ c_Nat_OSuc @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) )
        | ( B
          = ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
        | ~ ( C @ class_Rings_Oidom ) )
      & ( ( B @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) )
        | ( B
          = ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
        | ~ ( C @ class_Rings_Oidom ) ) ),
    inference(cnf,[status(esa)],[1319]) ).

thf(1321,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) )
      | ( B
        = ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
      | ~ ( C @ class_Rings_Oidom ) ),
    inference(cnfConj,[status(thm)],[1320]) ).

thf(1323,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( C @ class_Rings_Oidom )
      | ( B
        = ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(lifteq,[status(thm)],[1321]) ).

thf(485,axiom,
    ! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__square) ).

thf(3148,plain,
    ! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(65,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 @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__le) ).

thf(1509,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 @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(1510,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
       != ( F @ c_Groups_Oone__class_Oone ) )
      | ~ ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( F @ class_Rings_Olinordered__semiring__1 ) ),
    inference(cnf,[status(esa)],[1509]) ).

thf(1511,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( A @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( A @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( B @ ( F @ c_Groups_Ozero__class_Ozero @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( D @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( D @ ( E @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( F @ class_Rings_Olinordered__semiring__1 )
      | ( ( A @ ( B @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
       != ( F @ c_Groups_Oone__class_Oone ) ) ),
    inference(lifteq,[status(thm)],[1510]) ).

thf(262,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring )
     => ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).

thf(2274,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring )
     => ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[262]) ).

thf(593,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__comm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).

thf(3485,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)],[593]) ).

thf(15661,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_da____ @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ ( v_mazh @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ $true
      | ~ ( B @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1542,10698]) ).

thf(15662,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_da____ @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ ( v_mazh @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( B @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[15661]) ).

thf(15663,plain,
    ( ~ ( v_mazh @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
    | ~ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(pattern_uni,[status(thm)],[15662:[bind(A,$thf( v_da____ )),bind(B,$thf( tc_Nat_Onat @ c_Groups_Oone__class_Oone ))]]) ).

thf(144,axiom,
    ! [A: $i] :
      ( ( ( A
         != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
       => ( ( ~ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
              = ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) ) )
          & ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
              = ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) )
      & ( ( A
          = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
          = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zsgn__def) ).

thf(1819,plain,
    ! [A: $i] :
      ( ( ( A
         != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
       => ( ( ~ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
              = ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) ) )
          & ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
              = ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) )
      & ( ( A
          = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
          = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(1820,plain,
    ( ! [A: $i] :
        ( ( A
         != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
       => ( ( ~ ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
              = ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) ) )
          & ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
              = ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) )
    & ! [A: $i] :
        ( ( A
          = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
          = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
    inference(miniscope,[status(thm)],[1819]) ).

thf(1821,plain,
    ! [B: $i,A: $i] :
      ( ( ( ( B @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
          = ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) )
        | ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
        | ( B
          = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
      & ( ( ( B @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
          = ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
        | ~ ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
        | ( B
          = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
      & ( ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
          = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
        | ( A
         != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
    inference(cnf,[status(esa)],[1820]) ).

thf(1822,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
        = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
      | ( A
       != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(cnfConj,[status(thm)],[1821]) ).

thf(1825,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
        = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
      | ( A
       != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(lifteq,[status(thm)],[1822]) ).

thf(1826,plain,
    ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Osgn__class_Osgn ) )
    = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
    inference(simp,[status(thm)],[1825]) ).

thf(1113,axiom,
    tc_Nat_Onat @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

thf(5130,plain,
    tc_Nat_Onat @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).

thf(562,axiom,
    tc_Nat_Onat @ class_Rings_Olinordered__comm__semiring__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).

thf(3410,plain,
    tc_Nat_Onat @ class_Rings_Olinordered__comm__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(673,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/sandbox2/benchmark/theBenchmark.p',fact_add1__zle__eq) ).

thf(3749,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)],[673]) ).

thf(1127,axiom,
    tc_Int_Oint @ class_Groups_Oabs__if,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oabs__if) ).

thf(5182,plain,
    tc_Int_Oint @ class_Groups_Oabs__if,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).

thf(334,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 @ hAPP ) @ hAPP ) )
          = ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__left__cancel) ).

thf(2562,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 @ hAPP ) @ hAPP ) )
            = ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
        & ( ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
            = ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(24410,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[23438,1427]) ).

thf(24411,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[24410]) ).

thf(24412,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[24411:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(26186,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[24412,1427]) ).

thf(26187,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[26186]) ).

thf(26188,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[26187:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(35261,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[26188,1427]) ).

thf(35262,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[35261]) ).

thf(35263,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[35262:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(40953,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[35263,1427]) ).

thf(40954,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[40953]) ).

thf(40955,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[40954:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(47905,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[40955,1427]) ).

thf(47906,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[47905]) ).

thf(47907,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[47906:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(999,axiom,
    tc_Complex_Ocomplex @ class_Groups_Ouminus,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ouminus) ).

thf(4766,plain,
    tc_Complex_Ocomplex @ class_Groups_Ouminus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).

thf(52,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semiring__strict )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).

thf(1462,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semiring__strict )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[52]) ).

thf(891,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/sandbox2/benchmark/theBenchmark.p',fact_add__eq__0__iff) ).

thf(4428,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)],[891]) ).

thf(78,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessI) ).

thf(1545,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)],[78]) ).

thf(21208,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
    | ( v_cs____ != v_da____ )
    | ~ ( v_mazh @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,19269]) ).

thf(21220,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Nat_Onat )
    | ( v_cs____ != v_da____ )
    | ~ ( v_mazh @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[21208]) ).

thf(1140,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/sandbox2/benchmark/theBenchmark.p',fact_less__Suc0) ).

thf(5215,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)],[1140]) ).

thf(5216,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 ) ) ) )
    & ! [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 ) ) ) ),
    inference(miniscope,[status(thm)],[5215]) ).

thf(5217,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
        | ( B
         != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
      & ( ( 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 ) ) ) ) ),
    inference(cnf,[status(esa)],[5216]) ).

thf(5219,plain,
    ! [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 ) ) ),
    inference(cnfConj,[status(thm)],[5217]) ).

thf(5221,plain,
    ! [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 ) ) ),
    inference(lifteq,[status(thm)],[5219]) ).

thf(5222,plain,
    tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ),
    inference(simp,[status(thm)],[5221]) ).

thf(15210,plain,
    tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ),
    inference(rewrite,[status(thm)],[5222,2249]) ).

thf(1338,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        | ( A
         != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
        | ~ ( B @ ( 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 ) )
        | ~ ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        | ~ ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(cnf,[status(esa)],[1337]) ).

thf(1340,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ( A
       != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
      | ~ ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(cnfConj,[status(thm)],[1338]) ).

thf(1342,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( B @ ( 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 ) ) ),
    inference(lifteq,[status(thm)],[1340]) ).

thf(1343,plain,
    ! [A: $i] :
      ( ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[1342]) ).

thf(15228,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( 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 @ ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[15210,1343]) ).

thf(15229,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( 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 @ ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[15228]) ).

thf(15230,plain,
    tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ),
    inference(pattern_uni,[status(thm)],[15229:[bind(A,$thf( tc_Nat_Onat @ c_Groups_Oone__class_Oone ))]]) ).

thf(302,axiom,
    ! [A: $i,B: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
        = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
    <=> ( ( A
          = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
        & ( B
          = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).

thf(2418,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 @ hAPP ) @ hAPP ) ) ) )
      & ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
          = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
       => ( ( 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)],[302]) ).

thf(2419,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 @ hAPP ) @ hAPP ) ) ) )
    & ! [A: $i,B: $i] :
        ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
          = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
       => ( ( A
            = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
          & ( B
            = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ) ),
    inference(miniscope,[status(thm)],[2418]) ).

thf(2420,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
          = ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
        | ( C
         != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
        | ( D
         != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) )
      & ( ( A
          = ( 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 @ hAPP ) @ hAPP ) ) ) )
      & ( ( 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 @ hAPP ) @ hAPP ) ) ) ) ),
    inference(cnf,[status(esa)],[2419]) ).

thf(2423,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
        = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ( A
       != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
      | ( B
       != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ),
    inference(cnfConj,[status(thm)],[2420]) ).

thf(2426,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( 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(lifteq,[status(thm)],[2423]) ).

thf(2427,plain,
    ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
    = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ),
    inference(simp,[status(thm)],[2426]) ).

thf(32229,plain,
    tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ),
    inference(rewrite,[status(thm)],[15230,2427]) ).

thf(1028,axiom,
    tc_Int_Oint @ class_Rings_Olinordered__ring__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).

thf(4862,plain,
    tc_Int_Oint @ class_Rings_Olinordered__ring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).

thf(1111,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Opreorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).

thf(5127,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Opreorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).

thf(97,axiom,
    ! [A: $i] :
      ( ( ( A
         != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
       => ( ( ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
              = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ) )
          & ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
              = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) ) ) )
      & ( ( A
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__real__def) ).

thf(1609,plain,
    ! [A: $i] :
      ( ( ( A
         != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
       => ( ( ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
              = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ) )
          & ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
              = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) ) ) )
      & ( ( A
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(348,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).

thf(2635,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(135,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 @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__0__iff__dvd) ).

thf(1773,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oidom )
     => ( ( ( B @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) )
         => ( ( 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 @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(879,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/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).

thf(4390,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)],[879]) ).

thf(1002,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Opreorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).

thf(4771,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Opreorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).

thf(327,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Omonoid__mult )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult) ).

thf(2533,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Omonoid__mult )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(1066,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/sandbox2/benchmark/theBenchmark.p',fact_sgn0) ).

thf(4967,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)],[1066]) ).

thf(995,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Opreorder )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).

thf(4756,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Opreorder )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).

thf(30,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 @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono2) ).

thf(1379,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 @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(553,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/sandbox2/benchmark/theBenchmark.p',fact_divide_Odiff) ).

thf(3385,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)],[553]) ).

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

thf(5256,plain,
    tc_RealDef_Oreal @ class_Rings_Olinordered__idom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).

thf(296,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 @ hAPP ) @ hAPP ) )
           != ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_no__zero__divisors) ).

thf(2403,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 @ hAPP ) @ hAPP ) )
           != ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(67,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).

thf(1514,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B = A )
       => ( ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
          = ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
      & ( ( ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
          = ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(807,axiom,
    ! [A: $i] :
      ( ( A @ class_Groups_Ocancel__comm__monoid__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ocancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).

thf(4179,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)],[807]) ).

thf(1133,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/sandbox2/benchmark/theBenchmark.p',fact_diff__less__Suc) ).

thf(5193,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)],[1133]) ).

thf(912,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/sandbox2/benchmark/theBenchmark.p',fact_abs__le__D1) ).

thf(4492,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)],[912]) ).

thf(1228,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
        <=> ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).

thf(5397,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( ( A = B )
           => ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
          & ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( A = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).

thf(955,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/sandbox2/benchmark/theBenchmark.p',fact_real__add__less__0__iff) ).

thf(4622,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)],[955]) ).

thf(24,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oord )
     => ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).

thf(1344,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oord )
     => ( ( ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ! [E: $i] : ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(1345,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
        | ~ ( A @ ( B @ ( C @ ( D @ sk2 ) ) ) @ ( A @ hAPP ) @ ( A @ ( B @ ( C @ ( D @ sk2 ) ) ) @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
        | ~ ( D @ class_Orderings_Oord ) )
      & ( ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
        | ~ ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
        | ~ ( D @ class_Orderings_Oord ) ) ),
    inference(cnf,[status(esa)],[1344]) ).

thf(1347,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( A @ ( B @ ( C @ ( D @ sk2 ) ) ) @ ( A @ hAPP ) @ ( A @ ( B @ ( C @ ( D @ sk2 ) ) ) @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( D @ class_Orderings_Oord ) ),
    inference(cnfConj,[status(thm)],[1345]) ).

thf(855,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).

thf(4317,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)],[855]) ).

thf(646,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/sandbox2/benchmark/theBenchmark.p',fact_abs__of__neg) ).

thf(3657,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)],[646]) ).

thf(1090,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/sandbox2/benchmark/theBenchmark.p',fact_abs__add__one__gt__zero) ).

thf(5043,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)],[1090]) ).

thf(5044,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(cnf,[status(esa)],[5043]) ).

thf(1085,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_RealVector_Onorm__class_Onorm ) )
      = ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__norm__def) ).

thf(5031,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)],[1085]) ).

thf(5032,plain,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_RealVector_Onorm__class_Onorm ) )
      = ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) ) ),
    inference(cnf,[status(esa)],[5031]) ).

thf(5033,plain,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
      = ( A @ ( tc_RealDef_Oreal @ c_RealVector_Onorm__class_Onorm ) ) ),
    inference(lifteq,[status(thm)],[5032]) ).

thf(56855,plain,
    ! [A: $i] : ( A @ ( tc_RealDef_Oreal @ c_RealVector_Onorm__class_Onorm ) @ ( 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(rewrite,[status(thm)],[5044,5033]) ).

thf(1217,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/sandbox2/benchmark/theBenchmark.p',fact_real__less__def) ).

thf(5363,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)],[1217]) ).

thf(5364,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: $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 ) ) ) ) ) ),
    inference(miniscope,[status(thm)],[5363]) ).

thf(5365,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( D @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
        | ( D = C )
        | ~ ( C @ ( D @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( 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 ) ) ) ) ),
    inference(cnf,[status(esa)],[5364]) ).

thf(5367,plain,
    ! [B: $i,A: $i] :
      ( ( B != A )
      | ~ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(cnfConj,[status(thm)],[5365]) ).

thf(5369,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
      | ( B != A ) ),
    inference(lifteq,[status(thm)],[5367]) ).

thf(5370,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
    inference(simp,[status(thm)],[5369]) ).

thf(56896,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_RealDef_Oreal @ c_RealVector_Onorm__class_Onorm ) @ ( 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 ) ) )
       != ( B @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[56855,5370]) ).

thf(56897,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_RealVector_Onorm__class_Onorm ) @ ( 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 ) ) )
     != ( B @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[56896]) ).

thf(57034,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_RealDef_Oreal @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
       != B )
      | ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero )
       != B )
      | ( tc_RealDef_Oreal != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[56897]) ).

thf(57072,plain,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
     != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
    inference(simp,[status(thm)],[57034]) ).

thf(871,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ? [C: $i] :
          ( ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ 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 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Opos__bounded) ).

thf(4368,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ? [C: $i] :
          ( ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ 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 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).

thf(15068,plain,
    ! [A: $i] :
      ( ( ( v_c____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       != ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4294,5370]) ).

thf(15069,plain,
    ! [A: $i] :
      ( ( v_c____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     != ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[15068]) ).

thf(15138,plain,
    ! [A: $i] :
      ( ( ( v_c____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
       != A )
      | ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero )
       != A )
      | ( tc_RealDef_Oreal != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[15069]) ).

thf(15161,plain,
    ( ( v_c____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
   != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
    inference(simp,[status(thm)],[15138]) ).

thf(734,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oord )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( B = A )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__less__eq__trans) ).

thf(3951,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oord )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( B = A )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).

thf(192,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessD) ).

thf(2024,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)],[192]) ).

thf(103,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/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).

thf(1641,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)],[103]) ).

thf(875,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/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).

thf(4383,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)],[875]) ).

thf(142,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 @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__1__mult) ).

thf(1815,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 @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(441,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 @ hAPP ) @ hAPP ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__divide__eq__eq) ).

thf(2989,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 @ hAPP ) @ hAPP ) ) )
           => ( ( 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 @ hAPP ) @ hAPP ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(1102,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/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).

thf(5076,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)],[1102]) ).

thf(916,axiom,
    tc_Int_Oint @ class_Orderings_Oorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).

thf(4507,plain,
    tc_Int_Oint @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).

thf(159,axiom,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != ( A @ c_Nat_OSuc ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).

thf(1875,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != ( A @ c_Nat_OSuc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(520,axiom,
    ! [A: $i] :
      ( ~ ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_not__real__square__gt__zero) ).

thf(3269,plain,
    ! [A: $i] :
      ( ( ( A
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
       => ~ ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( 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)],[520]) ).

thf(3270,plain,
    ( ! [A: $i] :
        ( ( A
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
       => ~ ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
    & ! [A: $i] :
        ( ~ ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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(miniscope,[status(thm)],[3269]) ).

thf(3271,plain,
    ! [B: $i,A: $i] :
      ( ( ~ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
        | ( B
         != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
      & ( ( A
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
        | ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(cnf,[status(esa)],[3270]) ).

thf(3273,plain,
    ! [A: $i] :
      ( ~ ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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(cnfConj,[status(thm)],[3271]) ).

thf(3275,plain,
    ! [A: $i] :
      ( ~ ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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(lifteq,[status(thm)],[3273]) ).

thf(3276,plain,
    ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
    inference(simp,[status(thm)],[3275]) ).

thf(5672,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
    | ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( v_cs____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,3276]) ).

thf(5675,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( v_cs____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[5672]) ).

thf(6922,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
    | ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ~ ( v_cs____ @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( v_cs____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,5675]) ).

thf(6926,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ~ ( v_cs____ @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( v_cs____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[6922]) ).

thf(6933,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ~ ( v_cs____ @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( v_cs____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[6926]) ).

thf(6971,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
    | ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ~ ( v_cs____ @ ( v_cs____ @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( v_cs____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,6933]) ).

thf(6973,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ~ ( v_cs____ @ ( v_cs____ @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( v_cs____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[6971]) ).

thf(6983,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ~ ( v_cs____ @ ( v_cs____ @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( v_cs____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[6973]) ).

thf(832,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/sandbox2/benchmark/theBenchmark.p',fact_add__pos__pos) ).

thf(4258,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)],[832]) ).

thf(418,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).

thf(2893,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(984,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).

thf(4724,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)],[984]) ).

thf(33428,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[25499,1427]) ).

thf(33429,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[33428]) ).

thf(33430,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[33429:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(39520,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[33430,1427]) ).

thf(39521,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[39520]) ).

thf(39522,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[39521:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(46956,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[39522,1427]) ).

thf(46957,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[46956]) ).

thf(46958,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[46957:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(1120,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Opreorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).

thf(5156,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Opreorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).

thf(31,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).

thf(1381,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(1382,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) )
      | ~ ( B @ class_Rings_Ocomm__semiring__1 ) ),
    inference(cnf,[status(esa)],[1381]) ).

thf(1383,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Rings_Ocomm__semiring__1 )
      | ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(lifteq,[status(thm)],[1382]) ).

thf(429,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 @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( D @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__less) ).

thf(2950,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 @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( D @ ( E @ c_Groups_Oabs__class_Oabs ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(249,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).

thf(2237,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(1074,axiom,
    tc_Int_Oint @ class_Rings_Oring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).

thf(4988,plain,
    tc_Int_Oint @ class_Rings_Oring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).

thf(1245,axiom,
    tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__1__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).

thf(5433,plain,
    tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__1__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).

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

thf(1296,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Ozero )
     => ( ( ( ( A
              = ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
            & ( B
              = ( C @ c_Groups_Ozero__class_Ozero ) ) )
         => ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) )
            = ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) )
        & ( ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) )
            = ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A
              = ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
            & ( B
              = ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(1297,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) )
          = ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
        | ( A
         != ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
        | ( B
         != ( C @ c_Groups_Ozero__class_Ozero ) )
        | ~ ( C @ class_Groups_Ozero ) )
      & ( ( A
          = ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
        | ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) )
         != ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
        | ~ ( C @ class_Groups_Ozero ) )
      & ( ( B
          = ( C @ c_Groups_Ozero__class_Ozero ) )
        | ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) )
         != ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
        | ~ ( C @ class_Groups_Ozero ) ) ),
    inference(cnf,[status(esa)],[1296]) ).

thf(1299,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) )
       != ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
      | ~ ( C @ class_Groups_Ozero ) ),
    inference(cnfConj,[status(thm)],[1297]) ).

thf(1302,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ class_Groups_Ozero )
      | ( A
        = ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) )
       != ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(lifteq,[status(thm)],[1299]) ).

thf(389,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ominus) ).

thf(2794,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

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

thf(2324,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__ring__1 )
     => ( ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) )
        & ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
         => ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(717,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred) ).

thf(3887,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)],[717]) ).

thf(737,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Opreorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
          & ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).

thf(3966,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Opreorder )
     => ( ( ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
         => ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).

thf(499,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/sandbox2/benchmark/theBenchmark.p',fact_poly__zero) ).

thf(3199,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)],[499]) ).

thf(805,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/sandbox2/benchmark/theBenchmark.p',fact_ab__diff__minus) ).

thf(4173,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)],[805]) ).

thf(729,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 @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__le__divide__eq) ).

thf(3934,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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).

thf(1042,axiom,
    tc_Complex_Ocomplex @ class_Groups_Ominus,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ominus) ).

thf(4903,plain,
    tc_Complex_Ocomplex @ class_Groups_Ominus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).

thf(896,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Int_Oring__char__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).

thf(4443,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)],[896]) ).

thf(772,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/sandbox2/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).

thf(4072,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)],[772]) ).

thf(22394,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[21857,1427]) ).

thf(22395,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[22394]) ).

thf(22396,plain,
    tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[22395:[bind(A,$thf( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(22759,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22396,1427]) ).

thf(22760,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[22759]) ).

thf(22761,plain,
    tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[22760:[bind(A,$thf( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(23146,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[22761,1427]) ).

thf(23147,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[23146]) ).

thf(23148,plain,
    tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[23147:[bind(A,$thf( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(23998,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[23148,1427]) ).

thf(23999,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[23998]) ).

thf(24000,plain,
    tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[23999:[bind(A,$thf( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(901,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/sandbox2/benchmark/theBenchmark.p',fact_zero__le__divide__iff) ).

thf(4454,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)],[901]) ).

thf(950,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/sandbox2/benchmark/theBenchmark.p',fact_abs__not__less__zero) ).

thf(4600,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)],[950]) ).

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

thf(3295,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
        = ( B @ ( A @ ( C @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(988,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/sandbox2/benchmark/theBenchmark.p',fact_real__abs__def) ).

thf(4733,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)],[988]) ).

thf(257,axiom,
    ! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__1__left) ).

thf(2259,plain,
    ! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(22,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__left) ).

thf(1334,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(605,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/sandbox2/benchmark/theBenchmark.p',fact_zminus__0) ).

thf(3526,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)],[605]) ).

thf(3527,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(lifteq,[status(thm)],[3526]) ).

thf(575,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oord )
     => ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
          & ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).

thf(3438,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oord )
     => ( ( ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) )
         => ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless ) ) )
         => ( ~ ( B @ ( A @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(156,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/sandbox2/benchmark/theBenchmark.p',fact_less__trans__Suc) ).

thf(1864,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)],[156]) ).

thf(739,axiom,
    ! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).

thf(3972,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)],[739]) ).

thf(3973,plain,
    ! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(cnf,[status(esa)],[3972]) ).

thf(179,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).

thf(1978,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( D @ c_Groups_Oone__class_Oone @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(619,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/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).

thf(3569,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)],[619]) ).

thf(329,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Ofield__inverse__zero )
     => ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__over) ).

thf(2540,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Ofield__inverse__zero )
     => ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Rings_Oinverse__class_Odivide ) ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

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

thf(5311,plain,
    tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).

thf(726,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/sandbox2/benchmark/theBenchmark.p',fact_real__add__minus__iff) ).

thf(3923,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)],[726]) ).

thf(1116,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( B != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).

thf(5135,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)],[1116]) ).

thf(469,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__divide__less__eq) ).

thf(3093,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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(782,axiom,
    tc_Int_Oint @ class_Rings_Olinordered__idom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).

thf(4115,plain,
    tc_Int_Oint @ class_Rings_Olinordered__idom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).

thf(278,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
    <=> ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I2_J) ).

thf(2335,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) )
      & ( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
       => ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

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

thf(5457,plain,
    tc_RealDef_Oreal @ class_Rings_Osemiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1261]) ).

thf(385,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).

thf(2777,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(1214,axiom,
    tc_RealDef_Oreal @ class_Rings_Odivision__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).

thf(5360,plain,
    tc_RealDef_Oreal @ class_Rings_Odivision__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).

thf(932,axiom,
    tc_Complex_Ocomplex @ class_Groups_Ocomm__monoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).

thf(4556,plain,
    tc_Complex_Ocomplex @ class_Groups_Ocomm__monoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).

thf(1164,axiom,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).

thf(5259,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).

thf(9,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Oab__group__add )
     => ( ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) @ ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) @ ( E @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( C @ ( E @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Polynomial_OpCons ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__pCons) ).

thf(1281,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Oab__group__add )
     => ( ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) @ ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) @ ( E @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( C @ ( E @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Polynomial_OpCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(1282,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) @ ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) @ ( E @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( C @ ( E @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Polynomial_OpCons ) ) ) )
      | ~ ( E @ class_Groups_Oab__group__add ) ),
    inference(cnf,[status(esa)],[1281]) ).

thf(1283,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ class_Groups_Oab__group__add )
      | ( ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) @ ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) @ ( E @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( C @ ( E @ tc_Polynomial_Opoly @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Polynomial_OpCons ) ) ) ) ),
    inference(lifteq,[status(thm)],[1282]) ).

thf(682,axiom,
    tc_Int_Oint @ class_Groups_Olinordered__ab__group__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).

thf(3771,plain,
    tc_Int_Oint @ class_Groups_Olinordered__ab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

thf(1013,axiom,
    tc_Nat_Onat @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).

thf(4810,plain,
    tc_Nat_Onat @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).

thf(801,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/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__code_I1_J) ).

thf(4162,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)],[801]) ).

thf(150,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).

thf(1843,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(610,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/sandbox2/benchmark/theBenchmark.p',fact_add__less__le__mono) ).

thf(3537,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)],[610]) ).

thf(406,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( C
          = ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
       => ( ( C @ ( B @ ( 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 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).

thf(2861,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( C
          = ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
       => ( ( C @ ( B @ ( 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 ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(1104,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/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).

thf(5096,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)],[1104]) ).

thf(1220,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/sandbox2/benchmark/theBenchmark.p',fact_real__0__le__divide__iff) ).

thf(5375,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)],[1220]) ).

thf(25,axiom,
    ! [A: $i] :
      ( A
     != ( A @ c_Nat_OSuc ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).

thf(1348,plain,
    ! [A: $i] :
      ( A
     != ( A @ c_Nat_OSuc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(1349,plain,
    ~ ? [A: $i] :
        ( A
        = ( A @ c_Nat_OSuc ) ),
    inference(miniscope,[status(thm)],[1348]) ).

thf(1350,plain,
    ! [A: $i] :
      ( A
     != ( A @ c_Nat_OSuc ) ),
    inference(cnf,[status(esa)],[1349]) ).

thf(1351,plain,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc )
     != A ),
    inference(lifteq,[status(thm)],[1350]) ).

thf(350,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).

thf(2639,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)],[350]) ).

thf(380,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).

thf(2750,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 @ hAPP ) @ hAPP ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) )
      & ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
          = ( 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)],[380]) ).

thf(618,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/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).

thf(3559,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)],[618]) ).

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

thf(3378,plain,
    v_c____ @ ( v_z____ @ ( tc_Complex_Ocomplex @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( v_aa____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( 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)],[550]) ).

thf(1091,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/sandbox2/benchmark/theBenchmark.p',fact_divide__zero) ).

thf(5045,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)],[1091]) ).

thf(1096,axiom,
    tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).

thf(5059,plain,
    tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).

thf(766,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/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).

thf(4055,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)],[766]) ).

thf(1255,axiom,
    tc_RealDef_Oreal @ class_Groups_Oab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).

thf(5448,plain,
    tc_RealDef_Oreal @ class_Groups_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255]) ).

thf(1213,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/sandbox2/benchmark/theBenchmark.p',fact_norm__le__zero__iff) ).

thf(5353,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)],[1213]) ).

thf(653,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/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).

thf(3685,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)],[653]) ).

thf(161,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/sandbox2/benchmark/theBenchmark.p',fact_order__root) ).

thf(1886,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)],[161]) ).

thf(690,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/sandbox2/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).

thf(3808,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)],[690]) ).

thf(453,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ? [C: $i] :
            ( ! [D: $i] :
                ( ( ( ( B @ ( D @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
                    = A )
                  & ( D @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
               => ( D = C ) )
            & ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
              = A )
            & ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__pos__nth__unique) ).

thf(3036,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ? [C: $i] :
            ( ! [D: $i] :
                ( ( ( ( B @ ( D @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
                    = A )
                  & ( D @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
               => ( D = C ) )
            & ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
              = A )
            & ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(869,axiom,
    tc_Int_Oint @ class_Rings_Oordered__ring__abs,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).

thf(4364,plain,
    tc_Int_Oint @ class_Rings_Oordered__ring__abs,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).

thf(288,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/sandbox2/benchmark/theBenchmark.p',fact_poly__add) ).

thf(2371,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)],[288]) ).

thf(34,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/sandbox2/benchmark/theBenchmark.p',fact_sgn__0__0) ).

thf(1388,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)],[34]) ).

thf(1389,plain,
    ! [B: $i,A: $i] :
      ( ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
          = ( B @ c_Groups_Ozero__class_Ozero ) )
        | ( A
         != ( B @ c_Groups_Ozero__class_Ozero ) )
        | ~ ( 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 ) )
        | ~ ( B @ class_Rings_Olinordered__idom ) ) ),
    inference(cnf,[status(esa)],[1388]) ).

thf(1391,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) )
      | ( A
       != ( B @ c_Groups_Ozero__class_Ozero ) )
      | ~ ( B @ class_Rings_Olinordered__idom ) ),
    inference(cnfConj,[status(thm)],[1389]) ).

thf(1393,plain,
    ! [B: $i,A: $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 ) ) ),
    inference(lifteq,[status(thm)],[1391]) ).

thf(1394,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Rings_Olinordered__idom )
      | ( ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Osgn__class_Osgn ) )
        = ( A @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(simp,[status(thm)],[1393]) ).

thf(488,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__eq__right) ).

thf(3157,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(70,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 @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__num__frac) ).

thf(1526,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 @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(1194,axiom,
    tc_RealDef_Oreal @ class_Groups_Oordered__ab__group__add__abs,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).

thf(5321,plain,
    tc_RealDef_Oreal @ class_Groups_Oordered__ab__group__add__abs,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).

thf(222,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field__inverse__zero )
     => ( ! [D: $i] :
            ( ( D @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( C @ c_Groups_Oone__class_Oone @ ( D @ ( C @ c_Orderings_Oord__class_Oless ) ) )
             => ( A @ ( B @ ( D @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
       => ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__le__mult__one__interval) ).

thf(2137,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Fields_Olinordered__field__inverse__zero )
     => ( ! [D: $i] :
            ( ( D @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( C @ c_Groups_Oone__class_Oone @ ( D @ ( C @ c_Orderings_Oord__class_Oless ) ) )
             => ( A @ ( B @ ( D @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) )
       => ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(20053,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_da____ @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
       != v_da____ )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3313,19267]) ).

thf(20054,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_da____ @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
       != v_da____ ) ),
    inference(simp,[status(thm)],[20053]) ).

thf(20110,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != v_da____ )
      | ( A != v_mazh )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
       != v_da____ ) ),
    inference(simp,[status(thm)],[20054]) ).

thf(20120,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != v_da____ )
    | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_da____ ) ),
    inference(simp,[status(thm)],[20110]) ).

thf(20958,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
    | ( v_cs____ != v_da____ )
    | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_da____ ) ),
    inference(paramod_ordered,[status(thm)],[1280,20120]) ).

thf(20963,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Nat_Onat )
    | ( v_cs____ != v_da____ )
    | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_da____ ) ),
    inference(simp,[status(thm)],[20958]) ).

thf(24631,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[24000,1427]) ).

thf(24632,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[24631]) ).

thf(24633,plain,
    tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[24632:[bind(A,$thf( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(28745,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[24633,1427]) ).

thf(28746,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[28745]) ).

thf(28747,plain,
    tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[28746:[bind(A,$thf( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(187,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Ofield__inverse__zero )
     => ( ( A @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__divide) ).

thf(2002,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Fields_Ofield__inverse__zero )
     => ( ( A @ ( B @ ( C @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(735,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/sandbox2/benchmark/theBenchmark.p',fact_nonzero__norm__divide) ).

thf(3955,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)],[735]) ).

thf(710,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/sandbox2/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).

thf(3870,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)],[710]) ).

thf(629,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( B != A )
       => ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I12_J) ).

thf(3606,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( B != A )
       => ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(945,axiom,
    tc_Int_Oint @ class_Rings_Ocomm__semiring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).

thf(4588,plain,
    tc_Int_Oint @ class_Rings_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).

thf(1201,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Opreorder )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).

thf(5328,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Opreorder )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).

thf(956,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
        <=> ( B = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).

thf(4628,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( ( B = A )
           => ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
          & ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
           => ( B = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).

thf(497,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 @ hAPP ) @ hAPP ) @ ( D @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
           != ( A @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).

thf(3184,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 @ hAPP ) @ hAPP ) @ ( D @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
           != ( A @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(416,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).

thf(2884,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(574,axiom,
    ! [A: $i] :
      ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).

thf(3435,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)],[574]) ).

thf(622,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/sandbox2/benchmark/theBenchmark.p',fact_divide__le__0__iff) ).

thf(3582,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)],[622]) ).

thf(446,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 @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).

thf(3011,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 @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(1231,axiom,
    tc_RealDef_Oreal @ class_Rings_Oring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).

thf(5406,plain,
    tc_RealDef_Oreal @ class_Rings_Oring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).

thf(582,axiom,
    tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).

thf(3459,plain,
    tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(530,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).

thf(3301,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(353,axiom,
    ( ( v_cs____
     != ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
   => ? [A: $i] :
      ! [B: $i] :
        ( ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( v_aa____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_calculation) ).

thf(2646,plain,
    ( ( v_cs____
     != ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
   => ? [A: $i] :
      ! [B: $i] :
        ( ( B @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B @ ( v_cs____ @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( v_aa____ @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(704,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/sandbox2/benchmark/theBenchmark.p',fact_norm__eq__zero) ).

thf(3852,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)],[704]) ).

thf(1123,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/sandbox2/benchmark/theBenchmark.p',fact_right__inverse__eq) ).

thf(5167,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)],[1123]) ).

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

thf(5034,plain,
    tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).

thf(167,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Omonoid__mult )
     => ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__right) ).

thf(1915,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Omonoid__mult )
     => ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(351,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/sandbox2/benchmark/theBenchmark.p',fact_sgn__one) ).

thf(2641,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)],[351]) ).

thf(95,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 @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).

thf(1604,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 @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(719,axiom,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ! [D: $i] :
          ( ( B @ ( D @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( C @ ( D @ ( A @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ 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 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__bound__exists) ).

thf(3897,plain,
    ! [A: $i,B: $i] :
    ? [C: $i] :
      ( ! [D: $i] :
          ( ( B @ ( D @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( C @ ( D @ ( A @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ 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 ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).

thf(3898,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ sk26 ) @ ( C @ ( A @ ( tc_Complex_Ocomplex @ c_Polynomial_Opoly ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
        | ~ ( B @ ( C @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( A @ ( B @ sk26 ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(cnf,[status(esa)],[3897]) ).

thf(3899,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ sk26 ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ),
    inference(cnfConj,[status(thm)],[3898]) ).

thf(1124,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/sandbox2/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).

thf(5174,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)],[1124]) ).

thf(470,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__times) ).

thf(3097,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(1038,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__0 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).

thf(4893,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)],[1038]) ).

thf(423,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 @ hAPP ) @ hAPP ) )
              = B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq) ).

thf(2910,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 @ hAPP ) @ hAPP ) )
                = 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 @ hAPP ) @ hAPP ) )
                = B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(946,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/sandbox2/benchmark/theBenchmark.p',fact_divide__nonneg__neg) ).

thf(4589,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)],[946]) ).

thf(882,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/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).

thf(4407,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)],[882]) ).

thf(1036,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zminus) ).

thf(4886,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)],[1036]) ).

thf(4887,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
      = A ),
    inference(cnf,[status(esa)],[4886]) ).

thf(4888,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
      = A ),
    inference(lifteq,[status(thm)],[4887]) ).

thf(46,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__diff__eq__iff) ).

thf(1438,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(661,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/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__divide) ).

thf(3720,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)],[661]) ).

thf(1251,axiom,
    tc_RealDef_Oreal @ class_Groups_Oab__semigroup__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).

thf(5443,plain,
    tc_RealDef_Oreal @ class_Groups_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).

thf(230,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mono) ).

thf(2164,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(47222,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
       != ( v_ma @ ( v_mazh @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) )
      | ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero )
       != v_mazh )
      | ( v_mzh != v_da____ ) ),
    inference(paramod_ordered,[status(thm)],[3681,15428]) ).

thf(47263,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) )
       != v_ma )
      | ( A != v_mazh )
      | ( tc_RealDef_Oreal != tc_RealDef_Oreal )
      | ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero )
       != v_mazh )
      | ( v_mzh != v_da____ ) ),
    inference(simp,[status(thm)],[47222]) ).

thf(47299,plain,
    ( ( ( v_mazh @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) )
     != v_ma )
    | ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero )
     != v_mazh )
    | ( v_mzh != v_da____ ) ),
    inference(simp,[status(thm)],[47263]) ).

thf(1118,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/sandbox2/benchmark/theBenchmark.p',fact_less__minus__iff) ).

thf(5142,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)],[1118]) ).

thf(933,axiom,
    ! [A: $i] :
      ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).

thf(4557,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)],[933]) ).

thf(1237,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/sandbox2/benchmark/theBenchmark.p',fact_real__le__linear) ).

thf(5416,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)],[1237]) ).

thf(376,axiom,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != ( A @ c_Nat_OSuc ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).

thf(2737,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != ( A @ c_Nat_OSuc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

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

thf(1311,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oidom )
     => ( A @ ( A @ ( B @ ( C @ c_Polynomial_Oorder ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(458,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 @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).

thf(3054,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 @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(760,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/sandbox2/benchmark/theBenchmark.p',fact_divide__less__0__iff) ).

thf(4031,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)],[760]) ).

thf(345,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 @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff1) ).

thf(2621,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 @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(1202,axiom,
    v_mzh @ ( v_ma @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

thf(5330,plain,
    v_mzh @ ( v_ma @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( 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)],[1202]) ).

thf(16595,plain,
    ( ( ( v_mzh @ ( v_ma @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     != ( v_mazh @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[5330,1263]) ).

thf(16596,plain,
    ( ( v_mzh @ ( v_ma @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
   != ( v_mazh @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(simp,[status(thm)],[16595]) ).

thf(16647,plain,
    ( ( v_mzh != v_mazh )
    | ( ( v_ma @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
     != v_da____ )
    | ( tc_RealDef_Oreal != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[16596]) ).

thf(16659,plain,
    ( ( v_mzh != v_mazh )
    | ( ( v_ma @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
     != v_da____ ) ),
    inference(simp,[status(thm)],[16647]) ).

thf(28208,plain,
    ( ( v_mzh != v_mazh )
    | ( ( v_ma @ ( v_da____ @ ( tc_RealDef_Oreal @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
     != v_da____ ) ),
    inference(rewrite,[status(thm)],[16659,5033]) ).

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

thf(4059,plain,
    tc_Int_Oint @ class_Groups_Ominus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).

thf(1205,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/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__triangle__sub) ).

thf(5334,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)],[1205]) ).

thf(200,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 @ hAPP ) @ hAPP ) )
      = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).

thf(2061,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 @ hAPP ) @ hAPP ) )
      = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(614,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/sandbox2/benchmark/theBenchmark.p',fact_abs__div__pos) ).

thf(3550,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)],[614]) ).

thf(1174,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).

thf(5281,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).

thf(101,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Rings_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__right) ).

thf(1636,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(259,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
      <=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__dvd__iff) ).

thf(2264,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
         => ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) )
        & ( ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
         => ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(1387,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( C @ class_Rings_Ocomm__semiring__1 ) ),
    inference(cnf,[status(esa)],[1386]) ).

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

thf(3261,plain,
    ! [A: $i] :
      ( ( ( A
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
       => ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      & ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       => ( A
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(17870,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       != ( v_mazh @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[5270,1263]) ).

thf(17871,plain,
    ! [A: $i] :
      ( ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     != ( v_mazh @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(simp,[status(thm)],[17870]) ).

thf(17918,plain,
    ! [A: $i] :
      ( ( A != v_mazh )
      | ( A != v_da____ )
      | ( tc_RealDef_Oreal != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[17871]) ).

thf(17936,plain,
    v_mazh != v_da____,
    inference(simp,[status(thm)],[17918]) ).

thf(303,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
     => ( B != A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__neq) ).

thf(2428,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(27,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Omult__zero )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__left) ).

thf(1355,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Omult__zero )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(914,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/sandbox2/benchmark/theBenchmark.p',fact_psize__eq__0__iff) ).

thf(4499,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)],[914]) ).

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

thf(1923,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
          | ( A
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
       => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) )
      & ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
       => ( ( B
            = ( 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)],[170]) ).

thf(1924,plain,
    ( ! [A: $i,B: $i] :
        ( ( ( B
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
          | ( A
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
       => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) )
    & ! [A: $i,B: $i] :
        ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
       => ( ( B
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
          | ( A
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(miniscope,[status(thm)],[1923]) ).

thf(1925,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( ( C @ ( D @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
        | ( D
         != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) )
      & ( ( ( C @ ( D @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
        | ( C
         != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
      & ( ( B
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
        | ( A
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
        | ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
         != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ) ),
    inference(cnf,[status(esa)],[1924]) ).

thf(1927,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
      | ( A
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(cnfConj,[status(thm)],[1925]) ).

thf(1930,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
      | ( A
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(lifteq,[status(thm)],[1927]) ).

thf(1931,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
      = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
    inference(simp,[status(thm)],[1930]) ).

thf(41352,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
      = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ),
    inference(rewrite,[status(thm)],[1931,2249]) ).

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

thf(5206,plain,
    tc_Complex_Ocomplex @ class_Rings_Ocomm__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).

thf(359,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__ring__1 )
     => ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
       => ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
         => ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diff) ).

thf(2673,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__ring__1 )
     => ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
       => ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
         => ( A @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(1093,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/sandbox2/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).

thf(5049,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)],[1093]) ).

thf(668,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/sandbox2/benchmark/theBenchmark.p',fact_nonzero__minus__divide__divide) ).

thf(3735,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)],[668]) ).

thf(755,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oorder )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C = A )
         => ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I2_J) ).

thf(4016,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oorder )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C = A )
         => ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).

thf(628,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/sandbox2/benchmark/theBenchmark.p',fact_divide_Ozero) ).

thf(3603,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)],[628]) ).

thf(339,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ class_Rings_Osemiring__0 )
        & ( C @ class_Rings_Odvd ) )
     => ( ? [D: $i] : ( D @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
      <=> ? [D: $i] :
            ( ( D @ ( B @ hAPP ) @ hBOOL )
            & ( C @ c_Groups_Ozero__class_Ozero @ ( D @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unity__coeff__ex) ).

thf(2596,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ class_Rings_Osemiring__0 )
        & ( C @ class_Rings_Odvd ) )
     => ( ( ? [D: $i] :
              ( ( D @ ( B @ hAPP ) @ hBOOL )
              & ( C @ c_Groups_Ozero__class_Ozero @ ( D @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) )
         => ? [D: $i] : ( D @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) )
        & ( ? [D: $i] : ( D @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
         => ? [D: $i] :
              ( ( D @ ( B @ hAPP ) @ hBOOL )
              & ( C @ c_Groups_Ozero__class_Ozero @ ( D @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(708,axiom,
    tc_Nat_Onat @ class_Groups_Oordered__comm__monoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).

thf(3867,plain,
    tc_Nat_Onat @ class_Groups_Oordered__comm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(1079,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/sandbox2/benchmark/theBenchmark.p',fact_one__is__add) ).

thf(5002,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)],[1079]) ).

thf(1075,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/sandbox2/benchmark/theBenchmark.p',fact_int__0__less__1) ).

thf(4989,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)],[1075]) ).

thf(108,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ? [C: $i] :
            ( ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
              = A )
            & ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__pos__nth) ).

thf(1676,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       => ? [C: $i] :
            ( ( ( B @ ( C @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
              = A )
            & ( C @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(1260,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/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq) ).

thf(5455,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)],[1260]) ).

thf(829,axiom,
    ! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).

thf(4252,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)],[829]) ).

thf(15392,plain,
    ! [A: $i] :
      ( ( ( v_ma @ ( v_mazh @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( v_mzh @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       != ( A @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[5323,2983]) ).

thf(15393,plain,
    ! [A: $i] :
      ( ( v_ma @ ( v_mazh @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( v_mzh @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
     != ( A @ ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(simp,[status(thm)],[15392]) ).

thf(15406,plain,
    ! [A: $i] :
      ( ( ( v_ma @ ( v_mazh @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
       != A )
      | ( ( A @ c_Nat_OSuc )
       != v_mzh )
      | ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[15393]) ).

thf(15427,plain,
    ( ( ( v_ma @ ( v_mazh @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ c_Nat_OSuc )
     != v_mzh )
    | ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[15406]) ).

thf(25063,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
       != ( v_ma @ ( v_mazh @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) )
      | ( ( A @ c_Nat_OSuc )
       != v_mzh )
      | ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
    inference(paramod_ordered,[status(thm)],[3662,15427]) ).

thf(25087,plain,
    ! [A: $i] :
      ( ( A != v_ma )
      | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != v_mazh )
      | ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( ( A @ c_Nat_OSuc )
       != v_mzh )
      | ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[25063]) ).

thf(25123,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != v_mazh )
    | ( ( v_ma @ c_Nat_OSuc )
     != v_mzh )
    | ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[25087]) ).

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

thf(2969,plain,
    ! [A: $i] :
      ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(862,axiom,
    tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).

thf(4344,plain,
    tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).

thf(745,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/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).

thf(3989,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)],[745]) ).

thf(789,axiom,
    tc_Complex_Ocomplex @ class_Power_Opower,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).

thf(4128,plain,
    tc_Complex_Ocomplex @ class_Power_Opower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).

thf(513,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__div__algebra )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult) ).

thf(3239,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__div__algebra )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(511,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ocomm__monoid__mult )
     => ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).

thf(3233,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ocomm__monoid__mult )
     => ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(548,axiom,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).

thf(3371,plain,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(715,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/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).

thf(3884,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)],[715]) ).

thf(487,axiom,
    ! [A: $i,B: $i] :
      ( ( B
       != ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) )
     => ( ( A
         != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
       => ? [C: $i] : ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( C @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone @ ( tc_Complex_Ocomplex @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reduce__poly__simple) ).

thf(3154,plain,
    ! [A: $i,B: $i] :
      ( ( B
       != ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) )
     => ( ( A
         != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
       => ? [C: $i] : ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( A @ ( C @ ( tc_Complex_Ocomplex @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone @ ( tc_Complex_Ocomplex @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(480,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc__right) ).

thf(3134,plain,
    ! [A: $i,B: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(5752,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ class_Rings_Ocomm__semiring__1 )
       != ( A @ class_Rings_Ocomm__semiring__1 ) )
      | ~ $true
      | ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Polynomial_OpCons ) ) )
        = ( A @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone ) ) ),
    inference(paramod_ordered,[status(thm)],[4030,1318]) ).

thf(5753,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ class_Rings_Ocomm__semiring__1 )
       != ( A @ class_Rings_Ocomm__semiring__1 ) )
      | ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Polynomial_OpCons ) ) )
        = ( A @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone ) ) ),
    inference(simp,[status(thm)],[5752]) ).

thf(5754,plain,
    ( ( tc_Nat_Onat @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Polynomial_OpCons ) ) )
    = ( tc_Nat_Onat @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone ) ),
    inference(pattern_uni,[status(thm)],[5753:[bind(A,$thf( tc_Nat_Onat ))]]) ).

thf(693,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/sandbox2/benchmark/theBenchmark.p',fact_nonzero__abs__divide) ).

thf(3814,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)],[693]) ).

thf(440,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).

thf(2986,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(1227,axiom,
    tc_RealDef_Oreal @ class_Rings_Olinordered__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).

thf(5396,plain,
    tc_RealDef_Oreal @ class_Rings_Olinordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).

thf(966,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/sandbox2/benchmark/theBenchmark.p',fact_norm__diff__triangle__ineq) ).

thf(4661,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)],[966]) ).

thf(294,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 @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff2) ).

thf(2396,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 @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[294]) ).

thf(652,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/sandbox2/benchmark/theBenchmark.p',fact_norm__divide) ).

thf(3682,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)],[652]) ).

thf(588,axiom,
    tc_Nat_Onat @ class_Groups_Ominus,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).

thf(3471,plain,
    tc_Nat_Onat @ class_Groups_Ominus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(525,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).

thf(3286,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(796,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/sandbox2/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).

thf(4140,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)],[796]) ).

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

thf(1920,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
     => ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(942,axiom,
    tc_Nat_Onat @ class_Rings_Odvd,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).

thf(4585,plain,
    tc_Nat_Onat @ class_Rings_Odvd,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).

thf(1356,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) )
      | ~ ( B @ class_Rings_Omult__zero ) ),
    inference(cnf,[status(esa)],[1355]) ).

thf(1357,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Rings_Omult__zero )
      | ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(lifteq,[status(thm)],[1356]) ).

thf(9299,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Rings_Omult__zero )
       != ( B @ class_Rings_Omult__zero ) )
      | ~ $true
      | ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(paramod_ordered,[status(thm)],[5361,1357]) ).

thf(9300,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Rings_Omult__zero )
       != ( B @ class_Rings_Omult__zero ) )
      | ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(simp,[status(thm)],[9299]) ).

thf(9301,plain,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
    inference(pattern_uni,[status(thm)],[9300:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal ))]]) ).

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

thf(3282,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
     => ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(432,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).

thf(2958,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
       => ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( 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)],[432]) ).

thf(733,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/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).

thf(3948,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)],[733]) ).

thf(736,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/sandbox2/benchmark/theBenchmark.p',fact_zabs__less__one__iff) ).

thf(3958,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)],[736]) ).

thf(849,axiom,
    tc_Nat_Onat @ class_Rings_Oordered__comm__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).

thf(4295,plain,
    tc_Nat_Onat @ class_Rings_Oordered__comm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).

thf(172,axiom,
    ! [A: $i,B: $i] :
      ( ( B
       != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
     => ( ( B @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
      <=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
          = ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mult__cancel1) ).

thf(1938,plain,
    ! [A: $i,B: $i] :
      ( ( B
       != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
     => ( ( ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
            = ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
         => ( B @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) )
        & ( ( B @ ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
         => ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
            = ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(1222,axiom,
    tc_RealDef_Oreal @ class_Groups_Omonoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).

thf(5391,plain,
    tc_RealDef_Oreal @ class_Groups_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).

thf(411,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono_H) ).

thf(2873,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(743,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/sandbox2/benchmark/theBenchmark.p',fact_zero__less__norm__iff) ).

thf(3980,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)],[743]) ).

thf(19236,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_da____ @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ $true
      | ~ ( v_mazh @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1542,17860]) ).

thf(19237,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_da____ @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ ( v_mazh @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[19236]) ).

thf(19254,plain,
    ! [A: $i] :
      ( ( A != v_da____ )
      | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
       != v_mazh )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ~ ( v_mazh @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[19237]) ).

thf(19273,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_mazh )
    | ~ ( v_mazh @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[19254]) ).

thf(1025,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/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).

thf(4849,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)],[1025]) ).

thf(814,axiom,
    tc_Int_Oint @ class_Groups_Ocomm__monoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).

thf(4192,plain,
    tc_Int_Oint @ class_Groups_Ocomm__monoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).

thf(468,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Odiff) ).

thf(3090,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(82,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono) ).

thf(1555,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(277,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( C
          = ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
       => ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).

thf(2332,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( C
          = ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
       => ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(533,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).

thf(3314,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( A @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( 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)],[533]) ).

thf(481,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).

thf(3137,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[481]) ).

thf(1125,axiom,
    ! [A: $i] :
      ~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).

thf(5177,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).

thf(617,axiom,
    ! [A: $i,B: $i] :
      ( ( B
       != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
     => ( ( B @ ( A @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
       => ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__imp__le__int) ).

thf(3556,plain,
    ! [A: $i,B: $i] :
      ( ( B
       != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
     => ( ( B @ ( A @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
       => ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(876,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/sandbox2/benchmark/theBenchmark.p',fact_zless__linear) ).

thf(4385,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)],[876]) ).

thf(1015,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/sandbox2/benchmark/theBenchmark.p',fact_zless__le) ).

thf(4812,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)],[1015]) ).

thf(4813,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: $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 ) ) ) ) ) ),
    inference(miniscope,[status(thm)],[4812]) ).

thf(4814,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
        | ( D = C )
        | ~ ( C @ ( D @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( B != A )
        | ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
        | ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(cnf,[status(esa)],[4813]) ).

thf(4816,plain,
    ! [B: $i,A: $i] :
      ( ( B != A )
      | ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(cnfConj,[status(thm)],[4814]) ).

thf(4818,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
      | ( B != A ) ),
    inference(lifteq,[status(thm)],[4816]) ).

thf(4819,plain,
    ! [A: $i] :
      ~ ( A @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ),
    inference(simp,[status(thm)],[4818]) ).

thf(47412,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       != ( B @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[5155,4819]) ).

thf(47413,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
     != ( B @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[47412]) ).

thf(47456,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
       != B )
      | ( A != B )
      | ( tc_Int_Oint != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[47413]) ).

thf(47491,plain,
    ! [A: $i] :
      ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
     != A ),
    inference(simp,[status(thm)],[47456]) ).

thf(47502,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
       != ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
      | ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero )
       != B ) ),
    inference(paramod_ordered,[status(thm)],[3681,47491]) ).

thf(47575,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) )
       != ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
      | ( A
       != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
      | ( tc_Int_Oint != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[47502]) ).

thf(47593,plain,
    ( ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) )
     != ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
    | ( tc_Int_Oint != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[47575]) ).

thf(47695,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
       != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) )
      | ( A
       != ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
      | ( tc_Int_Oint != tc_RealDef_Oreal ) ),
    inference(paramod_ordered,[status(thm)],[4888,47593]) ).

thf(47739,plain,
    ( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
     != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
    | ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( tc_Int_Oint != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[47695]) ).

thf(47754,plain,
    ( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
     != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
    | ( tc_Int_Oint != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[47739]) ).

thf(49169,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
       != ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) )
      | ( A
       != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
      | ( tc_Int_Oint != tc_RealDef_Oreal ) ),
    inference(paramod_ordered,[status(thm)],[4888,47754]) ).

thf(49218,plain,
    ( ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
     != ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
    | ( tc_Int_Oint != tc_Int_Oint )
    | ( tc_Int_Oint != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[49169]) ).

thf(49220,plain,
    ( ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
     != ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
    | ( tc_Int_Oint != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[49218]) ).

thf(1081,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/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).

thf(5021,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)],[1081]) ).

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

thf(3877,plain,
    ! [A: $i] :
      ( ( A @ class_RealVector_Oreal__normed__algebra )
     => ? [B: $i] :
          ( ! [C: $i,D: $i] : ( B @ ( D @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( C @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( 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 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).

thf(931,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/sandbox2/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).

thf(4553,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)],[931]) ).

thf(626,axiom,
    tc_Int_Oint @ class_Groups_Oab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).

thf(3600,plain,
    tc_Int_Oint @ class_Groups_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(111,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/sandbox2/benchmark/theBenchmark.p',fact_sgn__zero__iff) ).

thf(1687,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)],[111]) ).

thf(612,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/sandbox2/benchmark/theBenchmark.p',fact_diff__self) ).

thf(3546,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)],[612]) ).

thf(1088,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

thf(5038,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)],[1088]) ).

thf(483,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 @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono2) ).

thf(3144,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 @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(609,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 @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__div__pos__le) ).

thf(3535,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 @ hAPP ) @ hAPP ) @ ( 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)],[609]) ).

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

thf(1787,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 @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
            = ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) )
        & ( ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
            = ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) )
         => ( ( C = A )
            | ( D = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(886,axiom,
    tc_Int_Oint @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).

thf(4417,plain,
    tc_Int_Oint @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).

thf(450,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).

thf(3028,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(456,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 @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__left__mono) ).

thf(3050,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 @ hAPP ) @ hAPP ) @ ( 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)],[456]) ).

thf(280,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__left) ).

thf(2344,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(678,axiom,
    tc_Int_Oint @ class_Rings_Olinordered__semidom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).

thf(3763,plain,
    tc_Int_Oint @ class_Rings_Olinordered__semidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(377,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 @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__eq__iff) ).

thf(2741,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 @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(1390,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( B @ c_Groups_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
       != ( B @ c_Groups_Ozero__class_Ozero ) )
      | ~ ( B @ class_Rings_Olinordered__idom ) ),
    inference(cnfConj,[status(thm)],[1389]) ).

thf(1392,plain,
    ! [B: $i,A: $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 ) ) ),
    inference(lifteq,[status(thm)],[1390]) ).

thf(650,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/sandbox2/benchmark/theBenchmark.p',fact_zero__less__abs__iff) ).

thf(3667,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)],[650]) ).

thf(987,axiom,
    tc_Int_Oint @ class_Rings_Oidom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).

thf(4732,plain,
    tc_Int_Oint @ class_Rings_Oidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).

thf(215,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
       => ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
         => ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__add) ).

thf(2112,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
       => ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
         => ( A @ ( B @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(774,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/sandbox2/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).

thf(4080,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)],[774]) ).

thf(727,axiom,
    tc_Int_Oint @ class_Rings_Ocomm__ring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).

thf(3931,plain,
    tc_Int_Oint @ class_Rings_Ocomm__ring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).

thf(452,axiom,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0__right) ).

thf(3033,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(560,axiom,
    tc_Nat_Onat @ class_Rings_Oordered__cancel__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).

thf(3408,plain,
    tc_Nat_Onat @ class_Rings_Oordered__cancel__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(124,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/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).

thf(1740,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)],[124]) ).

thf(973,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/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).

thf(4680,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)],[973]) ).

thf(686,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_Rings_Odvd__class_Odvd ) ) )
         => ( ( B @ ( A @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
           => ( B = A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__antisym__nonneg) ).

thf(3799,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_Rings_Odvd__class_Odvd ) ) )
         => ( ( B @ ( A @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
           => ( B = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(384,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).

thf(2769,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
       => ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(577,axiom,
    tc_Complex_Ocomplex @ class_Rings_Odvd,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odvd) ).

thf(3445,plain,
    tc_Complex_Ocomplex @ class_Rings_Odvd,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(1100,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/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).

thf(5066,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)],[1100]) ).

thf(666,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/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).

thf(3731,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)],[666]) ).

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

thf(4957,plain,
    tc_Nat_Onat @ class_Rings_Olinordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).

thf(227,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).

thf(2157,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(368,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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq) ).

thf(2709,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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

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

thf(5362,plain,
    tc_RealDef_Oreal @ class_Rings_Ocomm__ring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).

thf(1035,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/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).

thf(4883,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)],[1035]) ).

thf(1187,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/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__minus__le__complex__mod) ).

thf(5313,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)],[1187]) ).

thf(787,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/sandbox2/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).

thf(4123,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)],[787]) ).

thf(251,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__self) ).

thf(2245,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(1131,axiom,
    tc_Nat_Onat @ class_Groups_Oordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).

thf(5189,plain,
    tc_Nat_Onat @ class_Groups_Oordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).

thf(586,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__0 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).

thf(3467,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__0 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(685,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/sandbox2/benchmark/theBenchmark.p',fact_add__is__1) ).

thf(3782,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)],[685]) ).

thf(592,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/sandbox2/benchmark/theBenchmark.p',fact_abs__add__abs) ).

thf(3482,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)],[592]) ).

thf(1094,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).

thf(5053,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).

thf(323,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
        & ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).

thf(2515,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
          & ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
          & ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(211,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
       != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
     => ( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
      <=> ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mono) ).

thf(2100,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
       != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
     => ( ( ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
         => ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) )
        & ( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
         => ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(153,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 @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__mono2) ).

thf(1851,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 @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(1105,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/sandbox2/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).

thf(5098,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)],[1105]) ).

thf(290,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Oidom )
     => ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
      <=> ( ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
          | ( C
            = ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel__left) ).

thf(2377,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Oidom )
     => ( ( ( ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
            | ( C
              = ( D @ c_Groups_Ozero__class_Ozero ) ) )
         => ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) )
        & ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
         => ( ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
            | ( C
              = ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

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

thf(5238,plain,
    tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).

thf(918,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/sandbox2/benchmark/theBenchmark.p',fact_odd__less__0) ).

thf(4512,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)],[918]) ).

thf(361,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).

thf(2683,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)],[361]) ).

thf(2684,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(cnf,[status(esa)],[2683]) ).

thf(2685,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ c_Nat_OSuc ) ),
    inference(lifteq,[status(thm)],[2684]) ).

thf(1068,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__field )
     => ? [C: $i] :
          ( ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( B @ c_Rings_Oinverse__class_Odivide ) ) @ ( 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__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Ononneg__bounded) ).

thf(4974,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__field )
     => ? [C: $i] :
          ( ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( B @ c_Rings_Oinverse__class_Odivide ) ) @ ( 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__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).

thf(706,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 @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_norm__ratiotest__lemma) ).

thf(3862,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 @ hAPP ) @ hAPP ) @ ( 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)],[706]) ).

thf(1211,axiom,
    tc_RealDef_Oreal @ class_Rings_Olinordered__semidom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).

thf(5345,plain,
    tc_RealDef_Oreal @ class_Rings_Olinordered__semidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).

thf(20,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oidom )
     => ( ( B
         != ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
       => ~ ( B @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ c_Nat_OSuc @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__2) ).

thf(1328,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oidom )
     => ( ( B
         != ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
       => ~ ( B @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ c_Nat_OSuc @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(14443,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 ) ) )
     != ( v_mazh @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4238,1263]) ).

thf(14444,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 ) ) )
   != ( v_mazh @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(simp,[status(thm)],[14443]) ).

thf(14480,plain,
    ( ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
     != v_mazh )
    | ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
     != v_da____ )
    | ( tc_Int_Oint != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[14444]) ).

thf(14933,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
    | ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
     != v_mazh )
    | ( v_cs____ != v_da____ )
    | ( tc_Int_Oint != tc_RealDef_Oreal ) ),
    inference(paramod_ordered,[status(thm)],[1280,14480]) ).

thf(14941,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Int_Oint )
    | ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
     != v_mazh )
    | ( v_cs____ != v_da____ )
    | ( tc_Int_Oint != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[14933]) ).

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

thf(2359,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__semiring__1 )
     => ( ( ( A
            = ( C @ c_Groups_Oone__class_Oone ) )
          | ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
       => ( B @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(909,axiom,
    tc_Int_Oint @ class_Rings_Oring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).

thf(4486,plain,
    tc_Int_Oint @ class_Rings_Oring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).

thf(1008,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/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq3) ).

thf(4789,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)],[1008]) ).

thf(764,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/sandbox2/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).

thf(4048,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)],[764]) ).

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

thf(1498,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(89,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0) ).

thf(1588,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(1589,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(cnf,[status(esa)],[1588]) ).

thf(1590,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(lifteq,[status(thm)],[1589]) ).

thf(38924,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
      | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(paramod_ordered,[status(thm)],[1590,32682]) ).

thf(38925,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
    inference(simp,[status(thm)],[38924]) ).

thf(38959,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
      | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) )
       != ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) ) ) ),
    inference(simp,[status(thm)],[38925]) ).

thf(39004,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) )
     != ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) ) ),
    inference(simp,[status(thm)],[38959]) ).

thf(39047,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != A )
      | ( ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes )
       != ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) ),
    inference(simp,[status(thm)],[39004]) ).

thf(39217,plain,
    ( ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes )
   != ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ),
    inference(simp,[status(thm)],[39047]) ).

thf(923,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/sandbox2/benchmark/theBenchmark.p',fact_norm__minus__commute) ).

thf(4525,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)],[923]) ).

thf(1423,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
      | ( C
       != ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( D @ class_Rings_Odvd ) ),
    inference(cnf,[status(esa)],[1422]) ).

thf(1424,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( D @ class_Rings_Odvd )
      | ( C
       != ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(lifteq,[status(thm)],[1423]) ).

thf(1425,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( C @ class_Rings_Odvd ) ),
    inference(simp,[status(thm)],[1424]) ).

thf(472,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
        <=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing__iff) ).

thf(3102,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
          & ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ 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)],[472]) ).

thf(1243,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oorder )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).

thf(5428,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oorder )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).

thf(657,axiom,
    tc_Int_Oint @ class_Rings_Ocomm__semiring__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).

thf(3704,plain,
    tc_Int_Oint @ class_Rings_Ocomm__semiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(1052,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/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).

thf(4930,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)],[1052]) ).

thf(118,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).

thf(1719,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)],[118]) ).

thf(821,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oord )
     => ( ( C = B )
       => ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__eq__less__trans) ).

thf(4227,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oord )
     => ( ( C = B )
       => ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).

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

thf(2858,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
     => ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(971,axiom,
    tc_Complex_Ocomplex @ class_Rings_Ozero__neq__one,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).

thf(4676,plain,
    tc_Complex_Ocomplex @ class_Rings_Ozero__neq__one,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).

thf(8634,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Rings_Ozero__neq__one )
       != ( A @ class_Rings_Ozero__neq__one ) )
      | ~ $true
      | ( ( A @ c_Groups_Oone__class_Oone )
       != ( A @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(paramod_ordered,[status(thm)],[4676,2395]) ).

thf(8635,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Rings_Ozero__neq__one )
       != ( A @ class_Rings_Ozero__neq__one ) )
      | ( ( A @ c_Groups_Oone__class_Oone )
       != ( A @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(simp,[status(thm)],[8634]) ).

thf(8636,plain,
    ( ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone )
   != ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) ),
    inference(pattern_uni,[status(thm)],[8635:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(1218,axiom,
    tc_RealDef_Oreal @ class_Groups_Oordered__ab__semigroup__add__imp__le,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).

thf(5373,plain,
    tc_RealDef_Oreal @ class_Groups_Oordered__ab__semigroup__add__imp__le,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).

thf(672,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/sandbox2/benchmark/theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).

thf(3746,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)],[672]) ).

thf(779,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/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).

thf(4109,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)],[779]) ).

thf(963,axiom,
    tc_Nat_Onat @ class_Rings_Ocomm__semiring__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).

thf(4655,plain,
    tc_Nat_Onat @ class_Rings_Ocomm__semiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).

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

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

thf(5685,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Nat_Onat @ class_Rings_Ocomm__semiring__0 )
       != ( B @ class_Rings_Ocomm__semiring__0 ) )
      | ~ $true
      | ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Osynthetic__div ) ) )
        = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(paramod_ordered,[status(thm)],[4655,1266]) ).

thf(5686,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Nat_Onat @ class_Rings_Ocomm__semiring__0 )
       != ( B @ class_Rings_Ocomm__semiring__0 ) )
      | ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Osynthetic__div ) ) )
        = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(simp,[status(thm)],[5685]) ).

thf(5687,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Polynomial_Osynthetic__div ) ) )
      = ( tc_Nat_Onat @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ),
    inference(pattern_uni,[status(thm)],[5686:[bind(A,$thf( A )),bind(B,$thf( tc_Nat_Onat ))]]) ).

thf(260,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/sandbox2/benchmark/theBenchmark.p',fact_less__SucE) ).

thf(2268,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)],[260]) ).

thf(819,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/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).

thf(4219,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)],[819]) ).

thf(5495,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Int_Oint @ class_Rings_Ocomm__semiring__0 )
       != ( B @ class_Rings_Ocomm__semiring__0 ) )
      | ~ $true
      | ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Osynthetic__div ) ) )
        = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(paramod_ordered,[status(thm)],[3704,1266]) ).

thf(5496,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Int_Oint @ class_Rings_Ocomm__semiring__0 )
       != ( B @ class_Rings_Ocomm__semiring__0 ) )
      | ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Osynthetic__div ) ) )
        = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(simp,[status(thm)],[5495]) ).

thf(5497,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Polynomial_Osynthetic__div ) ) )
      = ( tc_Int_Oint @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ),
    inference(pattern_uni,[status(thm)],[5496:[bind(A,$thf( A )),bind(B,$thf( tc_Int_Oint ))]]) ).

thf(444,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      <=> ( A
          = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel1) ).

thf(3001,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_Oone__class_Oone ) )
         => ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
        & ( ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
         => ( A
            = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(1040,axiom,
    tc_Int_Oint @ class_Groups_Osgn__if,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osgn__if) ).

thf(4898,plain,
    tc_Int_Oint @ class_Groups_Osgn__if,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).

thf(35,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oring )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__right) ).

thf(1395,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oring )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(1396,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( C @ class_Rings_Oring ) ),
    inference(cnf,[status(esa)],[1395]) ).

thf(1397,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ class_Rings_Oring )
      | ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(lifteq,[status(thm)],[1396]) ).

thf(836,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/sandbox2/benchmark/theBenchmark.p',fact_diff__0__right) ).

thf(4263,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)],[836]) ).

thf(1071,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/sandbox2/benchmark/theBenchmark.p',fact_abs__zero) ).

thf(4983,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)],[1071]) ).

thf(1288,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) )
          = ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) ) )
        | ( C != A )
        | ( D != B )
        | ~ ( E @ class_Groups_Ozero ) )
      & ( ( C = A )
        | ( ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) )
         != ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) ) )
        | ~ ( E @ class_Groups_Ozero ) )
      & ( ( D = B )
        | ( ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) )
         != ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) ) )
        | ~ ( E @ class_Groups_Ozero ) ) ),
    inference(cnf,[status(esa)],[1287]) ).

thf(1289,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D = B )
      | ( ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) )
       != ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) ) )
      | ~ ( E @ class_Groups_Ozero ) ),
    inference(cnfConj,[status(thm)],[1288]) ).

thf(1292,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ class_Groups_Ozero )
      | ( D = B )
      | ( ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) )
       != ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) ) ) ),
    inference(lifteq,[status(thm)],[1289]) ).

thf(38,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 @ hAPP ) @ hAPP ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__sgn__abs) ).

thf(1414,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 @ hAPP ) @ hAPP ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(5629,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__0 )
       != ( B @ class_Rings_Ocomm__semiring__0 ) )
      | ~ $true
      | ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Osynthetic__div ) ) )
        = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(paramod_ordered,[status(thm)],[4344,1266]) ).

thf(5630,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__0 )
       != ( B @ class_Rings_Ocomm__semiring__0 ) )
      | ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Osynthetic__div ) ) )
        = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(simp,[status(thm)],[5629]) ).

thf(5631,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ c_Polynomial_Osynthetic__div ) ) )
      = ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ),
    inference(pattern_uni,[status(thm)],[5630:[bind(A,$thf( A )),bind(B,$thf( tc_Complex_Ocomplex ))]]) ).

thf(33237,plain,
    ! [A: $i] :
      ( ( A @ ( v_cs____ @ ( tc_Complex_Ocomplex @ c_Polynomial_Osynthetic__div ) ) )
      = v_cs____ ),
    inference(rewrite,[status(thm)],[5631,1280]) ).

thf(206,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Oring__1 )
     => ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__squared__diff__one__factored) ).

thf(2085,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Oring__1 )
     => ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

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

thf(1504,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(1505,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( B @ class_Rings_Ocomm__semiring__1 ) ),
    inference(cnf,[status(esa)],[1504]) ).

thf(56062,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__1 )
       != ( B @ class_Rings_Ocomm__semiring__1 ) )
      | ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[5238,1505]) ).

thf(56063,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__1 )
       != ( B @ class_Rings_Ocomm__semiring__1 ) )
      | ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[56062]) ).

thf(56064,plain,
    ! [A: $i] : ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Rings_Odvd__class_Odvd ) ) ),
    inference(pattern_uni,[status(thm)],[56063:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal ))]]) ).

thf(39,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Power_Opower )
     => ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc) ).

thf(1417,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Power_Opower )
     => ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(1418,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ~ ( C @ class_Power_Opower ) ),
    inference(cnf,[status(esa)],[1417]) ).

thf(1419,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ class_Power_Opower )
      | ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
    inference(lifteq,[status(thm)],[1418]) ).

thf(87,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__ring__strict )
     => ( ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).

thf(1567,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 @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) )
            = ( C @ c_Groups_Ozero__class_Ozero ) ) )
        & ( ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[87]) ).

thf(311,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/sandbox2/benchmark/theBenchmark.p',fact_sgn__sgn) ).

thf(2460,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)],[311]) ).

thf(856,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 @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__divide__eq) ).

thf(4320,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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).

thf(482,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).

thf(3141,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(1059,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oone ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).

thf(4951,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oone ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).

thf(413,axiom,
    ! [A: $i] : ( A @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).

thf(2877,plain,
    ! [A: $i] : ( A @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(919,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).

thf(4518,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)],[919]) ).

thf(537,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 @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).

thf(3326,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 @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(1122,axiom,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).

thf(5164,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)],[1122]) ).

thf(5165,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = A ),
    inference(cnf,[status(esa)],[5164]) ).

thf(5166,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = A ),
    inference(lifteq,[status(thm)],[5165]) ).

thf(177,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oring__no__zero__divisors )
     => ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
          = ( C @ c_Groups_Ozero__class_Ozero ) )
      <=> ( ( A
            = ( C @ c_Groups_Ozero__class_Ozero ) )
          | ( B
            = ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).

thf(1964,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 @ hAPP ) @ hAPP ) )
            = ( C @ c_Groups_Ozero__class_Ozero ) ) )
        & ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
            = ( 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)],[177]) ).

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

thf(2142,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(2143,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = A ),
    inference(cnf,[status(esa)],[2142]) ).

thf(2144,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = A ),
    inference(lifteq,[status(thm)],[2143]) ).

thf(49682,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) ) )
      | ( A
       != ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2144,39017]) ).

thf(49740,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) )
       != A )
      | ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) )
       != ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ),
    inference(simp,[status(thm)],[49682]) ).

thf(49807,plain,
    ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) )
   != ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ),
    inference(simp,[status(thm)],[49740]) ).

thf(502,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 @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).

thf(3210,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 @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(983,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/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).

thf(4721,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)],[983]) ).

thf(1457,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( 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(cnfConj,[status(thm)],[1454]) ).

thf(1461,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( 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(simp,[status(thm)],[1457]) ).

thf(4423,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(miniscope,[status(thm)],[4422]) ).

thf(4424,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(cnf,[status(esa)],[4423]) ).

thf(4425,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(lifteq,[status(thm)],[4424]) ).

thf(56047,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Int_Oint @ class_Rings_Ocomm__semiring__1 )
       != ( B @ class_Rings_Ocomm__semiring__1 ) )
      | ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4588,1505]) ).

thf(56048,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Int_Oint @ class_Rings_Ocomm__semiring__1 )
       != ( B @ class_Rings_Ocomm__semiring__1 ) )
      | ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[56047]) ).

thf(56049,plain,
    ! [A: $i] : ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ),
    inference(pattern_uni,[status(thm)],[56048:[bind(A,$thf( A )),bind(B,$thf( tc_Int_Oint ))]]) ).

thf(664,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oabs__if ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oabs__if) ).

thf(3728,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oabs__if ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(409,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
     => ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__not__less) ).

thf(2868,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
     => ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(878,axiom,
    tc_Int_Oint @ class_Groups_Omonoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).

thf(4389,plain,
    tc_Int_Oint @ class_Groups_Omonoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).

thf(888,axiom,
    tc_Int_Oint @ class_Rings_Olinordered__semiring__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).

thf(4421,plain,
    tc_Int_Oint @ class_Rings_Olinordered__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).

thf(309,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__ring )
     => ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).

thf(2455,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__ring )
     => ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[309]) ).

thf(993,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/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).

thf(4750,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)],[993]) ).

thf(928,axiom,
    tc_Complex_Ocomplex @ class_Rings_Omult__zero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).

thf(4545,plain,
    tc_Complex_Ocomplex @ class_Rings_Omult__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).

thf(1207,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/sandbox2/benchmark/theBenchmark.p',fact_add__right__mono) ).

thf(5337,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)],[1207]) ).

thf(991,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/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).

thf(4744,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)],[991]) ).

thf(1139,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ~ ( B @ ( A @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__not__zless) ).

thf(5213,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ~ ( B @ ( A @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).

thf(213,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
     => ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__not__sym) ).

thf(2108,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
     => ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(49,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 @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
          = ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__left) ).

thf(1446,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 @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
          = ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(662,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Opreorder )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).

thf(3723,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Opreorder )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(358,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
          = ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
      <=> ( ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).

thf(2666,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( ( ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
            = A )
         => ( ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
            = ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
        & ( ( ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
            = ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
         => ( ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
            = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(36346,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[28747,1427]) ).

thf(36347,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[36346]) ).

thf(36348,plain,
    tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[36347:[bind(A,$thf( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

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

thf(3555,plain,
    tc_Int_Oint @ class_Rings_Ocomm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(437,axiom,
    ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero )
   != ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).

thf(2978,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)],[437]) ).

thf(354,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Omult__zero )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__right) ).

thf(2649,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Omult__zero )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

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

thf(3242,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
     => ( ( B
         != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
       => ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(917,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/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).

thf(4508,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)],[917]) ).

thf(81,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Ouminus )
     => ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus ) @ hAPP ) )
        = ( A @ ( B @ hAPP ) @ ( D @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__apply) ).

thf(1552,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Ouminus )
     => ( ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Groups_Ouminus__class_Ouminus ) @ hAPP ) )
        = ( A @ ( B @ hAPP ) @ ( D @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(555,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/sandbox2/benchmark/theBenchmark.p',fact_real__0__le__add__iff) ).

thf(3390,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)],[555]) ).

thf(981,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__not__less) ).

thf(4717,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).

thf(822,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( B != A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).

thf(4231,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( B != A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).

thf(561,axiom,
    tc_Nat_Onat @ class_Groups_Ocancel__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).

thf(3409,plain,
    tc_Nat_Onat @ class_Groups_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(383,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( D @ ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
     => ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 ) ) )
       => ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( F @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
               => ( B @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).

thf(2766,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( D @ ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
     => ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 ) ) )
       => ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( D @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( F @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
               => ( B @ ( E @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(1060,axiom,
    tc_Nat_Onat @ class_Power_Opower,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).

thf(4953,plain,
    tc_Nat_Onat @ class_Power_Opower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).

thf(725,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/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).

thf(3920,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)],[725]) ).

thf(5673,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
    | ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( v_cs____ @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,3276]) ).

thf(5676,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( v_cs____ @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[5673]) ).

thf(7319,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
    | ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ~ ( v_cs____ @ ( v_cs____ @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,5676]) ).

thf(7322,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ~ ( v_cs____ @ ( v_cs____ @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[7319]) ).

thf(7333,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ~ ( v_cs____ @ ( v_cs____ @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[7322]) ).

thf(656,axiom,
    tc_Int_Oint @ class_Rings_Omult__zero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).

thf(3703,plain,
    tc_Int_Oint @ class_Rings_Omult__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

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

thf(5063,plain,
    tc_Int_Oint @ class_Rings_Ocomm__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).

thf(1322,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ c_Nat_OSuc @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) )
      | ( B
        = ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
      | ~ ( C @ class_Rings_Oidom ) ),
    inference(cnfConj,[status(thm)],[1320]) ).

thf(1324,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_Polynomial_Oorder ) ) @ c_Nat_OSuc @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( C @ class_Rings_Oidom )
      | ( B
        = ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(lifteq,[status(thm)],[1322]) ).

thf(267,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__ring__1 )
     => ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__diff) ).

thf(2285,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__ring__1 )
     => ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( B @ ( C @ c_Groups_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( C @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(320,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).

thf(2504,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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( 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)],[320]) ).

thf(1190,axiom,
    tc_RealDef_Oreal @ class_Groups_Omonoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).

thf(5317,plain,
    tc_RealDef_Oreal @ class_Groups_Omonoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).

thf(1024,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/sandbox2/benchmark/theBenchmark.p',fact_diff__divide__distrib) ).

thf(4846,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)],[1024]) ).

thf(631,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/sandbox2/benchmark/theBenchmark.p',fact_less__bin__lemma) ).

thf(3611,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)],[631]) ).

thf(307,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oorder) ).

thf(2450,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(645,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
          = ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
       => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
             => ( C = A ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).

thf(3654,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
          = ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
       => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
             => ( C = A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(328,axiom,
    ! [A: $i,B: $i] :
      ( ( B = A )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oeq__refl) ).

thf(2536,plain,
    ! [A: $i,B: $i] :
      ( ( B = A )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(478,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 @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff1) ).

thf(3126,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 @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[478]) ).

thf(50,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/sandbox2/benchmark/theBenchmark.p',fact_le__SucE) ).

thf(1449,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)],[50]) ).

thf(1450,plain,
    ! [B: $i,A: $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 ) ) ) ),
    inference(cnf,[status(esa)],[1449]) ).

thf(1451,plain,
    ! [B: $i,A: $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 ) ) )
      | ( B
        = ( A @ c_Nat_OSuc ) ) ),
    inference(lifteq,[status(thm)],[1450]) ).

thf(1219,axiom,
    tc_RealDef_Oreal @ class_Rings_Oring__1__no__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).

thf(5374,plain,
    tc_RealDef_Oreal @ class_Rings_Oring__1__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).

thf(401,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__leD) ).

thf(2845,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)],[401]) ).

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

thf(3059,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(544,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__algebra__1 )
     => ( A @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__power__ineq) ).

thf(3354,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__algebra__1 )
     => ( A @ ( B @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(770,axiom,
    tc_Complex_Ocomplex @ class_Groups_Oab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).

thf(4068,plain,
    tc_Complex_Ocomplex @ class_Groups_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).

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 ) )
         => ( ( ( D @ ( B @ ( E @ c_Rings_Oinverse__class_Odivide ) ) )
              = ( C @ ( A @ ( E @ c_Rings_Oinverse__class_Odivide ) ) ) )
          <=> ( ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
              = ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__eq__eq) ).

thf(2387,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 @ hAPP ) @ hAPP ) )
                = ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
             => ( ( 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 @ hAPP ) @ hAPP ) )
                = ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(145,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 @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).

thf(1831,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 @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(1067,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__field )
     => ? [C: $i] :
          ( ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( B @ c_Rings_Oinverse__class_Odivide ) ) @ ( 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 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Opos__bounded) ).

thf(4970,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__field )
     => ? [C: $i] :
          ( ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( B @ c_Rings_Oinverse__class_Odivide ) ) @ ( 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 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).

thf(9369,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      | ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
       != tc_RealDef_Oreal )
      | ~ ( B @ c_Groups_Ozero__class_Ozero @ ( v_cs____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
      | ~ ( B @ class_Rings_Omult__zero ) ),
    inference(paramod_ordered,[status(thm)],[1357,5675]) ).

thf(9370,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( v_cs____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
    | ~ ( tc_RealDef_Oreal @ class_Rings_Omult__zero ) ),
    inference(pattern_uni,[status(thm)],[9369:[bind(A,$thf( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero )),bind(B,$thf( tc_RealDef_Oreal ))]]) ).

thf(9497,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( v_cs____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[9370,5361]) ).

thf(9498,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ~ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( v_cs____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[9497]) ).

thf(1147,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Opreorder )
     => ( ( B = A )
       => ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).

thf(5234,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Opreorder )
     => ( ( B = A )
       => ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).

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

thf(1668,plain,
    ! [A: $i] :
      ( ( ( A
          = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
       => ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      & ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       => ( A
          = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(178,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( 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 @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).

thf(1974,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( 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_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[178]) ).

thf(926,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/sandbox2/benchmark/theBenchmark.p',fact_abs__of__pos) ).

thf(4540,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)],[926]) ).

thf(49615,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) ) )
      | ( A
       != ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2957,39017]) ).

thf(49729,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
       != A )
      | ( ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) )
       != ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ),
    inference(simp,[status(thm)],[49615]) ).

thf(49792,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) )
     != ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ),
    inference(simp,[status(thm)],[49729]) ).

thf(785,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/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).

thf(4120,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)],[785]) ).

thf(1873,plain,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = A ),
    inference(cnf,[status(esa)],[1872]) ).

thf(1874,plain,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = A ),
    inference(lifteq,[status(thm)],[1873]) ).

thf(1182,axiom,
    tc_RealDef_Oreal @ class_Rings_Oordered__cancel__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).

thf(5305,plain,
    tc_RealDef_Oreal @ class_Rings_Oordered__cancel__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).

thf(474,axiom,
    ! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__refl) ).

thf(3109,plain,
    ! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

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

thf(3074,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
     => ( ( C @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( 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)],[463]) ).

thf(771,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/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__right) ).

thf(4069,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)],[771]) ).

thf(465,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( A @ ( A @ ( B @ c_Rings_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__refl) ).

thf(3083,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( A @ ( A @ ( B @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(490,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
    <=> ( B @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__reduce) ).

thf(3162,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
       => ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) )
      & ( ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
       => ( B @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(820,axiom,
    ! [A: $i] :
      ( ( A @ class_RealVector_Oreal__normed__algebra )
     => ? [B: $i] :
          ( ! [C: $i,D: $i] : ( B @ ( D @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( C @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( 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 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ononneg__bounded) ).

thf(4223,plain,
    ! [A: $i] :
      ( ( A @ class_RealVector_Oreal__normed__algebra )
     => ? [B: $i] :
          ( ! [C: $i,D: $i] : ( B @ ( D @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( C @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( 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 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).

thf(504,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
     => ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__asym_H) ).

thf(3215,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
     => ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(1154,axiom,
    ! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).

thf(5245,plain,
    ! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).

thf(580,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( B != A )
         => ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).

thf(3454,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( B != A )
         => ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(21,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__0 )
     => ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pCons) ).

thf(1331,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__0 )
     => ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(1332,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) )
      | ~ ( D @ class_Rings_Ocomm__semiring__0 ) ),
    inference(cnf,[status(esa)],[1331]) ).

thf(1333,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ class_Rings_Ocomm__semiring__0 )
      | ( ( A @ ( B @ ( D @ c_Polynomial_Opoly ) @ hAPP ) @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ ( D @ c_Polynomial_OpCons ) ) @ ( D @ c_Polynomial_Opoly ) @ hAPP ) ) ) ),
    inference(lifteq,[status(thm)],[1332]) ).

thf(674,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/sandbox2/benchmark/theBenchmark.p',fact_norm__not__less__zero) ).

thf(3755,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)],[674]) ).

thf(687,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/sandbox2/benchmark/theBenchmark.p',fact_minus__add__cancel) ).

thf(3802,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)],[687]) ).

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

thf(2203,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
     => ( ( B @ ( A @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
       => ( ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
          = ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(845,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/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).

thf(4288,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)],[845]) ).

thf(998,axiom,
    tc_Int_Oint @ class_Rings_Ono__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).

thf(4765,plain,
    tc_Int_Oint @ class_Rings_Ono__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).

thf(1073,axiom,
    tc_Complex_Ocomplex @ class_Groups_Ozero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).

thf(4987,plain,
    tc_Complex_Ocomplex @ class_Groups_Ozero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).

thf(6276,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Groups_Ozero )
       != ( A @ class_Groups_Ozero ) )
      | ~ $true
      | ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Polynomial_OpCons ) ) )
        = ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(paramod_ordered,[status(thm)],[4987,1272]) ).

thf(6277,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Groups_Ozero )
       != ( A @ class_Groups_Ozero ) )
      | ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Polynomial_OpCons ) ) )
        = ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(simp,[status(thm)],[6276]) ).

thf(6278,plain,
    ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) )
    = ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ),
    inference(pattern_uni,[status(thm)],[6277:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(20766,plain,
    ( ( v_cs____ @ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) )
    = v_cs____ ),
    inference(rewrite,[status(thm)],[6278,1280]) ).

thf(85,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 @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).

thf(1563,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 @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(53,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__add__left) ).

thf(1464,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(1465,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) ) )
      | ~ ( D @ class_Rings_Ocomm__semiring__0 ) ),
    inference(cnf,[status(esa)],[1464]) ).

thf(1466,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ class_Rings_Ocomm__semiring__0 )
      | ( ( A @ ( B @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ ( D @ tc_Polynomial_Opoly @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(lifteq,[status(thm)],[1465]) ).

thf(298,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( C @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).

thf(2408,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( A @ ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( C @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(325,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 @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).

thf(2529,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 @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(698,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__ring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).

thf(3824,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)],[698]) ).

thf(1109,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/sandbox2/benchmark/theBenchmark.p',fact_add__left__cancel) ).

thf(5112,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)],[1109]) ).

thf(44,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ono__zero__divisors )
     => ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
          = ( C @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A
            = ( C @ c_Groups_Ozero__class_Ozero ) )
          | ( B
            = ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divisors__zero) ).

thf(1432,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ono__zero__divisors )
     => ( ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
          = ( 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)],[44]) ).

thf(1433,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( C @ c_Groups_Ozero__class_Ozero ) )
      | ( B
        = ( C @ c_Groups_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( C @ c_Groups_Ozero__class_Ozero ) )
      | ~ ( C @ class_Rings_Ono__zero__divisors ) ),
    inference(cnf,[status(esa)],[1432]) ).

thf(1434,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ class_Rings_Ono__zero__divisors )
      | ( A
        = ( C @ c_Groups_Ozero__class_Ozero ) )
      | ( B
        = ( C @ c_Groups_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( C @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(lifteq,[status(thm)],[1433]) ).

thf(810,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/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).

thf(4184,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)],[810]) ).

thf(508,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).

thf(3225,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(136,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring__strict )
     => ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).

thf(1779,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring__strict )
     => ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[136]) ).

thf(1346,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( D @ class_Orderings_Oord ) ),
    inference(cnfConj,[status(thm)],[1345]) ).

thf(8575,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       != ( v_mazh @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      | ~ $true
      | ~ ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( D @ class_Orderings_Oord ) ),
    inference(paramod_ordered,[status(thm)],[1346,1263]) ).

thf(8576,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( A @ hAPP ) @ ( E @ ( B @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       != ( v_mazh @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      | ~ ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( D @ class_Orderings_Oord ) ),
    inference(simp,[status(thm)],[8575]) ).

thf(8599,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( A @ hAPP ) )
       != v_mazh )
      | ( ( E @ ( B @ hAPP ) )
       != v_da____ )
      | ( D != tc_RealDef_Oreal )
      | ~ ( A @ ( B @ ( D @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( D @ class_Orderings_Oord ) ),
    inference(simp,[status(thm)],[8576]) ).

thf(8611,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ hAPP ) )
       != v_mazh )
      | ( ( D @ ( B @ hAPP ) )
       != v_da____ )
      | ~ ( A @ ( B @ ( tc_RealDef_Oreal @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( tc_RealDef_Oreal @ class_Orderings_Oord ) ),
    inference(simp,[status(thm)],[8599]) ).

thf(1225,axiom,
    tc_RealDef_Oreal @ class_Orderings_Oord,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oord) ).

thf(5394,plain,
    tc_RealDef_Oreal @ class_Orderings_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).

thf(9093,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ hAPP ) )
       != v_mazh )
      | ( ( D @ ( B @ hAPP ) )
       != v_da____ )
      | ~ ( A @ ( B @ ( tc_RealDef_Oreal @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ $true ),
    inference(rewrite,[status(thm)],[8611,5394]) ).

thf(9094,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ hAPP ) )
       != v_mazh )
      | ( ( D @ ( B @ hAPP ) )
       != v_da____ )
      | ~ ( A @ ( B @ ( tc_RealDef_Oreal @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(simp,[status(thm)],[9093]) ).

thf(938,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 @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_divide__left__mono__neg) ).

thf(4567,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 @ hAPP ) @ hAPP ) @ ( 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)],[938]) ).

thf(48949,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
       != ( B @ ( B @ ( 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 )
       != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(paramod_ordered,[status(thm)],[5192,4425]) ).

thf(48950,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
     != ( B @ ( B @ ( 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(simp,[status(thm)],[48949]) ).

thf(49015,plain,
    ! [B: $i,A: $i] :
      ( ( A != B )
      | ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
       != ( B @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
      | ( tc_Int_Oint != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[48950]) ).

thf(49071,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
     != ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) ),
    inference(simp,[status(thm)],[49015]) ).

thf(522,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 @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_rabs__ratiotest__lemma) ).

thf(3279,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 @ hAPP ) @ hAPP ) @ ( 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)],[522]) ).

thf(1037,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ? [C: $i] :
          ( ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ 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 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Opos__bounded) ).

thf(4889,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ? [C: $i] :
          ( ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ 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 ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).

thf(624,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/sandbox2/benchmark/theBenchmark.p',fact_divide__self__if) ).

thf(3592,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)],[624]) ).

thf(151,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 @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).

thf(1846,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 @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(1246,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/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).

thf(5434,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)],[1246]) ).

thf(2970,plain,
    ! [A: $i] :
      ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = A ),
    inference(cnf,[status(esa)],[2969]) ).

thf(2971,plain,
    ! [A: $i] :
      ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = A ),
    inference(lifteq,[status(thm)],[2970]) ).

thf(50470,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) ) )
      | ( A
       != ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ),
    inference(paramod_ordered,[status(thm)],[2971,49807]) ).

thf(50500,plain,
    ( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
     != ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
    | ( ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) )
     != ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) ),
    inference(simp,[status(thm)],[50470]) ).

thf(50517,plain,
    ( ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) )
   != ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ),
    inference(simp,[status(thm)],[50500]) ).

thf(16811,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
    | ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Int_Oint )
    | ( v_cs____ != v_mazh )
    | ( v_cs____ != v_da____ )
    | ( tc_Int_Oint != tc_RealDef_Oreal ) ),
    inference(paramod_ordered,[status(thm)],[1280,14941]) ).

thf(16814,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Int_Oint )
    | ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Int_Oint )
    | ( v_cs____ != v_mazh )
    | ( v_cs____ != v_da____ )
    | ( tc_Int_Oint != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[16811]) ).

thf(16825,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Int_Oint )
    | ( v_cs____ != v_mazh )
    | ( v_cs____ != v_da____ )
    | ( tc_Int_Oint != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[16814]) ).

thf(535,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).

thf(3321,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(1254,axiom,
    v_z____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( v_aa____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_h) ).

thf(5447,plain,
    v_z____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( v_c____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( v_aa____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( 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)],[1254]) ).

thf(287,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/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__shift) ).

thf(2368,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)],[287]) ).

thf(1238,axiom,
    ! [A: $i] : ( A @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__refl) ).

thf(5418,plain,
    ! [A: $i] : ( A @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238]) ).

thf(5419,plain,
    ! [A: $i] : ( A @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(cnf,[status(esa)],[5418]) ).

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

thf(3639,plain,
    tc_Int_Oint @ class_Rings_Olinordered__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(162,axiom,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I3_J) ).

thf(1895,plain,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(237,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
       => ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult2) ).

thf(2189,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
       => ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(1610,plain,
    ( ! [A: $i] :
        ( ( A
         != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
       => ( ( ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
              = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ) )
          & ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
              = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) ) ) )
    & ! [A: $i] :
        ( ( A
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
    inference(miniscope,[status(thm)],[1609]) ).

thf(1611,plain,
    ! [B: $i,A: $i] :
      ( ( ( ( B @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
          = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) )
        | ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
        | ( B
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
      & ( ( ( B @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
          = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) )
        | ~ ( B @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
        | ( B
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) )
      & ( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
        | ( A
         != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
    inference(cnf,[status(esa)],[1610]) ).

thf(1612,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
        = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
      | ( A
       != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(cnfConj,[status(thm)],[1611]) ).

thf(1615,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
        = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
      | ( A
       != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(lifteq,[status(thm)],[1612]) ).

thf(1616,plain,
    ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
    = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
    inference(simp,[status(thm)],[1615]) ).

thf(1157,axiom,
    tc_RealDef_Oreal @ class_Rings_Oordered__comm__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).

thf(5249,plain,
    tc_RealDef_Oreal @ class_Rings_Oordered__comm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).

thf(356,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 @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono1) ).

thf(2662,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 @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(750,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/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq) ).

thf(4004,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)],[750]) ).

thf(186,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
    <=> ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__dvd__conv_I1_J) ).

thf(1996,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) )
      & ( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

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

thf(4308,plain,
    tc_Complex_Ocomplex @ class_Groups_Ogroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).

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

thf(2729,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(1200,axiom,
    tc_RealDef_Oreal @ class_Groups_Oordered__ab__group__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).

thf(5327,plain,
    tc_RealDef_Oreal @ class_Groups_Oordered__ab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).

thf(2073,plain,
    ( ! [A: $i,B: $i] :
        ( ( B = A )
       => ( ( B @ c_Nat_OSuc )
          = ( A @ c_Nat_OSuc ) ) )
    & ! [A: $i,B: $i] :
        ( ( ( B @ c_Nat_OSuc )
          = ( A @ c_Nat_OSuc ) )
       => ( B = A ) ) ),
    inference(miniscope,[status(thm)],[2072]) ).

thf(2074,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( ( D @ c_Nat_OSuc )
          = ( C @ c_Nat_OSuc ) )
        | ( D != C ) )
      & ( ( B = A )
        | ( ( B @ c_Nat_OSuc )
         != ( A @ c_Nat_OSuc ) ) ) ),
    inference(cnf,[status(esa)],[2073]) ).

thf(2075,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( ( B @ c_Nat_OSuc )
       != ( A @ c_Nat_OSuc ) ) ),
    inference(cnfConj,[status(thm)],[2074]) ).

thf(2077,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( ( B @ c_Nat_OSuc )
       != ( A @ c_Nat_OSuc ) ) ),
    inference(lifteq,[status(thm)],[2075]) ).

thf(2078,plain,
    ? [A: $i > $i] :
    ! [B: $i] :
      ( ( B @ c_Nat_OSuc @ A )
      = B ),
    inference(detectInverse,[status(thm)],[2077]) ).

thf(2079,plain,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc @ sk8 )
      = A ),
    inference(cnf,[status(esa)],[2078]) ).

thf(18968,plain,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc @ sk8 )
      = A ),
    inference(lifteq,[status(thm)],[2079]) ).

thf(1479,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
        = ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
      | ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
      | ( A
        = ( B @ c_Groups_Ozero__class_Ozero ) )
      | ~ ( B @ class_Groups_Osgn__if ) ),
    inference(cnfConj,[status(thm)],[1476]) ).

thf(1483,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) )
      | ~ ( B @ class_Groups_Osgn__if )
      | ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
        = ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
      | ( A
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(lifteq,[status(thm)],[1479]) ).

thf(1092,axiom,
    tc_Int_Oint @ class_Power_Opower,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).

thf(5048,plain,
    tc_Int_Oint @ class_Power_Opower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).

thf(935,axiom,
    tc_Int_Oint @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

thf(4562,plain,
    tc_Int_Oint @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).

thf(526,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__right) ).

thf(3289,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(340,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
     => ( ( C
         != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__mult__cancel) ).

thf(2602,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
     => ( ( C
         != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(940,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       => ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__pos__nat) ).

thf(4577,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       => ( 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)],[940]) ).

thf(475,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).

thf(3111,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(839,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( ( B = A )
          | ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).

thf(4269,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ( ( ( B = A )
            | ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
         => ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( ( B = A )
            | ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).

thf(248,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Oidom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).

thf(2235,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Oidom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(1050,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/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).

thf(4921,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)],[1050]) ).

thf(300,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 @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__order) ).

thf(2413,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 @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(479,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 @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).

thf(3130,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 @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(949,axiom,
    tc_Nat_Onat @ class_Rings_Ozero__neq__one,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).

thf(4599,plain,
    tc_Nat_Onat @ class_Rings_Ozero__neq__one,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).

thf(8639,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ class_Rings_Ozero__neq__one )
       != ( A @ class_Rings_Ozero__neq__one ) )
      | ~ $true
      | ( ( A @ c_Groups_Oone__class_Oone )
       != ( A @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(paramod_ordered,[status(thm)],[4599,2395]) ).

thf(8640,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ class_Rings_Ozero__neq__one )
       != ( A @ class_Rings_Ozero__neq__one ) )
      | ( ( A @ c_Groups_Oone__class_Oone )
       != ( A @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(simp,[status(thm)],[8639]) ).

thf(8641,plain,
    ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
   != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(pattern_uni,[status(thm)],[8640:[bind(A,$thf( tc_Nat_Onat ))]]) ).

thf(976,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/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).

thf(4685,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)],[976]) ).

thf(422,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__idom )
     => ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
          = ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
      <=> ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__1__neg) ).

thf(2904,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_Osgn__class_Osgn ) )
            = ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) )
        & ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
            = ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) )
         => ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(113,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 @ hAPP ) @ hAPP ) )
        = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__left) ).

thf(1698,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 @ hAPP ) @ hAPP ) )
        = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(332,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Lattices_Oboolean__algebra )
     => ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).

thf(2556,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Lattices_Oboolean__algebra )
     => ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(783,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/sandbox2/benchmark/theBenchmark.p',fact_zero__le__one) ).

thf(4116,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)],[783]) ).

thf(254,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
     => ( ( A @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
       => ( B @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__zdiffD) ).

thf(2253,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
     => ( ( A @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
       => ( B @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(225,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
    <=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).

thf(2149,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 @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      & ( ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[225]) ).

thf(4167,plain,
    ( v_c____
   != ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) ),
    inference(polarity_switch,[status(thm)],[4166]) ).

thf(4168,plain,
    ( ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero )
   != v_c____ ),
    inference(lifteq,[status(thm)],[4167]) ).

thf(11103,plain,
    ! [B: $i,A: $i] :
      ( ( B
       != ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) )
      | ( A != v_c____ )
      | ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1370,4168]) ).

thf(11104,plain,
    ! [A: $i] :
      ( ( A != v_c____ )
      | ~ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(pattern_uni,[status(thm)],[11103:[bind(A,$thf( A )),bind(B,$thf( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ))]]) ).

thf(12119,plain,
    ( ~ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( v_c____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
    | ~ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[11104]) ).

thf(15694,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( v_c____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ $true
      | ~ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1542,12119]) ).

thf(15695,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( v_c____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[15694]) ).

thf(15714,plain,
    ! [A: $i] :
      ( ( A
       != ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) )
      | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
       != v_c____ )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ~ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[15695]) ).

thf(15722,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_c____ )
    | ~ ( v_c____ @ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[15714]) ).

thf(23276,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_c____ @ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
       != v_c____ )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3313,15722]) ).

thf(23277,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_c____ @ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
       != v_c____ ) ),
    inference(simp,[status(thm)],[23276]) ).

thf(23347,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != v_c____ )
      | ( A
       != ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
       != v_c____ ) ),
    inference(simp,[status(thm)],[23277]) ).

thf(23365,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != v_c____ )
    | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_c____ ) ),
    inference(simp,[status(thm)],[23347]) ).

thf(517,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
       => ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__left) ).

thf(3257,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
       => ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(718,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/sandbox2/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).

thf(3890,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)],[718]) ).

thf(1031,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/sandbox2/benchmark/theBenchmark.p',fact_diff__def) ).

thf(4874,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)],[1031]) ).

thf(1173,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/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).

thf(5278,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)],[1173]) ).

thf(49705,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) ) )
      | ( A
       != ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2971,39017]) ).

thf(49725,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
       != A )
      | ( ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) )
       != ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ),
    inference(simp,[status(thm)],[49705]) ).

thf(49788,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) )
     != ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ),
    inference(simp,[status(thm)],[49725]) ).

thf(1146,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oorder )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C = A )
         => ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I4_J) ).

thf(5230,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oorder )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C = A )
         => ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).

thf(126,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ouminus )
     => ( B @ ( A @ tc_fun ) @ class_Groups_Ouminus ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).

thf(1747,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ouminus )
     => ( B @ ( A @ tc_fun ) @ class_Groups_Ouminus ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(79,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).

thf(1548,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(669,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/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__less) ).

thf(3738,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)],[669]) ).

thf(1298,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( C @ c_Groups_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) )
       != ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
      | ~ ( C @ class_Groups_Ozero ) ),
    inference(cnfConj,[status(thm)],[1297]) ).

thf(1301,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ class_Groups_Ozero )
      | ( B
        = ( C @ c_Groups_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) )
       != ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(lifteq,[status(thm)],[1298]) ).

thf(860,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/sandbox2/benchmark/theBenchmark.p',fact_minus__diff__eq) ).

thf(4340,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)],[860]) ).

thf(549,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Rings_Osemiring__0 )
        & ( B @ class_Power_Opower ) )
     => ( ( A @ c_Nat_OSuc @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__Suc) ).

thf(3375,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Rings_Osemiring__0 )
        & ( B @ class_Power_Opower ) )
     => ( ( A @ c_Nat_OSuc @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

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

thf(3523,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( B != A )
         => ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(374,axiom,
    ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
   != ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__neq__1) ).

thf(2732,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)],[374]) ).

thf(2733,plain,
    ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
   != ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
    inference(polarity_switch,[status(thm)],[2732]) ).

thf(2734,plain,
    ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
   != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
    inference(lifteq,[status(thm)],[2733]) ).

thf(870,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/sandbox2/benchmark/theBenchmark.p',fact_diff__poly__code_I2_J) ).

thf(4365,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)],[870]) ).

thf(556,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/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).

thf(3396,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)],[556]) ).

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

thf(4453,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__vector,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).

thf(99,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Power_Opower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).

thf(1631,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Power_Opower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(1150,axiom,
    tc_RealDef_Oreal @ class_Groups_Oabs__if,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oabs__if) ).

thf(5241,plain,
    tc_RealDef_Oreal @ class_Groups_Oabs__if,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).

thf(1007,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/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).

thf(4786,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)],[1007]) ).

thf(797,axiom,
    tc_Int_Oint @ class_Rings_Osemiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).

thf(4144,plain,
    tc_Int_Oint @ class_Rings_Osemiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).

thf(48926,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
       != ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) )
      | ( ( B @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
        = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(paramod_ordered,[status(thm)],[4888,5192]) ).

thf(48927,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
    inference(pattern_uni,[status(thm)],[48926:[bind(A,$thf( D )),bind(B,$thf( D @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ))]]) ).

thf(49036,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
      = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
    inference(simp,[status(thm)],[48927]) ).

thf(146,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 @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg) ).

thf(1833,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 @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(372,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 @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__pos) ).

thf(2727,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 @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(681,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/sandbox2/benchmark/theBenchmark.p',fact_divide_Ominus) ).

thf(3768,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)],[681]) ).

thf(426,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).

thf(2938,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 @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[426]) ).

thf(10699,plain,
    ! [B: $i,A: $i] :
      ( ( B != v_mazh )
      | ~ ( A @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1370,1263]) ).

thf(10700,plain,
    ! [A: $i] :
      ( ~ ( A @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( v_mazh @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(pattern_uni,[status(thm)],[10699:[bind(A,$thf( A )),bind(B,$thf( v_mazh ))]]) ).

thf(904,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Lattices_Oboolean__algebra )
     => ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
          = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).

thf(4465,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Lattices_Oboolean__algebra )
     => ( ( ( 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)],[904]) ).

thf(1167,axiom,
    tc_RealDef_Oreal @ class_Int_Oring__char__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).

thf(5271,plain,
    tc_RealDef_Oreal @ class_Int_Oring__char__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).

thf(1149,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Lattices_Oboolean__algebra )
     => ( ( 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/sandbox2/benchmark/theBenchmark.p',fact_compl__mono) ).

thf(5239,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Lattices_Oboolean__algebra )
     => ( ( 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)],[1149]) ).

thf(1056,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/sandbox2/benchmark/theBenchmark.p',fact_add__divide__distrib) ).

thf(4946,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)],[1056]) ).

thf(503,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 @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__pos) ).

thf(3213,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 @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(245,axiom,
    ! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__cube) ).

thf(2225,plain,
    ! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(602,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/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split) ).

thf(3504,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)],[602]) ).

thf(843,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/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).

thf(4283,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)],[843]) ).

thf(138,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 @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__divide__eq__iff) ).

thf(1784,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 @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(913,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/sandbox2/benchmark/theBenchmark.p',fact_abs__le__iff) ).

thf(4494,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)],[913]) ).

thf(28207,plain,
    v_mzh @ ( v_ma @ ( v_da____ @ ( tc_RealDef_Oreal @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ),
    inference(rewrite,[status(thm)],[5330,5033]) ).

thf(516,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
     => ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__asym) ).

thf(3255,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
     => ~ ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(691,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/sandbox2/benchmark/theBenchmark.p',fact_divide__nonpos__neg) ).

thf(3811,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)],[691]) ).

thf(1226,axiom,
    tc_RealDef_Oreal @ class_Rings_Oordered__ring__abs,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring__abs) ).

thf(5395,plain,
    tc_RealDef_Oreal @ class_Rings_Oordered__ring__abs,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).

thf(388,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__assoc) ).

thf(2791,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(630,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/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).

thf(3609,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)],[630]) ).

thf(800,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( B != A )
       => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).

thf(4159,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( B != A )
       => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).

thf(8468,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__0 )
       != ( B @ class_Rings_Ocomm__semiring__0 ) )
      | ~ $true
      | ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Osynthetic__div ) ) )
        = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(paramod_ordered,[status(thm)],[5311,1266]) ).

thf(8469,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__0 )
       != ( B @ class_Rings_Ocomm__semiring__0 ) )
      | ( ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( B @ c_Polynomial_Osynthetic__div ) ) )
        = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(simp,[status(thm)],[8468]) ).

thf(8470,plain,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Polynomial_Osynthetic__div ) ) )
      = ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ),
    inference(pattern_uni,[status(thm)],[8469:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal ))]]) ).

thf(854,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/sandbox2/benchmark/theBenchmark.p',fact_equation__minus__iff) ).

thf(4309,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)],[854]) ).

thf(589,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/sandbox2/benchmark/theBenchmark.p',fact_real__add__le__0__iff) ).

thf(3472,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)],[589]) ).

thf(317,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
    <=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        | ( C
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).

thf(2489,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          | ( C
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
       => ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      & ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          | ( C
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(128,axiom,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != ( A @ c_Nat_OSuc ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).

thf(1752,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != ( A @ c_Nat_OSuc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(104,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__left) ).

thf(1652,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(676,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/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).

thf(3758,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)],[676]) ).

thf(731,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).

thf(3945,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).

thf(3959,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 ) ) ) )
    & ! [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 ) ) ) ),
    inference(miniscope,[status(thm)],[3958]) ).

thf(3960,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
        | ( B
         != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
      & ( ( 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 ) ) ) ) ),
    inference(cnf,[status(esa)],[3959]) ).

thf(3962,plain,
    ! [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 ) ) ),
    inference(cnfConj,[status(thm)],[3960]) ).

thf(3964,plain,
    ! [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 ) ) ),
    inference(lifteq,[status(thm)],[3962]) ).

thf(3965,plain,
    tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ),
    inference(simp,[status(thm)],[3964]) ).

thf(16263,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       != ( A @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3965,4819]) ).

thf(16264,plain,
    ! [A: $i] :
      ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
     != ( A @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[16263]) ).

thf(16301,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
       != A )
      | ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
       != A )
      | ( tc_Int_Oint != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[16264]) ).

thf(16323,plain,
    ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
   != ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ),
    inference(simp,[status(thm)],[16301]) ).

thf(972,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/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).

thf(4677,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)],[972]) ).

thf(1669,plain,
    ( ! [A: $i] :
        ( ( A
          = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
       => ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
    & ! [A: $i] :
        ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       => ( A
          = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ) ),
    inference(miniscope,[status(thm)],[1668]) ).

thf(1670,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        | ( B
         != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) )
      & ( ( A
          = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
        | ~ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(cnf,[status(esa)],[1669]) ).

thf(1672,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ( A
       != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ),
    inference(cnfConj,[status(thm)],[1670]) ).

thf(1674,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ( A
       != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) ),
    inference(lifteq,[status(thm)],[1672]) ).

thf(1675,plain,
    tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ),
    inference(simp,[status(thm)],[1674]) ).

thf(13714,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_da____ @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ ( v_mazh @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ $true
      | ~ ( A @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1675,10698]) ).

thf(13715,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_da____ @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ ( v_mazh @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( A @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[13714]) ).

thf(13783,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
       != v_da____ )
      | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
       != A )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ~ ( v_mazh @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( A @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[13715]) ).

thf(13795,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_da____ )
    | ~ ( v_mazh @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
    | ~ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[13783]) ).

thf(14140,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
     != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
    | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_da____ )
    | ~ ( v_mazh @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1675,13795]) ).

thf(14141,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
     != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
    | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_da____ )
    | ~ ( v_mazh @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(simp,[status(thm)],[14140]) ).

thf(14171,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
    | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_da____ )
    | ( tc_Nat_Onat != tc_Nat_Onat )
    | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_da____ )
    | ~ ( v_mazh @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(simp,[status(thm)],[14141]) ).

thf(14183,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_da____ )
    | ~ ( v_mazh @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(simp,[status(thm)],[14171]) ).

thf(17879,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       != ( v_mazh @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
       != v_da____ )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[5270,14183]) ).

thf(17880,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       != ( v_mazh @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
       != v_da____ ) ),
    inference(simp,[status(thm)],[17879]) ).

thf(17913,plain,
    ! [A: $i] :
      ( ( A != v_mazh )
      | ( A
       != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
      | ( tc_RealDef_Oreal != tc_RealDef_Oreal )
      | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
       != v_da____ ) ),
    inference(simp,[status(thm)],[17880]) ).

thf(17931,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_mazh )
    | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_da____ ) ),
    inference(simp,[status(thm)],[17913]) ).

thf(1011,axiom,
    tc_Complex_Ocomplex @ class_Rings_Oring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).

thf(4801,plain,
    tc_Complex_Ocomplex @ class_Rings_Oring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).

thf(786,axiom,
    tc_Nat_Onat @ class_Rings_Osemiring__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).

thf(4122,plain,
    tc_Nat_Onat @ class_Rings_Osemiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).

thf(74,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/sandbox2/benchmark/theBenchmark.p',fact_divide__1) ).

thf(1535,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)],[74]) ).

thf(19658,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
       != ( A @ c_Nat_OSuc ) )
      | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ sk16 )
        = A ) ),
    inference(paramod_ordered,[status(thm)],[2249,19653]) ).

thf(19659,plain,
    ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ sk16 )
    = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(pattern_uni,[status(thm)],[19658:[bind(A,$thf( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ))]]) ).

thf(114,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
     => ( ! [D: $i] :
            ( ( D @ ( B @ hAPP ) @ hBOOL )
           => ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ hAPP ) @ hBOOL ) )
       => ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ! [D: $i] :
              ( ( D @ ( B @ hAPP ) @ hBOOL )
             => ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ hAPP ) @ hBOOL ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incr__mult__lemma) ).

thf(1701,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
     => ( ! [D: $i] :
            ( ( D @ ( B @ hAPP ) @ hBOOL )
           => ( C @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ hAPP ) @ hBOOL ) )
       => ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ! [D: $i] :
              ( ( D @ ( B @ hAPP ) @ hBOOL )
             => ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ hAPP ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(623,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/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).

thf(3590,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)],[623]) ).

thf(709,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/sandbox2/benchmark/theBenchmark.p',fact_divide__right__mono) ).

thf(3868,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)],[709]) ).

thf(996,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/sandbox2/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).

thf(4758,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)],[996]) ).

thf(1001,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/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).

thf(4769,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)],[1001]) ).

thf(221,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/sandbox2/benchmark/theBenchmark.p',fact_abs__one) ).

thf(2134,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)],[221]) ).

thf(21908,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
    | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_mazh )
    | ( v_cs____ != v_mazh ) ),
    inference(paramod_ordered,[status(thm)],[1280,21570]) ).

thf(21909,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Nat_Onat )
    | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_mazh )
    | ( v_cs____ != v_mazh ) ),
    inference(simp,[status(thm)],[21908]) ).

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

thf(3599,plain,
    tc_Complex_Ocomplex @ class_Rings_Oring__1__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(239,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oidom )
     => ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
      <=> ( ( B
            = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
          | ( B = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__two__disj) ).

thf(2193,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oidom )
     => ( ( ( ( B
              = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
            | ( B = A ) )
         => ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) )
        & ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( A @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
         => ( ( B
              = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
            | ( B = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(811,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
        | ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).

thf(4186,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
        | ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).

thf(541,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 ) ) )
     => ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__pos__lemma) ).

thf(3340,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 ) ) )
     => ( ( C @ ( A @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ ( 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)],[541]) ).

thf(231,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
     => ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
       => ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__less__trans) ).

thf(2166,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
     => ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
       => ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(310,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 @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).

thf(2457,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 @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(566,axiom,
    tc_Nat_Onat @ class_Orderings_Oord,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).

thf(3416,plain,
    tc_Nat_Onat @ class_Orderings_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(531,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__ring__strict )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).

thf(3304,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 @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[531]) ).

thf(14934,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
    | ( v_cs____ != v_mazh )
    | ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
     != v_da____ )
    | ( tc_Int_Oint != tc_RealDef_Oreal ) ),
    inference(paramod_ordered,[status(thm)],[1280,14480]) ).

thf(14942,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Int_Oint )
    | ( v_cs____ != v_mazh )
    | ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
     != v_da____ )
    | ( tc_Int_Oint != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[14934]) ).

thf(660,axiom,
    tc_Nat_Onat @ class_Groups_Oab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).

thf(3719,plain,
    tc_Nat_Onat @ class_Groups_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(492,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).

thf(3170,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(43,axiom,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__not__Zero) ).

thf(1428,plain,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(507,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__group__add__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs) ).

thf(3223,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)],[507]) ).

thf(13195,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__1 )
       != ( B @ class_Rings_Ocomm__semiring__1 ) )
      | ~ $true
      | ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(paramod_ordered,[status(thm)],[4958,1383]) ).

thf(13196,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__1 )
       != ( B @ class_Rings_Ocomm__semiring__1 ) )
      | ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(simp,[status(thm)],[13195]) ).

thf(13197,plain,
    ! [A: $i] :
      ( ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Complex_Ocomplex @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) ),
    inference(pattern_uni,[status(thm)],[13196:[bind(A,$thf( A )),bind(B,$thf( tc_Complex_Ocomplex ))]]) ).

thf(1502,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
      = ( A @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
    inference(cnf,[status(esa)],[1501]) ).

thf(1503,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
      = ( A @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
    inference(lifteq,[status(thm)],[1502]) ).

thf(1129,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/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).

thf(5185,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)],[1129]) ).

thf(1069,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/sandbox2/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).

thf(4978,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)],[1069]) ).

thf(477,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__ring__strict )
     => ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).

thf(3118,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 @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[477]) ).

thf(788,axiom,
    tc_Complex_Ocomplex @ class_Groups_Ocancel__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).

thf(4127,plain,
    tc_Complex_Ocomplex @ class_Groups_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).

thf(29,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C = B )
     => ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
       => ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__eq__less__trans) ).

thf(1371,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C = B )
     => ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
       => ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(1023,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/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).

thf(4837,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)],[1023]) ).

thf(1312,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( C @ c_Polynomial_Oorder ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( C @ class_Rings_Oidom ) ),
    inference(cnf,[status(esa)],[1311]) ).

thf(59,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Opreorder) ).

thf(1490,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(1491,plain,
    ! [A: $i] :
      ( ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder )
      | ~ ( A @ class_Rings_Olinordered__idom ) ),
    inference(cnf,[status(esa)],[1490]) ).

thf(49528,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Rings_Olinordered__idom )
       != ( A @ class_Rings_Olinordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[5256,1491]) ).

thf(49529,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Rings_Olinordered__idom )
       != ( A @ class_Rings_Olinordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder ) ),
    inference(simp,[status(thm)],[49528]) ).

thf(49530,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Orderings_Opreorder,
    inference(pattern_uni,[status(thm)],[49529:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(15096,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       != ( v_c____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4294,3407]) ).

thf(15097,plain,
    ! [A: $i] :
      ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     != ( v_c____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[15096]) ).

thf(15137,plain,
    ! [A: $i] :
      ( ( ( v_c____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
      | ( A
       != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
      | ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[15097]) ).

thf(15160,plain,
    ( ( ( v_c____ @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
    | ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[15137]) ).

thf(539,axiom,
    ! [A: $i] :
      ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
    <=> ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
        = ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd1__eq) ).

thf(3330,plain,
    ! [A: $i] :
      ( ( ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
          = ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
       => ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) )
      & ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
       => ( ( A @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
          = ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(501,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 @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult__ineq) ).

thf(3208,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 @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(1203,axiom,
    tc_RealDef_Oreal @ class_Orderings_Oorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).

thf(5331,plain,
    tc_RealDef_Oreal @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).

thf(648,axiom,
    ! [A: $i] :
      ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).

thf(3663,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)],[648]) ).

thf(969,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/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).

thf(4672,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)],[969]) ).

thf(425,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) )
      = ( B @ ( A @ ( tc_RealDef_Oreal @ c_Rings_Oinverse__class_Odivide ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__divide__square__eq) ).

thf(2935,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[425]) ).

thf(1016,axiom,
    tc_Complex_Ocomplex @ class_Groups_Ocancel__comm__monoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add) ).

thf(4822,plain,
    tc_Complex_Ocomplex @ class_Groups_Ocancel__comm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).

thf(1138,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/sandbox2/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).

thf(5207,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)],[1138]) ).

thf(594,axiom,
    tc_Int_Oint @ class_Rings_Oordered__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).

thf(3487,plain,
    tc_Int_Oint @ class_Rings_Oordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(768,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/sandbox2/benchmark/theBenchmark.p',fact_real__0__less__add__iff) ).

thf(4060,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)],[768]) ).

thf(1256,axiom,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__div__algebra,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).

thf(5449,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__div__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256]) ).

thf(1121,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__eq) ).

thf(5158,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)],[1121]) ).

thf(337,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/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq) ).

thf(2584,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)],[337]) ).

thf(2585,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: $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 ) ) ) ) ) ),
    inference(miniscope,[status(thm)],[2584]) ).

thf(2586,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( C @ c_Nat_OSuc @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
        | ( D != C ) )
      & ( ( C @ c_Nat_OSuc @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
        | ~ ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( 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 ) ) ) ) ),
    inference(cnf,[status(esa)],[2585]) ).

thf(2589,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
      | ( B != A ) ),
    inference(cnfConj,[status(thm)],[2586]) ).

thf(2592,plain,
    ! [B: $i,A: $i] :
      ( ( A @ c_Nat_OSuc @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
      | ( B != A ) ),
    inference(lifteq,[status(thm)],[2589]) ).

thf(2593,plain,
    ! [A: $i] : ( A @ c_Nat_OSuc @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    inference(simp,[status(thm)],[2592]) ).

thf(19056,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_Nat_OSuc @ ( A @ ( 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 @ ( B @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2593,1343]) ).

thf(19057,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_Nat_OSuc @ ( A @ ( 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 @ ( B @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[19056]) ).

thf(19058,plain,
    tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ),
    inference(pattern_uni,[status(thm)],[19057:[bind(A,$thf( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )),bind(B,$thf( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ))]]) ).

thf(45349,plain,
    tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ),
    inference(rewrite,[status(thm)],[19058,2249,2841]) ).

thf(315,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Rings_Osemiring__0 )
        & ( B @ class_Power_Opower ) )
     => ( ( ( A
           != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
            = ( B @ c_Groups_Ozero__class_Ozero ) ) )
        & ( ( A
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
            = ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__left) ).

thf(2474,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ class_Rings_Osemiring__0 )
        & ( B @ class_Power_Opower ) )
     => ( ( ( A
           != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
            = ( B @ c_Groups_Ozero__class_Ozero ) ) )
        & ( ( A
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
            = ( B @ c_Groups_Oone__class_Oone ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(102,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 @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).

thf(1638,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 @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(828,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/sandbox2/benchmark/theBenchmark.p',fact_abs__eq__0) ).

thf(4245,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)],[828]) ).

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

thf(1336,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_RealVector_Oreal__normed__algebra )
      | ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(lifteq,[status(thm)],[1335]) ).

thf(7527,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra )
       != ( B @ class_RealVector_Oreal__normed__algebra ) )
      | ~ $true
      | ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(paramod_ordered,[status(thm)],[3495,1336]) ).

thf(7528,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra )
       != ( B @ class_RealVector_Oreal__normed__algebra ) )
      | ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(simp,[status(thm)],[7527]) ).

thf(7529,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) ),
    inference(pattern_uni,[status(thm)],[7528:[bind(A,$thf( A )),bind(B,$thf( tc_Complex_Ocomplex ))]]) ).

thf(369,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Ocomm__semiring__1 )
     => ( ( C @ ( D @ ( E @ c_Rings_Odvd__class_Odvd ) ) )
       => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power__le) ).

thf(2721,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Ocomm__semiring__1 )
     => ( ( C @ ( D @ ( E @ c_Rings_Odvd__class_Odvd ) ) )
       => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(915,axiom,
    tc_Nat_Onat @ class_Groups_Ozero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).

thf(4506,plain,
    tc_Nat_Onat @ class_Groups_Ozero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).

thf(5669,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ class_Groups_Ozero )
       != ( A @ class_Groups_Ozero ) )
      | ~ $true
      | ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Polynomial_OpCons ) ) )
        = ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(paramod_ordered,[status(thm)],[4506,1272]) ).

thf(5670,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ class_Groups_Ozero )
       != ( A @ class_Groups_Ozero ) )
      | ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Ozero__class_Ozero @ ( A @ c_Polynomial_OpCons ) ) )
        = ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(simp,[status(thm)],[5669]) ).

thf(5671,plain,
    ( ( tc_Nat_Onat @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Polynomial_OpCons ) ) )
    = ( tc_Nat_Onat @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ),
    inference(pattern_uni,[status(thm)],[5670:[bind(A,$thf( tc_Nat_Onat ))]]) ).

thf(1153,axiom,
    tc_RealDef_Oreal @ class_Rings_Oordered__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).

thf(5244,plain,
    tc_RealDef_Oreal @ class_Rings_Oordered__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).

thf(21435,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
    | ( v_cs____ != v_mazh )
    | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != v_da____ ) ),
    inference(paramod_ordered,[status(thm)],[1280,21237]) ).

thf(21436,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Nat_Onat )
    | ( v_cs____ != v_mazh )
    | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != v_da____ ) ),
    inference(simp,[status(thm)],[21435]) ).

thf(24707,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
    | ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Nat_Onat )
    | ( v_cs____ != v_mazh )
    | ( v_cs____ != v_da____ ) ),
    inference(paramod_ordered,[status(thm)],[1280,21436]) ).

thf(24712,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Nat_Onat )
    | ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Nat_Onat )
    | ( v_cs____ != v_mazh )
    | ( v_cs____ != v_da____ ) ),
    inference(simp,[status(thm)],[24707]) ).

thf(24720,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Nat_Onat )
    | ( v_cs____ != v_mazh )
    | ( v_cs____ != v_da____ ) ),
    inference(simp,[status(thm)],[24712]) ).

thf(69,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).

thf(1524,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)],[69]) ).

thf(568,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__field,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__field) ).

thf(3419,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__field,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(256,axiom,
    ! [A: $i] :
      ( ( A @ class_Groups_Ozero )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ozero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).

thf(2257,plain,
    ! [A: $i] :
      ( ( A @ class_Groups_Ozero )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(795,axiom,
    tc_Int_Oint @ class_Groups_Ogroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).

thf(4139,plain,
    tc_Int_Oint @ class_Groups_Ogroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).

thf(419,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 @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
          = ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__right) ).

thf(2896,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 @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
          = ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(1003,axiom,
    tc_Complex_Ocomplex @ class_Rings_Oidom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).

thf(4773,plain,
    tc_Complex_Ocomplex @ class_Rings_Oidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).

thf(489,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).

thf(3160,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

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

thf(4388,plain,
    tc_Int_Oint @ class_Rings_Ozero__neq__one,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).

thf(1051,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/sandbox2/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).

thf(4927,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)],[1051]) ).

thf(4928,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(cnf,[status(esa)],[4927]) ).

thf(4929,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(lifteq,[status(thm)],[4928]) ).

thf(15698,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_mazh @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ ( B @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ $true
      | ~ ( B @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1542,10700]) ).

thf(15699,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_mazh @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ ( B @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( B @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[15698]) ).

thf(15700,plain,
    ( ~ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
    | ~ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(pattern_uni,[status(thm)],[15699:[bind(A,$thf( v_mazh )),bind(B,$thf( tc_Nat_Onat @ c_Groups_Oone__class_Oone ))]]) ).

thf(748,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/sandbox2/benchmark/theBenchmark.p',fact_abs__poly__def) ).

thf(3996,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)],[748]) ).

thf(638,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/sandbox2/benchmark/theBenchmark.p',fact_abs__real__def) ).

thf(3631,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)],[638]) ).

thf(154,axiom,
    ! [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_RealVector_Onorm__class_Onorm ) )
            = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) )
        & ( ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_RealVector_Onorm__class_Onorm ) )
            = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__sgn) ).

thf(1853,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_RealVector_Onorm__class_Onorm ) )
            = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) )
        & ( ( A
            = ( B @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_RealVector_Onorm__class_Onorm ) )
            = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(679,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__leE) ).

thf(3764,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).

thf(8676,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( F @ ( D @ hAPP ) ) )
      | ( ( F @ ( C @ hAPP ) )
       != v_mazh )
      | ( ( B @ c_Groups_Ozero__class_Ozero )
       != v_da____ )
      | ~ ( C @ ( D @ ( tc_RealDef_Oreal @ ( E @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( tc_RealDef_Oreal @ class_Orderings_Oord )
      | ~ ( B @ class_RealVector_Oreal__normed__algebra ) ),
    inference(paramod_ordered,[status(thm)],[1336,8611]) ).

thf(8677,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ hAPP ) )
       != v_mazh )
      | ( ( D @ c_Groups_Ozero__class_Ozero )
       != v_da____ )
      | ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_RealDef_Oreal @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( tc_RealDef_Oreal @ class_Orderings_Oord )
      | ~ ( D @ class_RealVector_Oreal__normed__algebra ) ),
    inference(pattern_uni,[status(thm)],[8676:[bind(A,$thf( A )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( J @ c_Groups_Ozero__class_Ozero @ ( J @ c_Groups_Otimes__class_Otimes @ hAPP ) )),bind(E,$thf( E )),bind(F,$thf( A ))]]) ).

thf(8693,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ hAPP ) )
       != v_mazh )
      | ( ( D @ c_Groups_Ozero__class_Ozero )
       != v_da____ )
      | ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_RealDef_Oreal @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( tc_RealDef_Oreal @ class_Orderings_Oord )
      | ~ ( D @ class_RealVector_Oreal__normed__algebra ) ),
    inference(simp,[status(thm)],[8677]) ).

thf(8928,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra )
       != ( D @ class_RealVector_Oreal__normed__algebra ) )
      | ( ( A @ ( B @ hAPP ) )
       != v_mazh )
      | ( ( D @ c_Groups_Ozero__class_Ozero )
       != v_da____ )
      | ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_RealDef_Oreal @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( tc_RealDef_Oreal @ class_Orderings_Oord )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3495,8693]) ).

thf(8929,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra )
       != ( D @ class_RealVector_Oreal__normed__algebra ) )
      | ( ( A @ ( B @ hAPP ) )
       != v_mazh )
      | ( ( D @ c_Groups_Ozero__class_Ozero )
       != v_da____ )
      | ~ ( B @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_RealDef_Oreal @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( tc_RealDef_Oreal @ class_Orderings_Oord ) ),
    inference(simp,[status(thm)],[8928]) ).

thf(8930,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ hAPP ) )
       != v_mazh )
      | ( ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero )
       != v_da____ )
      | ~ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_RealDef_Oreal @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( tc_RealDef_Oreal @ class_Orderings_Oord ) ),
    inference(pattern_uni,[status(thm)],[8929:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( tc_Complex_Ocomplex ))]]) ).

thf(9210,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ hAPP ) )
       != v_mazh )
      | ( ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero )
       != v_da____ )
      | ~ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_RealDef_Oreal @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ $true ),
    inference(rewrite,[status(thm)],[8930,5394]) ).

thf(9211,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ hAPP ) )
       != v_mazh )
      | ( ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero )
       != v_da____ )
      | ~ ( B @ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_RealDef_Oreal @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(simp,[status(thm)],[9210]) ).

thf(9264,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
       != ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ hAPP ) )
       != v_mazh )
      | ( ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero )
       != v_da____ )
      | ~ ( B @ ( v_cs____ @ ( tc_Complex_Ocomplex @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_RealDef_Oreal @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,9211]) ).

thf(9271,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
       != tc_Complex_Ocomplex )
      | ( ( A @ ( B @ hAPP ) )
       != v_mazh )
      | ( ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero )
       != v_da____ )
      | ~ ( B @ ( v_cs____ @ ( tc_Complex_Ocomplex @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_RealDef_Oreal @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(simp,[status(thm)],[9264]) ).

thf(9586,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
       != ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) )
      | ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
       != tc_Complex_Ocomplex )
      | ( ( A @ ( B @ hAPP ) )
       != v_mazh )
      | ( v_cs____ != v_da____ )
      | ~ ( B @ ( v_cs____ @ ( tc_Complex_Ocomplex @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_RealDef_Oreal @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,9271]) ).

thf(9592,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
       != tc_Complex_Ocomplex )
      | ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
       != tc_Complex_Ocomplex )
      | ( ( A @ ( B @ hAPP ) )
       != v_mazh )
      | ( v_cs____ != v_da____ )
      | ~ ( B @ ( v_cs____ @ ( tc_Complex_Ocomplex @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_RealDef_Oreal @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(simp,[status(thm)],[9586]) ).

thf(9614,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
       != tc_Complex_Ocomplex )
      | ( ( A @ ( B @ hAPP ) )
       != v_mazh )
      | ( v_cs____ != v_da____ )
      | ~ ( B @ ( v_cs____ @ ( tc_Complex_Ocomplex @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_RealDef_Oreal @ ( C @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(simp,[status(thm)],[9592]) ).

thf(24483,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
    | ( v_cs____ != v_c____ )
    | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_c____ ) ),
    inference(paramod_ordered,[status(thm)],[1280,23365]) ).

thf(24484,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Nat_Onat )
    | ( v_cs____ != v_c____ )
    | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_c____ ) ),
    inference(simp,[status(thm)],[24483]) ).

thf(301,axiom,
    ! [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_Osgn__class_Osgn ) )
          = ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__neg) ).

thf(2415,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_Osgn__class_Osgn ) )
          = ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Ouminus__class_Ouminus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(1107,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/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).

thf(5103,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)],[1107]) ).

thf(349,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Odvd ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Odvd) ).

thf(2637,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Odvd ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(1198,axiom,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__vector,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).

thf(5325,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__vector,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).

thf(1047,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/sandbox2/benchmark/theBenchmark.p',fact_abs__add__one__not__less__self) ).

thf(4914,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)],[1047]) ).

thf(1602,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(cnf,[status(esa)],[1601]) ).

thf(1603,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ c_Nat_OSuc ) ),
    inference(lifteq,[status(thm)],[1602]) ).

thf(271,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oring__1 )
     => ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus) ).

thf(2299,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oring__1 )
     => ( ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(473,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/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).

thf(3106,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)],[473]) ).

thf(943,axiom,
    tc_Int_Oint @ class_Rings_Oring__1__no__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).

thf(4586,plain,
    tc_Int_Oint @ class_Rings_Oring__1__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).

thf(1232,axiom,
    tc_RealDef_Oreal @ class_Rings_Ono__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).

thf(5407,plain,
    tc_RealDef_Oreal @ class_Rings_Ono__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).

thf(427,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Osemiring )
     => ( ( A @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_combine__common__factor) ).

thf(2945,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Osemiring )
     => ( ( A @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( B @ ( D @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(1212,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/sandbox2/benchmark/theBenchmark.p',fact_abs__le__interval__iff) ).

thf(5346,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)],[1212]) ).

thf(1103,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( B = A )
          | ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).

thf(5093,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( B = A )
          | ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).

thf(404,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Orderings_Opreorder )
     => ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).

thf(2856,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Orderings_Opreorder )
     => ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(806,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/sandbox2/benchmark/theBenchmark.p',fact_add__minus__cancel) ).

thf(4176,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)],[806]) ).

thf(601,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__divide__le__eq) ).

thf(3500,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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(49531,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ class_Rings_Olinordered__idom )
       != ( A @ class_Rings_Olinordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4115,1491]) ).

thf(49532,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ class_Rings_Olinordered__idom )
       != ( A @ class_Rings_Olinordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder ) ),
    inference(simp,[status(thm)],[49531]) ).

thf(49533,plain,
    tc_Int_Oint @ tc_Polynomial_Opoly @ class_Orderings_Opreorder,
    inference(pattern_uni,[status(thm)],[49532:[bind(A,$thf( tc_Int_Oint ))]]) ).

thf(10695,plain,
    ! [B: $i,A: $i] :
      ( ( B != tc_RealDef_Oreal )
      | ~ ( v_mazh @ ( v_da____ @ ( A @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1370,1263]) ).

thf(10696,plain,
    ! [A: $i] :
      ( ~ ( v_mazh @ ( v_da____ @ ( A @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( tc_RealDef_Oreal @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(pattern_uni,[status(thm)],[10695:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal ))]]) ).

thf(234,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Omonoid__mult )
     => ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__right) ).

thf(2180,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Omonoid__mult )
     => ( ( B @ c_Groups_Oone__class_Oone @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(816,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/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__iff) ).

thf(4203,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)],[816]) ).

thf(957,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/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonpos) ).

thf(4635,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)],[957]) ).

thf(1087,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).

thf(5035,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)],[1087]) ).

thf(48137,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      | ~ $true
      | ~ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5270,15700]) ).

thf(48138,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      | ~ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[48137]) ).

thf(48205,plain,
    ! [A: $i] :
      ( ( A
       != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
      | ( A != v_da____ )
      | ( tc_RealDef_Oreal != tc_RealDef_Oreal )
      | ~ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[48138]) ).

thf(48240,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_da____ )
    | ~ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[48205]) ).

thf(939,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( ( B = A )
          | ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).

thf(4569,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( ( ( B = A )
            | ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
         => ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( B = A )
            | ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).

thf(185,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 @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oprod__diff__prod) ).

thf(1993,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 @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

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

thf(2780,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( ( B @ c_Nat_OSuc @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
          = ( B @ c_Nat_OSuc @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
       => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( C = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(808,axiom,
    tc_Int_Oint @ class_Orderings_Oord,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).

thf(4181,plain,
    tc_Int_Oint @ class_Orderings_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).

thf(859,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/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).

thf(4332,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)],[859]) ).

thf(850,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/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).

thf(4296,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)],[850]) ).

thf(1126,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oorder )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).

thf(5180,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oorder )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).

thf(357,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ? [C: $i] :
        ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Obounded) ).

thf(2664,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ? [C: $i] :
        ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(436,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 @ hAPP ) @ hAPP ) ) )
         => ( ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
            = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__imp) ).

thf(2974,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 @ hAPP ) @ hAPP ) ) )
         => ( ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
            = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(1076,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Oidom )
     => ( A @ tc_Polynomial_Opoly @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

thf(4990,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)],[1076]) ).

thf(393,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 @ hAPP ) @ hAPP ) )
      = ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).

thf(2812,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 @ hAPP ) @ hAPP ) )
      = ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(347,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oab__semigroup__mult )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).

thf(2632,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Oab__semigroup__mult )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(897,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/sandbox2/benchmark/theBenchmark.p',fact_abs__diff__less__iff) ).

thf(4445,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)],[897]) ).

thf(341,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/sandbox2/benchmark/theBenchmark.p',fact_less__antisym) ).

thf(2605,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)],[341]) ).

thf(83,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/sandbox2/benchmark/theBenchmark.p',fact_less__SucI) ).

thf(1557,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)],[83]) ).

thf(752,axiom,
    ! [A: $i] :
      ( ( A @ class_Groups_Ocancel__comm__monoid__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ocancel__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).

thf(4009,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)],[752]) ).

thf(219,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semiring__strict )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).

thf(2129,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semiring__strict )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[219]) ).

thf(346,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
          = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).

thf(2625,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( ( B = A )
         => ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
            = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
        & ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
            = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(902,axiom,
    tc_Int_Oint @ class_Rings_Olinordered__comm__semiring__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).

thf(4462,plain,
    tc_Int_Oint @ class_Rings_Olinordered__comm__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).

thf(1046,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/sandbox2/benchmark/theBenchmark.p',fact_diff__0) ).

thf(4911,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)],[1046]) ).

thf(258,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).

thf(2261,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(1250,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oorder )
     => ( ( C = B )
       => ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I3_J) ).

thf(5439,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oorder )
     => ( ( C = B )
       => ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250]) ).

thf(728,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oorder )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).

thf(3932,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oorder )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).

thf(165,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 @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__sgn) ).

thf(1909,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 @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(1176,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/sandbox2/benchmark/theBenchmark.p',fact_real__le__trans) ).

thf(5286,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)],[1176]) ).

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

thf(2446,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(840,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/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).

thf(4277,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)],[840]) ).

thf(1223,axiom,
    tc_RealDef_Oreal @ class_Fields_Olinordered__field__inverse__zero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).

thf(5392,plain,
    tc_RealDef_Oreal @ class_Fields_Olinordered__field__inverse__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).

thf(148,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__0 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).

thf(1838,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)],[148]) ).

thf(1191,axiom,
    tc_RealDef_Oreal @ class_Rings_Odivision__ring__inverse__zero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) ).

thf(5318,plain,
    tc_RealDef_Oreal @ class_Rings_Odivision__ring__inverse__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).

thf(529,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).

thf(3298,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(962,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/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__left) ).

thf(4652,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)],[962]) ).

thf(56088,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__1 )
       != ( B @ class_Rings_Ocomm__semiring__1 ) )
      | ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4958,1505]) ).

thf(56089,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__1 )
       != ( B @ class_Rings_Ocomm__semiring__1 ) )
      | ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[56088]) ).

thf(56090,plain,
    ! [A: $i] : ( A @ ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone @ ( tc_Complex_Ocomplex @ c_Rings_Odvd__class_Odvd ) ) ),
    inference(pattern_uni,[status(thm)],[56089:[bind(A,$thf( A )),bind(B,$thf( tc_Complex_Ocomplex ))]]) ).

thf(738,axiom,
    tc_Nat_Onat @ class_Rings_Omult__zero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).

thf(3971,plain,
    tc_Nat_Onat @ class_Rings_Omult__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).

thf(1290,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = A )
      | ( ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) )
       != ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) ) )
      | ~ ( E @ class_Groups_Ozero ) ),
    inference(cnfConj,[status(thm)],[1288]) ).

thf(1293,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ class_Groups_Ozero )
      | ( C = A )
      | ( ( C @ ( D @ ( E @ c_Polynomial_OpCons ) ) )
       != ( A @ ( B @ ( E @ c_Polynomial_OpCons ) ) ) ) ),
    inference(lifteq,[status(thm)],[1290]) ).

thf(264,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__ring )
     => ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__square__less__zero) ).

thf(2278,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__ring )
     => ~ ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(331,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
        = ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__abs) ).

thf(2553,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oabs__class_Oabs ) )
        = ( A @ ( B @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(486,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 @ hAPP ) @ hAPP ) )
            = A )
         => ( B
            = ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__imp) ).

thf(3150,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 @ hAPP ) @ hAPP ) )
            = A )
         => ( B
            = ( C @ ( A @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(975,axiom,
    tc_Nat_Onat @ class_Rings_Oordered__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).

thf(4684,plain,
    tc_Nat_Onat @ class_Rings_Oordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).

thf(400,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Odiff) ).

thf(2842,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(174,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).

thf(1952,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(701,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/sandbox2/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).

thf(3838,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)],[701]) ).

thf(1444,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(cnf,[status(esa)],[1443]) ).

thf(1445,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( B @ ( C @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
    inference(lifteq,[status(thm)],[1444]) ).

thf(5810,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__1 )
       != ( A @ class_Rings_Ocomm__semiring__1 ) )
      | ~ $true
      | ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Polynomial_OpCons ) ) )
        = ( A @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone ) ) ),
    inference(paramod_ordered,[status(thm)],[4958,1318]) ).

thf(5811,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Rings_Ocomm__semiring__1 )
       != ( A @ class_Rings_Ocomm__semiring__1 ) )
      | ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Polynomial_OpCons ) ) )
        = ( A @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone ) ) ),
    inference(simp,[status(thm)],[5810]) ).

thf(5812,plain,
    ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) )
    = ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone ) ),
    inference(pattern_uni,[status(thm)],[5811:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(20617,plain,
    ( ( v_cs____ @ ( tc_Complex_Ocomplex @ c_Groups_Oone__class_Oone @ ( tc_Complex_Ocomplex @ c_Polynomial_OpCons ) ) )
    = ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone ) ),
    inference(rewrite,[status(thm)],[5812,1280]) ).

thf(390,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
    <=> ( ( B = A )
        | ( C
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).

thf(2797,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( B = A )
          | ( C
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
       => ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
          = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
      & ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
          = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
       => ( ( B = A )
          | ( C
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(1049,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/sandbox2/benchmark/theBenchmark.p',fact_add__diff__cancel) ).

thf(4918,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)],[1049]) ).

thf(443,axiom,
    ! [A: $i] :
      ( ( A @ class_Groups_Ocancel__comm__monoid__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ocancel__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).

thf(2999,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)],[443]) ).

thf(203,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__div__algebra )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__mult) ).

thf(2069,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_RealVector_Oreal__normed__div__algebra )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(611,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/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).

thf(3539,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)],[611]) ).

thf(1020,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/sandbox2/benchmark/theBenchmark.p',fact_add__neg__neg) ).

thf(4832,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)],[1020]) ).

thf(1209,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oord )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( B = A )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__le__eq__trans) ).

thf(5340,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oord )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( B = A )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).

thf(1095,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/sandbox2/benchmark/theBenchmark.p',fact_divide__pos__pos) ).

thf(5057,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)],[1095]) ).

thf(1160,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Orderings_Opreorder )
     => ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).

thf(5254,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Orderings_Opreorder )
     => ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).

thf(286,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
        = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sgn__pos) ).

thf(2365,plain,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
        = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(1470,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Rings_Odvd )
        & ( D @ class_Rings_Ocomm__ring ) )
     => ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
       => ( ! [E: $i] :
              ( ? [F: $i] : ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
             => ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) )
          & ! [E: $i] :
              ( ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
             => ! [F: $i] : ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ) ),
    inference(miniscope,[status(thm)],[1469]) ).

thf(1471,plain,
    ! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( G @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
        | ~ ( A @ ( B @ ( H @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( G @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
        | ~ ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
        | ~ ( D @ class_Rings_Odvd )
        | ~ ( D @ class_Rings_Ocomm__ring ) )
      & ( ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
        | ~ ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
        | ~ ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
        | ~ ( D @ class_Rings_Odvd )
        | ~ ( D @ class_Rings_Ocomm__ring ) ) ),
    inference(cnf,[status(esa)],[1470]) ).

thf(1473,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( D @ class_Rings_Odvd )
      | ~ ( D @ class_Rings_Ocomm__ring ) ),
    inference(cnfConj,[status(thm)],[1471]) ).

thf(1474,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( D @ class_Rings_Odvd )
      | ~ ( D @ class_Rings_Ocomm__ring ) ),
    inference(simp,[status(thm)],[1473]) ).

thf(282,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 @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__divide__less__eq) ).

thf(2350,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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(371,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
       => ( ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
         => ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__trans) ).

thf(2725,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
       => ( ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
         => ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(199,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oidom )
     => ( ( ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
          = ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      <=> ( ( B
            = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
          | ( B = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__iff) ).

thf(2051,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 @ hAPP ) @ hAPP ) )
            = ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
        & ( ( ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
            = ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
         => ( ( B
              = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) )
            | ( B = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(316,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 @ hAPP ) @ hAPP ) )
            = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__eq__divide__eq) ).

thf(2481,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 @ hAPP ) @ hAPP ) )
              = 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 @ hAPP ) @ hAPP ) )
              = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(724,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ c_Complex_Orcis ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
      = ( B @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__rcis) ).

thf(3917,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ c_Complex_Orcis ) @ ( tc_Complex_Ocomplex @ c_RealVector_Onorm__class_Onorm ) )
      = ( B @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).

thf(15840,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       != ( v_mazh @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3973,1263]) ).

thf(15841,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     != ( v_mazh @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(simp,[status(thm)],[15840]) ).

thf(15884,plain,
    ! [A: $i] :
      ( ( A != v_mazh )
      | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != v_da____ )
      | ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[15841]) ).

thf(15895,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != v_da____ )
    | ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[15884]) ).

thf(15930,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
    | ( v_cs____ != v_da____ )
    | ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
    inference(paramod_ordered,[status(thm)],[1280,15895]) ).

thf(15933,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Nat_Onat )
    | ( v_cs____ != v_da____ )
    | ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[15930]) ).

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

thf(5248,plain,
    tc_RealDef_Oreal @ class_Groups_Ocomm__monoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).

thf(689,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).

thf(3806,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).

thf(201,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__eq ) ) )
       => ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__power) ).

thf(2064,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__eq ) ) )
       => ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(868,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/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing) ).

thf(4362,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)],[868]) ).

thf(1019,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/sandbox2/benchmark/theBenchmark.p',fact_abs__less__iff) ).

thf(4827,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)],[1019]) ).

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

thf(2288,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
     => ( ( B = A )
        | ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(979,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ class_Rings_Ozero__neq__one )
        & ( C @ class_Rings_Ono__zero__divisors )
        & ( C @ class_Rings_Omult__zero )
        & ( C @ class_Power_Opower ) )
     => ( ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
          = ( C @ c_Groups_Ozero__class_Ozero ) )
      <=> ( ( A
           != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
          & ( B
            = ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).

thf(4703,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ class_Rings_Ozero__neq__one )
        & ( C @ class_Rings_Ono__zero__divisors )
        & ( C @ class_Rings_Omult__zero )
        & ( C @ class_Power_Opower ) )
     => ( ( ( ( A
             != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
            & ( B
              = ( C @ c_Groups_Ozero__class_Ozero ) ) )
         => ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
            = ( C @ c_Groups_Ozero__class_Ozero ) ) )
        & ( ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
            = ( C @ c_Groups_Ozero__class_Ozero ) )
         => ( ( A
             != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
            & ( B
              = ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).

thf(851,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Oidom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Ono__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).

thf(4304,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Oidom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Ono__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).

thf(121,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
        = ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).

thf(1726,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) )
        = ( B @ ( A @ ( C @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(1199,axiom,
    tc_RealDef_Oreal @ class_Groups_Ogroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).

thf(5326,plain,
    tc_RealDef_Oreal @ class_Groups_Ogroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).

thf(112,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 @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff2) ).

thf(1694,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 @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(364,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).

thf(2693,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 @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[364]) ).

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

thf(2984,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)],[439]) ).

thf(907,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/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).

thf(4481,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)],[907]) ).

thf(596,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/sandbox2/benchmark/theBenchmark.p',fact_divide__self) ).

thf(3490,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)],[596]) ).

thf(906,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/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).

thf(4473,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)],[906]) ).

thf(775,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/sandbox2/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).

thf(4084,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)],[775]) ).

thf(858,axiom,
    tc_Complex_Ocomplex @ class_Int_Oring__char__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).

thf(4331,plain,
    tc_Complex_Ocomplex @ class_Int_Oring__char__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).

thf(890,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/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).

thf(4426,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)],[890]) ).

thf(130,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).

thf(1758,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)],[130]) ).

thf(5525,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) )
    | ( v_cs____ != v_c____ ) ),
    inference(paramod_ordered,[status(thm)],[1280,4168]) ).

thf(5528,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Complex_Ocomplex )
    | ( v_cs____ != v_c____ ) ),
    inference(simp,[status(thm)],[5525]) ).

thf(3570,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: $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 ) ) ) ),
    inference(miniscope,[status(thm)],[3569]) ).

thf(3571,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
        | ( B
         != ( C @ c_Nat_OSuc ) ) )
      & ( ( A
          = ( A @ sk22 @ c_Nat_OSuc ) )
        | ~ ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(cnf,[status(esa)],[3570]) ).

thf(3573,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
      | ( A
       != ( B @ c_Nat_OSuc ) ) ),
    inference(cnfConj,[status(thm)],[3571]) ).

thf(3575,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
      | ( A
       != ( B @ c_Nat_OSuc ) ) ),
    inference(lifteq,[status(thm)],[3573]) ).

thf(3576,plain,
    ! [A: $i] : ( A @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    inference(simp,[status(thm)],[3575]) ).

thf(355,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
         != ( B @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).

thf(2652,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
           != ( B @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) )
         => ( ( B != A )
            & ( D != C ) ) )
        & ( ( ( B != A )
            & ( D != C ) )
         => ( ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) )
           != ( B @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

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

thf(1420,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 @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(110,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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__mult) ).

thf(1684,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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(741,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/sandbox2/benchmark/theBenchmark.p',fact_abs__idempotent) ).

thf(3975,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)],[741]) ).

thf(1472,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( D @ class_Rings_Odvd )
      | ~ ( D @ class_Rings_Ocomm__ring ) ),
    inference(cnfConj,[status(thm)],[1471]) ).

thf(977,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/sandbox2/benchmark/theBenchmark.p',fact_minus__minus) ).

thf(4688,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)],[977]) ).

thf(26257,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
    | ( v_ma != v_cs____ )
    | ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( v_mzh != v_da____ ) ),
    inference(paramod_ordered,[status(thm)],[1280,25940]) ).

thf(26258,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Int_Oint )
    | ( v_ma != v_cs____ )
    | ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( v_mzh != v_da____ ) ),
    inference(simp,[status(thm)],[26257]) ).

thf(5761,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ class_Rings_Ocomm__semiring__1 )
       != ( A @ class_Rings_Ocomm__semiring__1 ) )
      | ~ $true
      | ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Polynomial_OpCons ) ) )
        = ( A @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone ) ) ),
    inference(paramod_ordered,[status(thm)],[4588,1318]) ).

thf(5762,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ class_Rings_Ocomm__semiring__1 )
       != ( A @ class_Rings_Ocomm__semiring__1 ) )
      | ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Polynomial_OpCons ) ) )
        = ( A @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone ) ) ),
    inference(simp,[status(thm)],[5761]) ).

thf(5763,plain,
    ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Polynomial_OpCons ) ) )
    = ( tc_Int_Oint @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone ) ),
    inference(pattern_uni,[status(thm)],[5762:[bind(A,$thf( tc_Int_Oint ))]]) ).

thf(1115,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/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono2) ).

thf(5133,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)],[1115]) ).

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

thf(2005,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__ring__1 )
     => ( ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
         => ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) )
        & ( ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
         => ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(37,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 @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).

thf(1410,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 @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

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

thf(1413,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ class_Rings_Oordered__cancel__semiring ) ),
    inference(cnfConj,[status(thm)],[1411]) ).

thf(712,axiom,
    tc_Int_Oint @ class_Groups_Omonoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).

thf(3881,plain,
    tc_Int_Oint @ class_Groups_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).

thf(989,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/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq2) ).

thf(4741,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)],[989]) ).

thf(250,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
     => ( ( C @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
      <=> ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__eq__int) ).

thf(2239,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
     => ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
         => ( C @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) )
        & ( ( C @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
         => ( A @ ( B @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(141,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).

thf(1809,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 @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[141]) ).

thf(1241,axiom,
    tc_RealDef_Oreal @ class_Rings_Oidom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).

thf(5424,plain,
    tc_RealDef_Oreal @ class_Rings_Oidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).

thf(430,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( D @ ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
     => ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( F @ ( D @ ( 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__eq ) ) )
           => ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( F @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
               => ( E @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).

thf(2952,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
      ( ( ( D @ ( E @ ( F @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
     => ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( F @ ( D @ ( 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__eq ) ) )
           => ( ( C @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
             => ( ( F @ ( C @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) )
               => ( E @ ( B @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(895,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).

thf(4441,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).

thf(793,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/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__right__mono__neg) ).

thf(4136,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)],[793]) ).

thf(209,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 @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).

thf(2096,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 @ hAPP ) @ hAPP ) @ ( 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)],[209]) ).

thf(13166,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__1 )
       != ( B @ class_Rings_Ocomm__semiring__1 ) )
      | ~ $true
      | ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(paramod_ordered,[status(thm)],[5238,1383]) ).

thf(13167,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__1 )
       != ( B @ class_Rings_Ocomm__semiring__1 ) )
      | ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(simp,[status(thm)],[13166]) ).

thf(13168,plain,
    ! [A: $i] :
      ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
    inference(pattern_uni,[status(thm)],[13167:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal ))]]) ).

thf(570,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/sandbox2/benchmark/theBenchmark.p',fact_norm__add__less) ).

thf(3427,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)],[570]) ).

thf(54,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 @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono) ).

thf(1467,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 @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(833,axiom,
    tc_Nat_Onat @ class_Groups_Omonoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).

thf(4260,plain,
    tc_Nat_Onat @ class_Groups_Omonoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).

thf(1083,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ? [C: $i] :
          ( ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ 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__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ononneg__bounded) ).

thf(5025,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ? [C: $i] :
          ( ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ 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__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).

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

thf(2271,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( A @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
     => ( ( B
         != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
       => ( A @ ( C @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(500,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Orderings_Oorder )
     => ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).

thf(3206,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Orderings_Oorder )
     => ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(765,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

thf(4052,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)],[765]) ).

thf(4318,plain,
    ! [A: $i] :
      ( ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(cnf,[status(esa)],[4317]) ).

thf(4319,plain,
    ! [A: $i] :
      ( ( A @ ( A @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
      = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(lifteq,[status(thm)],[4318]) ).

thf(484,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring__strict )
     => ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).

thf(3146,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring__strict )
     => ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[484]) ).

thf(1033,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/sandbox2/benchmark/theBenchmark.p',fact_less__half__sum) ).

thf(4879,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)],[1033]) ).

thf(847,axiom,
    ! [A: $i] :
      ( ( A @ class_Groups_Ocomm__monoid__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).

thf(4292,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)],[847]) ).

thf(184,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 @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).

thf(1990,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 @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(455,axiom,
    ! [A: $i] :
      ( ( A @ class_Groups_Oab__group__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).

thf(3048,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)],[455]) ).

thf(1027,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).

thf(4859,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)],[1027]) ).

thf(527,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).

thf(3292,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(420,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
      = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__0) ).

thf(2899,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
      = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(1072,axiom,
    tc_Complex_Ocomplex @ class_Rings_Oring__no__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).

thf(4986,plain,
    tc_Complex_Ocomplex @ class_Rings_Oring__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).

thf(703,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/sandbox2/benchmark/theBenchmark.p',fact_minus__unique) ).

thf(3849,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)],[703]) ).

thf(1236,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/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq2) ).

thf(5414,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)],[1236]) ).

thf(763,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A != B )
         => ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I11_J) ).

thf(4045,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A != B )
         => ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).

thf(1258,axiom,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__field,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__field) ).

thf(5452,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__field,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1258]) ).

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

thf(5229,plain,
    tc_RealDef_Oreal @ class_Rings_Ocomm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).

thf(134,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Omonoid__mult )
     => ( ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__commutes) ).

thf(1770,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Omonoid__mult )
     => ( ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(723,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oorder )
     => ( ( C = B )
       => ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I1_J) ).

thf(3913,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oorder )
     => ( ( C = B )
       => ( ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).

thf(25164,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
       != ( v_ma @ ( v_mazh @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) )
      | ( ( A @ c_Nat_OSuc )
       != v_mzh )
      | ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
    inference(paramod_ordered,[status(thm)],[4256,15427]) ).

thf(25194,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != v_ma )
      | ( A != v_mazh )
      | ( tc_Nat_Onat != tc_RealDef_Oreal )
      | ( ( A @ c_Nat_OSuc )
       != v_mzh )
      | ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[25164]) ).

thf(25213,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != v_ma )
    | ( ( v_mazh @ c_Nat_OSuc )
     != v_mzh )
    | ( tc_Nat_Onat != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[25194]) ).

thf(190,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
          = ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
      <=> ( ( A
            = ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
          & ( B
            = ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).

thf(2012,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( 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 ) )
            & ( B
              = ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) )
         => ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
            = ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) )
        & ( ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
            = ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
         => ( ( A
              = ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
            & ( B
              = ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(15770,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_c____ @ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( v_c____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3313,12119]) ).

thf(15771,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_c____ @ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( v_c____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[15770]) ).

thf(15791,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != v_c____ )
      | ( A
       != ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ~ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( v_c____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[15771]) ).

thf(15805,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != v_c____ )
    | ~ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( v_c____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[15791]) ).

thf(25318,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( v_c____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != v_c____ )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3313,15805]) ).

thf(25319,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( v_c____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != v_c____ ) ),
    inference(simp,[status(thm)],[25318]) ).

thf(25387,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) )
      | ( A != v_c____ )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != v_c____ ) ),
    inference(simp,[status(thm)],[25319]) ).

thf(25405,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) )
    | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != v_c____ ) ),
    inference(simp,[status(thm)],[25387]) ).

thf(26066,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
    | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) )
    | ( v_cs____ != v_c____ ) ),
    inference(paramod_ordered,[status(thm)],[1280,25405]) ).

thf(26078,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Nat_Onat )
    | ( tc_Nat_Onat != tc_Complex_Ocomplex )
    | ( v_cs____ != v_c____ ) ),
    inference(simp,[status(thm)],[26066]) ).

thf(959,axiom,
    tc_Nat_Onat @ class_Groups_Ocomm__monoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).

thf(4641,plain,
    tc_Nat_Onat @ class_Groups_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).

thf(395,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( 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/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).

thf(2821,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 @ hAPP ) @ hAPP ) )
          = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ) )
      & ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
          = ( 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)],[395]) ).

thf(874,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/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).

thf(4377,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)],[874]) ).

thf(396,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).

thf(2831,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)],[396]) ).

thf(1253,axiom,
    tc_RealDef_Oreal @ class_Rings_Ocomm__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring) ).

thf(5446,plain,
    tc_RealDef_Oreal @ class_Rings_Ocomm__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).

thf(322,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring__strict )
     => ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).

thf(2513,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring__strict )
     => ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[322]) ).

thf(4333,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: $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(miniscope,[status(thm)],[4332]) ).

thf(4334,plain,
    ! [B: $i,A: $i] :
      ( ( ( B
         != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
        | ~ ( 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
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
    inference(cnf,[status(esa)],[4333]) ).

thf(4336,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(cnfConj,[status(thm)],[4334]) ).

thf(4338,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 ) ) ),
    inference(lifteq,[status(thm)],[4336]) ).

thf(4339,plain,
    ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ),
    inference(simp,[status(thm)],[4338]) ).

thf(5522,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
    | ~ ( v_cs____ @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,4339]) ).

thf(5527,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Nat_Onat )
    | ~ ( v_cs____ @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[5522]) ).

thf(15284,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     != ( v_cs____ @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
    | ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Nat_Onat )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[15210,5527]) ).

thf(15285,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     != ( v_cs____ @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) )
    | ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[15284]) ).

thf(15304,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_cs____ )
    | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
    | ( tc_Nat_Onat != tc_Nat_Onat )
    | ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[15285]) ).

thf(15308,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_cs____ )
    | ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Nat_Onat ) ),
    inference(simp,[status(thm)],[15304]) ).

thf(640,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
           => ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__mono) ).

thf(3640,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
           => ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(93,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).

thf(1598,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(867,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/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq2__sym) ).

thf(4360,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)],[867]) ).

thf(1180,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( B = A )
      <=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
          & ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).

thf(5294,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
            & ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).

thf(1158,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).

thf(5250,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).

thf(702,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/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).

thf(3842,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)],[702]) ).

thf(1053,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/sandbox2/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).

thf(4937,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)],[1053]) ).

thf(1221,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/sandbox2/benchmark/theBenchmark.p',fact_zle__antisym) ).

thf(5388,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)],[1221]) ).

thf(18973,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc )
       != ( A @ c_Nat_OSuc ) )
      | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ sk8 )
        = A ) ),
    inference(paramod_ordered,[status(thm)],[2249,18968]) ).

thf(18974,plain,
    ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ sk8 )
    = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(pattern_uni,[status(thm)],[18973:[bind(A,$thf( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ))]]) ).

thf(125,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 @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__less__divide__eq) ).

thf(1743,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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(1058,axiom,
    tc_Int_Oint @ class_Rings_Olinordered__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).

thf(4950,plain,
    tc_Int_Oint @ class_Rings_Olinordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).

thf(925,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/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).

thf(4534,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)],[925]) ).

thf(584,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Opreorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).

thf(3462,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Opreorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(72,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ? [C: $i] :
        ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Obounded) ).

thf(1531,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__algebra )
     => ? [C: $i] :
        ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(857,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
        <=> ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).

thf(4324,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( ( A = B )
           => ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
          & ( ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
           => ( A = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).

thf(43445,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[36348,1427]) ).

thf(43446,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add )
       != ( A @ class_Groups_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add ) ),
    inference(simp,[status(thm)],[43445]) ).

thf(43447,plain,
    tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Groups_Oab__group__add,
    inference(pattern_uni,[status(thm)],[43446:[bind(A,$thf( tc_Int_Oint @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(403,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/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).

thf(2850,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)],[403]) ).

thf(57,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 @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).

thf(1484,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 @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(228,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 @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).

thf(2160,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 @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(921,axiom,
    tc_Int_Oint @ class_Groups_Oone,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).

thf(4522,plain,
    tc_Int_Oint @ class_Groups_Oone,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).

thf(930,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 @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__divide__le__eq) ).

thf(4549,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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).

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

thf(5276,plain,
    tc_RealDef_Oreal @ class_Rings_Oring__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).

thf(132,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/sandbox2/benchmark/theBenchmark.p',fact_sgn__zero) ).

thf(1763,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)],[132]) ).

thf(75,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__left) ).

thf(1538,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(1172,axiom,
    tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).

thf(5277,plain,
    tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).

thf(283,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/sandbox2/benchmark/theBenchmark.p',fact_le__SucI) ).

thf(2354,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)],[283]) ).

thf(449,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__ring__strict )
     => ( ( A @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).

thf(3019,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 @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[449]) ).

thf(379,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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemma__MVT) ).

thf(2747,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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(335,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/sandbox2/benchmark/theBenchmark.p',fact_poly__diff) ).

thf(2569,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)],[335]) ).

thf(894,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/sandbox2/benchmark/theBenchmark.p',fact_add__leE) ).

thf(4437,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)],[894]) ).

thf(641,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/sandbox2/benchmark/theBenchmark.p',fact_nonzero__minus__divide__right) ).

thf(3642,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)],[641]) ).

thf(864,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/sandbox2/benchmark/theBenchmark.p',fact_abs__le__D2) ).

thf(4346,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)],[864]) ).

thf(826,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/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).

thf(4240,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)],[826]) ).

thf(208,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 @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
        <=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).

thf(2092,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 @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
          & ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

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

thf(1987,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oring__1__no__zero__divisors )
     => ( ( B
         != ( C @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
         != ( C @ c_Groups_Ozero__class_Ozero ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(1239,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/sandbox2/benchmark/theBenchmark.p',fact_norm__ge__zero) ).

thf(5420,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)],[1239]) ).

thf(117,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_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
          = ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__power__divide) ).

thf(1716,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_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
          = ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(813,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/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).

thf(4190,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)],[813]) ).

thf(695,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Opreorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).

thf(3818,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Opreorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ~ ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(28500,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
       != ( v_ma @ ( v_mazh @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) )
      | ( A != v_mazh )
      | ( v_mzh != v_da____ ) ),
    inference(paramod_ordered,[status(thm)],[5141,15428]) ).

thf(28524,plain,
    ( ( v_ma != v_mazh )
    | ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
     != v_mazh )
    | ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( v_mzh != v_da____ ) ),
    inference(simp,[status(thm)],[28500]) ).

thf(476,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( C @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        & ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
     => ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
       => ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__trans) ).

thf(3114,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( C @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        & ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
     => ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
       => ( ~ ( C @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(365,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 @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
      <=> ( A @ ( B @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__iff1) ).

thf(2700,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 @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[365]) ).

thf(21553,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
    | ( v_cs____ != v_mazh )
    | ~ ( v_da____ @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,19272]) ).

thf(21554,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Nat_Onat )
    | ( v_cs____ != v_mazh )
    | ~ ( v_da____ @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[21553]) ).

thf(756,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/sandbox2/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).

thf(4020,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)],[756]) ).

thf(798,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/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).

thf(4145,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)],[798]) ).

thf(13147,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Int_Oint @ class_Rings_Ocomm__semiring__1 )
       != ( B @ class_Rings_Ocomm__semiring__1 ) )
      | ~ $true
      | ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(paramod_ordered,[status(thm)],[4588,1383]) ).

thf(13148,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Int_Oint @ class_Rings_Ocomm__semiring__1 )
       != ( B @ class_Rings_Ocomm__semiring__1 ) )
      | ( ( B @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(simp,[status(thm)],[13147]) ).

thf(13149,plain,
    ! [A: $i] :
      ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
    inference(pattern_uni,[status(thm)],[13148:[bind(A,$thf( A )),bind(B,$thf( tc_Int_Oint ))]]) ).

thf(263,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).

thf(2276,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ 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)],[263]) ).

thf(244,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
     => ( ( C @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      <=> ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pow__divides__eq__nat) ).

thf(2219,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
     => ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
         => ( C @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
        & ( ( C @ ( A @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
         => ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(180,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__imp__le) ).

thf(1980,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
        & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(1135,axiom,
    tc_Int_Oint @ class_Groups_Oordered__comm__monoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).

thf(5203,plain,
    tc_Int_Oint @ class_Groups_Oordered__comm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).

thf(791,axiom,
    tc_Int_Oint @ class_Groups_Oordered__ab__group__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).

thf(4132,plain,
    tc_Int_Oint @ class_Groups_Oordered__ab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).

thf(273,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 @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).

thf(2322,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 @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(1070,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).

thf(4982,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).

thf(634,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 @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__le__div__pos) ).

thf(3623,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 @ hAPP ) @ hAPP ) @ ( 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)],[634]) ).

thf(564,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/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq4) ).

thf(3412,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)],[564]) ).

thf(546,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Rings_Odvd )
        & ( D @ class_Rings_Ocomm__ring ) )
     => ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
       => ! [E: $i,F: $i] :
            ( ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
          <=> ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__period_I3_J) ).

thf(3359,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ class_Rings_Odvd )
        & ( D @ class_Rings_Ocomm__ring ) )
     => ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
       => ! [E: $i,F: $i] :
            ( ( ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
             => ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) )
            & ( ( A @ ( E @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
             => ( A @ ( B @ ( F @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(198,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 @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
          = ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) )
      <=> ( ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
          = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff1) ).

thf(2044,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 @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
            = A )
         => ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
            = ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) ) )
        & ( ( ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
            = ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) ) )
         => ( ( C @ ( D @ ( B @ ( E @ ( F @ c_Groups_Ominus__class_Ominus ) ) @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) )
            = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(123,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).

thf(1738,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)],[123]) ).

thf(1257,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/sandbox2/benchmark/theBenchmark.p',fact_zle__trans) ).

thf(5450,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)],[1257]) ).

thf(644,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/sandbox2/benchmark/theBenchmark.p',fact_add__le__less__mono) ).

thf(3652,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)],[644]) ).

thf(1064,axiom,
    tc_Int_Oint @ class_Groups_Ocancel__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).

thf(4959,plain,
    tc_Int_Oint @ class_Groups_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).

thf(597,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/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__mono) ).

thf(3493,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)],[597]) ).

thf(49616,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) ) )
      | ( A
       != ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2957,39017]) ).

thf(49763,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
       != B )
      | ( ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) )
       != ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) ),
    inference(simp,[status(thm)],[49616]) ).

thf(49837,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) )
     != ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ),
    inference(simp,[status(thm)],[49763]) ).

thf(953,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/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).

thf(4611,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)],[953]) ).

thf(10,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oab__group__add )
     => ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__code_I2_J) ).

thf(1284,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Oab__group__add )
     => ( ( A @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Polynomial_OpCons ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(140,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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq) ).

thf(1797,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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(462,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).

thf(3071,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(818,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring) ).

thf(4217,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).

thf(360,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/sandbox2/benchmark/theBenchmark.p',fact_one__reorient) ).

thf(2675,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)],[360]) ).

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

thf(5319,plain,
    tc_RealDef_Oreal @ class_Rings_Olinordered__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).

thf(171,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 @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
        <=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).

thf(1934,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 @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
          & ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(428,axiom,
    ! [A: $i] :
      ( ( A @ class_Groups_Ocomm__monoid__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).

thf(2948,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)],[428]) ).

thf(299,axiom,
    ! [A: $i,B: $i] : ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__minus__mult__self__le) ).

thf(2411,plain,
    ! [A: $i,B: $i] : ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[299]) ).

thf(595,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/sandbox2/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).

thf(3488,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)],[595]) ).

thf(77,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).

thf(1543,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(1012,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/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).

thf(4802,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)],[1012]) ).

thf(133,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( 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 @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).

thf(1766,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[133]) ).

thf(49680,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) ) )
      | ( A
       != ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1874,39017]) ).

thf(49742,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) )
       != A )
      | ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) )
       != ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ),
    inference(simp,[status(thm)],[49680]) ).

thf(49810,plain,
    ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) )
   != ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ),
    inference(simp,[status(thm)],[49742]) ).

thf(333,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
      <=> ( A @ ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).

thf(2558,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( ( A @ ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[333]) ).

thf(1141,axiom,
    tc_Complex_Ocomplex @ class_Rings_Odivision__ring__inverse__zero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).

thf(5223,plain,
    tc_Complex_Ocomplex @ class_Rings_Odivision__ring__inverse__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).

thf(792,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/sandbox2/benchmark/theBenchmark.p',fact_norm__minus__cancel) ).

thf(4133,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)],[792]) ).

thf(893,axiom,
    tc_Nat_Onat @ class_Rings_Ono__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).

thf(4436,plain,
    tc_Nat_Onat @ class_Rings_Ono__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).

thf(330,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_real__two__squares__add__zero__iff) ).

thf(2543,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 @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( B @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[330]) ).

thf(545,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).

thf(3356,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( A @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( B @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(992,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/sandbox2/benchmark/theBenchmark.p',fact_add__increasing2) ).

thf(4748,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)],[992]) ).

thf(175,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
            = ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
        <=> ( B = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__exp) ).

thf(1955,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( C @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( ( B = A )
           => ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
              = ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) )
          & ( ( ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
              = ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) )
           => ( B = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(16363,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
    | ( ( v_cs____ @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
     != ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ),
    inference(paramod_ordered,[status(thm)],[1280,16323]) ).

thf(16367,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Int_Oint )
    | ( ( v_cs____ @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) )
     != ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ),
    inference(simp,[status(thm)],[16363]) ).

thf(224,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
     => ( ( B = A )
       => ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oord__le__eq__trans) ).

thf(2145,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( B @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
     => ( ( B = A )
       => ( A @ ( C @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(1485,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( D @ class_Rings_Oordered__ring ) ),
    inference(cnf,[status(esa)],[1484]) ).

thf(64,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 @ hAPP ) @ hAPP ) )
        = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__right) ).

thf(1506,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 @ hAPP ) @ hAPP ) )
        = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(1259,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/sandbox2/benchmark/theBenchmark.p',fact_add__mono) ).

thf(5453,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)],[1259]) ).

thf(127,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ominus) ).

thf(1749,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(554,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).

thf(3388,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(823,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/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).

thf(4235,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)],[823]) ).

thf(321,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 @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).

thf(2511,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 @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(838,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Orderings_Opreorder )
     => ~ ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).

thf(4267,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Orderings_Opreorder )
     => ~ ( A @ ( A @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).

thf(194,axiom,
    ! [A: $i,B: $i] :
      ( ( B != A )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       => ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oneq__le__trans) ).

thf(2030,plain,
    ! [A: $i,B: $i] :
      ( ( B != A )
     => ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       => ( ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
          & ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(1106,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/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).

thf(5100,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)],[1106]) ).

thf(1010,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/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).

thf(4795,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)],[1010]) ).

thf(831,axiom,
    tc_Complex_Ocomplex @ class_Groups_Ocomm__monoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).

thf(4257,plain,
    tc_Complex_Ocomplex @ class_Groups_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).

thf(968,axiom,
    tc_Complex_Ocomplex @ class_Groups_Omonoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).

thf(4671,plain,
    tc_Complex_Ocomplex @ class_Groups_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).

thf(557,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/sandbox2/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).

thf(3398,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)],[557]) ).

thf(780,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
        | ( B = A )
        | ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).

thf(4111,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
        | ( B = A )
        | ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).

thf(884,axiom,
    tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add__imp__le,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).

thf(4414,plain,
    tc_Int_Oint @ class_Groups_Oordered__ab__semigroup__add__imp__le,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).

thf(944,axiom,
    tc_Complex_Ocomplex @ class_Fields_Ofield__inverse__zero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).

thf(4587,plain,
    tc_Complex_Ocomplex @ class_Fields_Ofield__inverse__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).

thf(1055,axiom,
    tc_Complex_Ocomplex @ class_Groups_Omonoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).

thf(4945,plain,
    tc_Complex_Ocomplex @ class_Groups_Omonoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).

thf(964,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/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).

thf(4656,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)],[964]) ).

thf(498,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
    <=> ( ( B
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
        | ( C = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel2) ).

thf(3188,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 @ hAPP ) @ hAPP ) )
          = ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
      & ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
          = ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
       => ( ( B
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
          | ( C = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(57811,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
       != ( B @ ( tc_RealDef_Oreal @ c_RealVector_Onorm__class_Onorm ) @ ( 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_Groups_Ozero__class_Ozero ) ) ),
    inference(paramod_ordered,[status(thm)],[3681,57072]) ).

thf(57812,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) )
     != ( B @ ( tc_RealDef_Oreal @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(simp,[status(thm)],[57811]) ).

thf(57894,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) )
       != ( B @ ( tc_RealDef_Oreal @ c_RealVector_Onorm__class_Onorm ) ) )
      | ( A
       != ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) )
      | ( tc_RealDef_Oreal != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[57812]) ).

thf(57927,plain,
    ! [A: $i] :
      ( ( A @ ( tc_RealDef_Oreal @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ),
    inference(simp,[status(thm)],[57894]) ).

thf(459,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__commute) ).

thf(3056,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( B @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(986,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/sandbox2/benchmark/theBenchmark.p',fact_norm__diff__ineq) ).

thf(4730,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)],[986]) ).

thf(412,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 @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).

thf(2875,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 @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(26033,plain,
    ( ( tc_Nat_Onat != tc_Complex_Ocomplex )
    | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != v_c____ ) ),
    inference(simp,[status(thm)],[25405]) ).

thf(491,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__mono) ).

thf(3168,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)],[491]) ).

thf(524,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__power__dvd) ).

thf(3284,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(381,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 @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).

thf(2760,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 @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(1421,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( D @ class_Rings_Oordered__semiring ) ),
    inference(cnf,[status(esa)],[1420]) ).

thf(558,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/sandbox2/benchmark/theBenchmark.p',fact_left__minus) ).

thf(3400,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)],[558]) ).

thf(590,axiom,
    tc_Complex_Ocomplex @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

thf(3478,plain,
    tc_Complex_Ocomplex @ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(573,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/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).

thf(3433,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)],[573]) ).

thf(732,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/sandbox2/benchmark/theBenchmark.p',fact_frac__le) ).

thf(3946,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)],[732]) ).

thf(633,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/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__commute) ).

thf(3620,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)],[633]) ).

thf(59175,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( tc_Nat_Onat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != tc_Int_Oint )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3313,55637]) ).

thf(59176,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( tc_Nat_Onat @ ( tc_Int_Oint @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[59175]) ).

thf(59264,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != tc_Nat_Onat )
      | ( A != tc_Int_Oint )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
       != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[59176]) ).

thf(59277,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != tc_Nat_Onat )
    | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero )
     != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[59264]) ).

thf(579,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/sandbox2/benchmark/theBenchmark.p',fact_divide__nonneg__pos) ).

thf(3452,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)],[579]) ).

thf(23328,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_c____ @ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
       != v_c____ )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1542,15722]) ).

thf(23329,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( v_c____ @ ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
       != v_c____ ) ),
    inference(simp,[status(thm)],[23328]) ).

thf(23340,plain,
    ! [A: $i] :
      ( ( A != v_c____ )
      | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
       != ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
       != v_c____ ) ),
    inference(simp,[status(thm)],[23329]) ).

thf(23360,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != ( tc_Complex_Ocomplex @ c_Groups_Ozero__class_Ozero ) )
    | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_c____ ) ),
    inference(simp,[status(thm)],[23340]) ).

thf(168,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
       => ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__right) ).

thf(1918,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
       => ( A @ ( B @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(794,axiom,
    tc_Int_Oint @ class_Rings_Odvd,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).

thf(4138,plain,
    tc_Int_Oint @ class_Rings_Odvd,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).

thf(581,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/sandbox2/benchmark/theBenchmark.p',fact_frac__less2) ).

thf(3457,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)],[581]) ).

thf(675,axiom,
    tc_Int_Oint @ class_Groups_Ocancel__comm__monoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).

thf(3757,plain,
    tc_Int_Oint @ class_Groups_Ocancel__comm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).

thf(1026,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/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).

thf(4851,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)],[1026]) ).

thf(985,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/sandbox2/benchmark/theBenchmark.p',fact_minus__zero) ).

thf(4727,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)],[985]) ).

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

thf(2088,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D @ ( E @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
     => ( ( ( B @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
         => ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) )
        & ( ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) )
         => ( B @ ( D @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ ( tc_Int_Oint @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(410,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/sandbox2/benchmark/theBenchmark.p',fact_poly__minus) ).

thf(2870,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)],[410]) ).

thf(802,axiom,
    tc_Complex_Ocomplex @ class_Groups_Oab__semigroup__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).

thf(4165,plain,
    tc_Complex_Ocomplex @ class_Groups_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).

thf(143,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Orderings_Oord )
     => ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).

thf(1817,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Orderings_Oord )
     => ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(42008,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) ) )
      | ( A
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1874,39004]) ).

thf(42162,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) )
       != A )
      | ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) )
       != ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) ),
    inference(simp,[status(thm)],[42008]) ).

thf(42334,plain,
    ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) )
   != ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ),
    inference(simp,[status(thm)],[42162]) ).

thf(281,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oring )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__left) ).

thf(2347,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oring )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ouminus__class_Ouminus ) )
        = ( A @ ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(1412,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ class_Rings_Oordered__cancel__semiring ) ),
    inference(cnfConj,[status(thm)],[1411]) ).

thf(42687,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) ) )
      | ( A
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2144,39004]) ).

thf(42858,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) )
       != A )
      | ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) )
       != ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) ),
    inference(simp,[status(thm)],[42687]) ).

thf(43011,plain,
    ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) )
   != ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ),
    inference(simp,[status(thm)],[42858]) ).

thf(137,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 @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__eq) ).

thf(1781,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 @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) @ ( E @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(40527,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ sk26 ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
       != ( C @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[3899,5370]) ).

thf(40528,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ sk26 ) @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
     != ( C @ ( C @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[40527]) ).

thf(40595,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ sk26 ) )
       != C )
      | ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero )
       != C )
      | ( tc_RealDef_Oreal != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[40528]) ).

thf(40614,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ sk26 ) )
     != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
    inference(simp,[status(thm)],[40595]) ).

thf(242,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 @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).

thf(2209,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 @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
        & ( ( C @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[242]) ).

thf(635,axiom,
    tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add__imp__le,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).

thf(3625,plain,
    tc_Nat_Onat @ class_Groups_Oordered__ab__semigroup__add__imp__le,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(663,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/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).

thf(3725,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)],[663]) ).

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

thf(2997,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( 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)],[442]) ).

thf(1447,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) )
      | ( C
        = ( D @ c_Groups_Ozero__class_Ozero ) )
      | ~ ( D @ class_Fields_Ofield__inverse__zero ) ),
    inference(cnf,[status(esa)],[1446]) ).

thf(1448,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ class_Fields_Ofield__inverse__zero )
      | ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) )
      | ( C
        = ( D @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(lifteq,[status(thm)],[1447]) ).

thf(778,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/sandbox2/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).

thf(4102,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)],[778]) ).

thf(751,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/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).

thf(4006,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)],[751]) ).

thf(214,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 @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).

thf(2110,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 @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(903,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__leI) ).

thf(4463,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)],[903]) ).

thf(1204,axiom,
    ! [A: $i] : ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__refl) ).

thf(5332,plain,
    ! [A: $i] : ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).

thf(44045,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) ) )
      | ( A
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2841,39004]) ).

thf(44252,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) )
       != A )
      | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) )
       != ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) ),
    inference(simp,[status(thm)],[44045]) ).

thf(44397,plain,
    ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) )
   != ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ),
    inference(simp,[status(thm)],[44252]) ).

thf(157,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/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).

thf(1866,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)],[157]) ).

thf(44745,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) ) )
      | ( A
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2957,39004]) ).

thf(44973,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
       != A )
      | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) )
       != ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) ),
    inference(simp,[status(thm)],[44745]) ).

thf(45117,plain,
    ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) )
   != ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ),
    inference(simp,[status(thm)],[44973]) ).

thf(367,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ominus )
     => ( B @ ( A @ tc_fun ) @ class_Groups_Ominus ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).

thf(2707,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Ominus )
     => ( B @ ( A @ tc_fun ) @ class_Groups_Ominus ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

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

thf(2174,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Oidom )
     => ( ( ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
            = ( C @ c_Groups_Ozero__class_Ozero ) )
         => ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) ) )
        & ( ( A @ ( C @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Polynomial_OpCons ) ) @ ( B @ ( C @ c_Polynomial_OpCons ) ) @ ( C @ tc_Polynomial_Opoly @ c_Rings_Odvd__class_Odvd ) ) )
         => ( ( B @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_Polynomial_Opoly ) @ hAPP ) )
            = ( C @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(1168,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
        | ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).

thf(5272,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
        | ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).

thf(297,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult__less) ).

thf(2406,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(1507,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ tc_Polynomial_Opoly @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) )
      | ~ ( B @ class_Rings_Ocomm__semiring__0 ) ),
    inference(cnf,[status(esa)],[1506]) ).

thf(1508,plain,
    ! [B: $i,A: $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 @ hAPP ) @ hAPP ) )
        = ( B @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(lifteq,[status(thm)],[1507]) ).

thf(506,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Omonoid__mult )
     => ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__left) ).

thf(3220,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Omonoid__mult )
     => ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(28230,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Oabs__class_Oabs ) )
       != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) ) )
      | ( ( A @ ( tc_RealDef_Oreal @ c_RealVector_Onorm__class_Onorm ) )
       != ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ),
    inference(paramod_ordered,[status(thm)],[5033,16323]) ).

thf(28239,plain,
    ! [A: $i] :
      ( ( A
       != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
      | ( tc_Int_Oint != tc_RealDef_Oreal )
      | ( ( A @ ( tc_RealDef_Oreal @ c_RealVector_Onorm__class_Onorm ) )
       != ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ),
    inference(simp,[status(thm)],[28230]) ).

thf(28245,plain,
    ( ( tc_Int_Oint != tc_RealDef_Oreal )
    | ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) ) ),
    inference(simp,[status(thm)],[28239]) ).

thf(342,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 @ hAPP ) @ hAPP ) )
          = ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__right__cancel) ).

thf(2608,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 @ hAPP ) @ hAPP ) )
            = ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
        & ( ( ( C @ ( B @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
            = ( C @ ( A @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(1034,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__semiring__1__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).

thf(4881,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)],[1034]) ).

thf(1017,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/sandbox2/benchmark/theBenchmark.p',fact_minus__add__distrib) ).

thf(4823,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)],[1017]) ).

thf(1163,axiom,
    tc_RealDef_Oreal @ class_Rings_Odvd,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odvd) ).

thf(5258,plain,
    tc_RealDef_Oreal @ class_Rings_Odvd,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).

thf(1188,axiom,
    tc_RealDef_Oreal @ class_Fields_Ofield__inverse__zero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).

thf(5315,plain,
    tc_RealDef_Oreal @ class_Fields_Ofield__inverse__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).

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

thf(2443,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Oone__class_Oone ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(32,axiom,
    ! [A: $i,B: $i] : ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__zpower__abs) ).

thf(1384,plain,
    ! [A: $i,B: $i] : ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( 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)],[32]) ).

thf(1385,plain,
    ! [B: $i,A: $i] : ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless__eq ) ) ),
    inference(cnf,[status(esa)],[1384]) ).

thf(338,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__Suc__le__self) ).

thf(2594,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(119,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).

thf(1721,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(1339,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
      | ~ ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ),
    inference(cnfConj,[status(thm)],[1338]) ).

thf(1341,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( B @ ( 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 ) ) ),
    inference(lifteq,[status(thm)],[1339]) ).

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 @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).

thf(2098,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring__strict )
     => ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[210]) ).

thf(1477,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) )
      | ( A
       != ( B @ c_Groups_Ozero__class_Ozero ) )
      | ~ ( B @ class_Groups_Osgn__if ) ),
    inference(cnfConj,[status(thm)],[1476]) ).

thf(1480,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Groups_Osgn__if )
      | ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) )
      | ( A
       != ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(lifteq,[status(thm)],[1477]) ).

thf(1481,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(simp,[status(thm)],[1480]) ).

thf(974,axiom,
    tc_Nat_Onat @ class_Groups_Oone,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).

thf(4683,plain,
    tc_Nat_Onat @ class_Groups_Oone,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).

thf(1009,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/sandbox2/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).

thf(4791,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)],[1009]) ).

thf(746,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/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).

thf(3991,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)],[746]) ).

thf(1144,axiom,
    tc_RealDef_Oreal @ class_Rings_Oordered__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).

thf(5228,plain,
    tc_RealDef_Oreal @ class_Rings_Oordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).

thf(193,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 @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
        <=> ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).

thf(2026,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 @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
          & ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) )
           => ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(705,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).

thf(3859,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)],[705]) ).

thf(899,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/sandbox2/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).

thf(4451,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)],[899]) ).

thf(834,axiom,
    tc_Complex_Ocomplex @ class_Rings_Ocomm__ring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).

thf(4261,plain,
    tc_Complex_Ocomplex @ class_Rings_Ocomm__ring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).

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

thf(3085,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

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

thf(2041,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Groups_Omonoid__mult )
     => ( ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( B @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(202,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/sandbox2/benchmark/theBenchmark.p',fact_sgn__minus) ).

thf(2066,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)],[202]) ).

thf(229,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Oordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).

thf(2162,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)],[229]) ).

thf(235,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/sandbox2/benchmark/theBenchmark.p',fact_poly__0) ).

thf(2183,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)],[235]) ).

thf(1442,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( D @ class_Rings_Olinordered__semidom ) ),
    inference(cnf,[status(esa)],[1441]) ).

thf(872,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/sandbox2/benchmark/theBenchmark.p',fact_even__less__0__iff) ).

thf(4372,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)],[872]) ).

thf(1206,axiom,
    tc_RealDef_Oreal @ class_Fields_Ofield,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield) ).

thf(5336,plain,
    tc_RealDef_Oreal @ class_Fields_Ofield,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).

thf(569,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/sandbox2/benchmark/theBenchmark.p',fact_abs__le__zero__iff) ).

thf(3420,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)],[569]) ).

thf(189,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 @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib) ).

thf(2009,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 @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(809,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Osgn__if ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Osgn__if) ).

thf(4182,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Osgn__if ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).

thf(742,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__0 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Omult__zero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).

thf(3978,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)],[742]) ).

thf(1181,axiom,
    tc_RealDef_Oreal @ class_Rings_Olinordered__comm__semiring__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).

thf(5304,plain,
    tc_RealDef_Oreal @ class_Rings_Olinordered__comm__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).

thf(496,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 @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__frac__eq) ).

thf(3181,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 @ hAPP ) @ hAPP ) @ ( D @ ( A @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Rings_Oinverse__class_Odivide ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(7254,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__1 )
       != ( A @ class_Rings_Ocomm__semiring__1 ) )
      | ~ $true
      | ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Polynomial_OpCons ) ) )
        = ( A @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone ) ) ),
    inference(paramod_ordered,[status(thm)],[5238,1318]) ).

thf(7255,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Rings_Ocomm__semiring__1 )
       != ( A @ class_Rings_Ocomm__semiring__1 ) )
      | ( ( A @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( A @ c_Groups_Oone__class_Oone @ ( A @ c_Polynomial_OpCons ) ) )
        = ( A @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone ) ) ),
    inference(simp,[status(thm)],[7254]) ).

thf(7256,plain,
    ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Polynomial_OpCons ) ) )
    = ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_Groups_Oone__class_Oone ) ),
    inference(pattern_uni,[status(thm)],[7255:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(951,axiom,
    tc_Int_Oint @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).

thf(4602,plain,
    tc_Int_Oint @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).

thf(1233,axiom,
    ! [A: $i,B: $i] :
      ( ( B = A )
     => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).

thf(5408,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)],[1233]) ).

thf(46033,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) ) )
      | ( A
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2971,39004]) ).

thf(46307,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
       != A )
      | ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) )
       != ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) ),
    inference(simp,[status(thm)],[46033]) ).

thf(46419,plain,
    ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) )
   != ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ),
    inference(simp,[status(thm)],[46307]) ).

thf(572,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/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).

thf(3430,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)],[572]) ).

thf(947,axiom,
    tc_Int_Oint @ class_Rings_Oring__no__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).

thf(4591,plain,
    tc_Int_Oint @ class_Rings_Oring__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).

thf(1004,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/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).

thf(4774,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)],[1004]) ).

thf(1108,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ( B != A )
       => ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).

thf(5109,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ( 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)],[1108]) ).

thf(1439,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) )
        = ( C @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) ) )
      | ( C
        = ( D @ c_Groups_Ozero__class_Ozero ) )
      | ~ ( D @ class_Fields_Ofield ) ),
    inference(cnf,[status(esa)],[1438]) ).

thf(1440,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ class_Fields_Ofield )
      | ( ( C @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ c_Rings_Oinverse__class_Odivide ) ) )
        = ( A @ ( C @ ( B @ ( D @ c_Rings_Oinverse__class_Odivide ) ) @ ( D @ c_Groups_Ominus__class_Ominus ) ) ) )
      | ( C
        = ( D @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(lifteq,[status(thm)],[1439]) ).

thf(276,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 @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).

thf(2330,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 @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(49706,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( C @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) ) )
      | ( A
       != ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) ) ) ),
    inference(paramod_ordered,[status(thm)],[2971,39017]) ).

thf(49766,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
       != B )
      | ( ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) )
       != ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) ),
    inference(simp,[status(thm)],[49706]) ).

thf(49842,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) )
     != ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ),
    inference(simp,[status(thm)],[49766]) ).

thf(15703,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( tc_RealDef_Oreal @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ ( v_mazh @ ( v_da____ @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ $true
      | ~ ( B @ ( tc_RealDef_Oreal @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1542,10696]) ).

thf(15704,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( tc_RealDef_Oreal @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ ( v_mazh @ ( v_da____ @ ( B @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( B @ ( tc_RealDef_Oreal @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[15703]) ).

thf(15705,plain,
    ( ~ ( v_mazh @ ( v_da____ @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ c_Orderings_Oord__class_Oless__eq ) ) )
    | ~ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(pattern_uni,[status(thm)],[15704:[bind(A,$thf( tc_RealDef_Oreal )),bind(B,$thf( tc_Nat_Onat @ c_Groups_Oone__class_Oone ))]]) ).

thf(55770,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ ( v_mazh @ ( v_da____ @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1542,15705]) ).

thf(55771,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ ( v_mazh @ ( v_da____ @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(simp,[status(thm)],[55770]) ).

thf(55812,plain,
    ! [A: $i] :
      ( ( A
       != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
      | ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
       != tc_RealDef_Oreal )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ~ ( v_mazh @ ( v_da____ @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(simp,[status(thm)],[55771]) ).

thf(55842,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != tc_RealDef_Oreal )
    | ~ ( v_mazh @ ( v_da____ @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(simp,[status(thm)],[55812]) ).

thf(96,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Orderings_Oord )
     => ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).

thf(1607,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Orderings_Oord )
     => ( ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(881,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/sandbox2/benchmark/theBenchmark.p',fact_norm__one) ).

thf(4404,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)],[881]) ).

thf(543,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( C @ ( B @ hAPP ) )
          = ( C @ ( A @ hAPP ) ) )
     => ( B = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).

thf(3351,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( C @ ( B @ hAPP ) )
          = ( C @ ( A @ hAPP ) ) )
     => ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(747,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/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def) ).

thf(3993,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)],[747]) ).

thf(66,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less) ).

thf(1512,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(1513,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) )
      | ~ ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
      | ~ ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
      | ~ ( C @ class_Rings_Olinordered__semidom ) ),
    inference(cnf,[status(esa)],[1512]) ).

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

thf(2902,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semiring )
     => ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[421]) ).

thf(1110,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/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).

thf(5119,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)],[1110]) ).

thf(269,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Omonoid__mult )
     => ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Oone__class_Oone ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).

thf(2294,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Groups_Omonoid__mult )
     => ( ( A @ ( B @ c_Groups_Oone__class_Oone @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Oone__class_Oone ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(195,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Oring )
     => ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__diff__mult) ).

thf(2036,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Oring )
     => ( ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) )
        = ( A @ ( B @ ( D @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ c_Groups_Ominus__class_Ominus ) ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(14,axiom,
    ( v_cs____
    = ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cs0) ).

thf(1309,plain,
    ( v_cs____
    = ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(642,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/sandbox2/benchmark/theBenchmark.p',fact_abs__divide) ).

thf(3645,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)],[642]) ).

thf(852,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oorder )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).

thf(4306,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oorder )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).

thf(1048,axiom,
    tc_Nat_Onat @ class_Rings_Ocomm__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).

thf(4917,plain,
    tc_Nat_Onat @ class_Rings_Ocomm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).

thf(721,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/sandbox2/benchmark/theBenchmark.p',fact_divide__zero__left) ).

thf(3907,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)],[721]) ).

thf(48958,plain,
    ! [B: $i,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_Oone__class_Oone @ ( B @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
      | ( ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero )
       != B ) ),
    inference(paramod_ordered,[status(thm)],[5192,47491]) ).

thf(48959,plain,
    ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
   != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
    inference(pattern_uni,[status(thm)],[48958:[bind(A,$thf( tc_Int_Oint @ c_Groups_Oone__class_Oone )),bind(B,$thf( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) ))]]) ).

thf(922,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/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).

thf(4523,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)],[922]) ).

thf(603,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).

thf(3521,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)],[603]) ).

thf(394,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Olinordered__idom )
     => ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
          = ( B @ c_Groups_Oone__class_Oone ) )
      <=> ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__1__pos) ).

thf(2815,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_Oone__class_Oone ) ) )
        & ( ( ( A @ ( B @ c_Groups_Osgn__class_Osgn ) )
            = ( B @ c_Groups_Oone__class_Oone ) )
         => ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(941,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/sandbox2/benchmark/theBenchmark.p',fact_abs__if) ).

thf(4579,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)],[941]) ).

thf(1155,axiom,
    tc_RealDef_Oreal @ class_Groups_Oordered__comm__monoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).

thf(5247,plain,
    tc_RealDef_Oreal @ class_Groups_Oordered__comm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).

thf(551,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/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).

thf(3379,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)],[551]) ).

thf(289,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).

thf(2374,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(761,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/sandbox2/benchmark/theBenchmark.p',fact_minus__less__iff) ).

thf(4039,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)],[761]) ).

thf(272,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 @ hAPP ) @ hAPP ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq) ).

thf(2302,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 @ hAPP ) @ hAPP ) ) ) ) )
         => ( ( 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 @ hAPP ) @ hAPP ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(48081,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1409,15700]) ).

thf(48082,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( v_mazh @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ~ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(simp,[status(thm)],[48081]) ).

thf(48207,plain,
    ! [A: $i] :
      ( ( A
       != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
      | ( A != v_mazh )
      | ( tc_Nat_Onat != tc_Nat_Onat )
      | ~ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(simp,[status(thm)],[48082]) ).

thf(48242,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_mazh )
    | ~ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( v_da____ @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(simp,[status(thm)],[48207]) ).

thf(658,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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__divide__eq) ).

thf(3705,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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(754,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).

thf(4014,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)],[754]) ).

thf(1112,axiom,
    tc_Int_Oint @ class_Groups_Ocancel__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).

thf(5129,plain,
    tc_Int_Oint @ class_Groups_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).

thf(905,axiom,
    tc_Int_Oint @ class_Int_Oring__char__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).

thf(4472,plain,
    tc_Int_Oint @ class_Int_Oring__char__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).

thf(291,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).

thf(2385,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)],[291]) ).

thf(46095,plain,
    ! [A: $i] :
      ( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) ) )
      | ( A
       != ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) ),
    inference(paramod_ordered,[status(thm)],[2971,43011]) ).

thf(46166,plain,
    ( ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
     != ( tc_Int_Oint @ c_Groups_Oone__class_Oone ) )
    | ( ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) )
     != ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ) ),
    inference(simp,[status(thm)],[46095]) ).

thf(46327,plain,
    ( ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) )
   != ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes ) ),
    inference(simp,[status(thm)],[46166]) ).

thf(226,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ ( C @ ( D @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd ) ) )
       => ( ( C @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ ( A @ ( D @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__dvd) ).

thf(2155,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ ( C @ ( D @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd ) ) )
       => ( ( C @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B @ ( A @ ( D @ ( E @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

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

thf(2255,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
     => ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(707,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/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__minus__self) ).

thf(3865,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)],[707]) ).

thf(1014,axiom,
    tc_Complex_Ocomplex @ class_Rings_Ono__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).

thf(4811,plain,
    tc_Complex_Ocomplex @ class_Rings_Ono__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).

thf(667,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/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq4) ).

thf(3733,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)],[667]) ).

thf(627,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/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).

thf(3601,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)],[627]) ).

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

thf(2233,plain,
    ! [A: $i] :
      ( ( A @ class_RealVector_Oreal__normed__algebra )
     => ? [B: $i] :
        ! [C: $i,D: $i] : ( B @ ( D @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( C @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(713,axiom,
    tc_Int_Oint @ class_Rings_Oordered__comm__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).

thf(3882,plain,
    tc_Int_Oint @ class_Rings_Oordered__comm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).

thf(744,axiom,
    ! [A: $i] :
      ( ( A @ class_Groups_Oab__group__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ouminus ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ouminus) ).

thf(3987,plain,
    ! [A: $i] :
      ( ( A @ class_Groups_Oab__group__add )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Ouminus ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).

thf(982,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/sandbox2/benchmark/theBenchmark.p',fact_divide__pos__neg) ).

thf(4719,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)],[982]) ).

thf(1244,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).

thf(5430,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Oorder )
     => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).

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

thf(2522,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
     => ( ( ( A = B )
         => ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
        & ( ( B @ ( A @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(471,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Ocomm__semiring__1 )
     => ( ( C @ ( D @ ( E @ c_Rings_Odvd__class_Odvd ) ) )
       => ( ( A @ ( B @ ( E @ c_Rings_Odvd__class_Odvd ) ) )
         => ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__dvd__mono) ).

thf(3100,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Rings_Ocomm__semiring__1 )
     => ( ( C @ ( D @ ( E @ c_Rings_Odvd__class_Odvd ) ) )
       => ( ( A @ ( B @ ( E @ c_Rings_Odvd__class_Odvd ) ) )
         => ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(91,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).

thf(1593,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(585,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/sandbox2/benchmark/theBenchmark.p',fact_minus__add) ).

thf(3464,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)],[585]) ).

thf(1380,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(cnf,[status(esa)],[1379]) ).

thf(911,axiom,
    tc_Nat_Onat @ class_Groups_Ocancel__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).

thf(4491,plain,
    tc_Nat_Onat @ class_Groups_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).

thf(967,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/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).

thf(4663,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)],[967]) ).

thf(599,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/sandbox2/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).

thf(3496,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)],[599]) ).

thf(587,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/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).

thf(3469,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)],[587]) ).

thf(1089,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/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).

thf(5041,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)],[1089]) ).

thf(697,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/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).

thf(3822,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)],[697]) ).

thf(538,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__semiring__1 )
     => ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__right) ).

thf(3328,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__semiring__1 )
     => ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(1928,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
      | ( B
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ),
    inference(cnfConj,[status(thm)],[1925]) ).

thf(1932,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) )
      | ( B
       != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ) ),
    inference(lifteq,[status(thm)],[1928]) ).

thf(1933,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
      = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ) ),
    inference(simp,[status(thm)],[1932]) ).

thf(51057,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
      = ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) ),
    inference(rewrite,[status(thm)],[1933,2249]) ).

thf(495,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 @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
        <=> ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).

thf(3177,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 @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) )
          & ( ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( B @ ( A @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(1208,axiom,
    tc_RealDef_Oreal @ class_Power_Opower,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Power_Opower) ).

thf(5339,plain,
    tc_RealDef_Oreal @ class_Power_Opower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).

thf(536,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).

thf(3323,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(451,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__commute) ).

thf(3030,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(688,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__div__algebra,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).

thf(3805,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__div__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(937,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/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).

thf(4565,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)],[937]) ).

thf(1005,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/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).

thf(4777,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)],[1005]) ).

thf(866,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ( B != A )
      <=> ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
          | ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).

thf(4350,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ( ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
            | ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) )
         => ( B != A ) )
        & ( ( B != A )
         => ( ( B @ ( A @ ( C @ c_Orderings_Oord__class_Oless ) ) )
            | ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).

thf(44800,plain,
    ! [A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( A @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
       != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) ) )
      | ( A
       != ( tc_Nat_Onat @ c_Power_Opower__class_Opower ) ) ),
    inference(paramod_ordered,[status(thm)],[2957,44397]) ).

thf(44896,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
    | ( ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) )
     != ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ) ),
    inference(simp,[status(thm)],[44800]) ).

thf(45050,plain,
    ( ( tc_Nat_Onat @ c_Power_Opower__class_Opower @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) )
   != ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes ) ),
    inference(simp,[status(thm)],[44896]) ).

thf(1495,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(cnfConj,[status(thm)],[1494]) ).

thf(1229,axiom,
    tc_RealDef_Oreal @ class_Fields_Olinordered__field,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).

thf(5404,plain,
    tc_RealDef_Oreal @ class_Fields_Olinordered__field,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).

thf(106,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
    <=> ( ( C
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
        | ( B = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel1) ).

thf(1657,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 @ hAPP ) @ hAPP ) )
          = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) )
      & ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
          = ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) )
       => ( ( C
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
          | ( B = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(1039,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Lattices_Oboolean__algebra )
     => ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__compl) ).

thf(4895,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Lattices_Oboolean__algebra )
     => ( ( A @ ( B @ c_Groups_Ouminus__class_Ouminus ) @ ( B @ c_Groups_Ouminus__class_Ouminus ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).

thf(844,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/sandbox2/benchmark/theBenchmark.p',fact_divide__right__mono__neg) ).

thf(4286,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)],[844]) ).

thf(521,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 @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).

thf(3277,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 @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(236,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__times__eq) ).

thf(2186,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Rings_Oinverse__class_Odivide ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(842,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__0 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__0) ).

thf(4281,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__0 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Osemiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).

thf(817,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/sandbox2/benchmark/theBenchmark.p',fact_equal__neg__zero) ).

thf(4210,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)],[817]) ).

thf(1080,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/sandbox2/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).

thf(5019,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)],[1080]) ).

thf(757,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Ozero__neq__one ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).

thf(4024,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)],[757]) ).

thf(336,axiom,
    ! [A: $i] :
      ( ( ( A
         != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
       => ( ( ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
              = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ) )
          & ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
              = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) ) ) )
      & ( ( A
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sgn__def) ).

thf(2572,plain,
    ! [A: $i] :
      ( ( ( A
         != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
       => ( ( ~ ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
              = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Groups_Ouminus__class_Ouminus ) ) ) )
          & ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless ) ) )
           => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
              = ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ) ) ) )
      & ( ( A
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) )
       => ( ( A @ ( tc_RealDef_Oreal @ c_Groups_Osgn__class_Osgn ) )
          = ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(1235,axiom,
    tc_RealDef_Oreal @ class_Rings_Osemiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).

thf(5413,plain,
    tc_RealDef_Oreal @ class_Rings_Osemiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).

thf(366,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).

thf(2704,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(591,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/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).

thf(3479,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)],[591]) ).

thf(815,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/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).

thf(4193,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)],[815]) ).

thf(344,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Olinordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).

thf(2619,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)],[344]) ).

thf(191,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Ocomm__monoid__mult )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult__distrib) ).

thf(2021,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Groups_Ocomm__monoid__mult )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(1195,axiom,
    tc_RealDef_Oreal @ class_Groups_Ocancel__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).

thf(5322,plain,
    tc_RealDef_Oreal @ class_Groups_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).

thf(387,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Oidom )
     => ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
      <=> ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
          | ( B
            = ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel__right) ).

thf(2783,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Oidom )
     => ( ( ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
            | ( B
              = ( D @ c_Groups_Ozero__class_Ozero ) ) )
         => ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) )
        & ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
         => ( ( A @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
            | ( B
              = ( D @ c_Groups_Ozero__class_Ozero ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

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

thf(5324,plain,
    tc_RealDef_Oreal @ class_Groups_Ouminus,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).

thf(1170,axiom,
    tc_RealDef_Oreal @ class_Groups_Olinordered__ab__group__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).

thf(5275,plain,
    tc_RealDef_Oreal @ class_Groups_Olinordered__ab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).

thf(740,axiom,
    tc_Complex_Ocomplex @ class_Fields_Ofield,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).

thf(3974,plain,
    tc_Complex_Ocomplex @ class_Fields_Ofield,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).

thf(784,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/sandbox2/benchmark/theBenchmark.p',fact_add__increasing) ).

thf(4118,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)],[784]) ).

thf(313,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult) ).

thf(2467,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(908,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/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq3) ).

thf(4484,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)],[908]) ).

thf(51824,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[45349,1497]) ).

thf(51825,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
       != ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) )
      | ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[51824]) ).

thf(51826,plain,
    tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ),
    inference(pattern_uni,[status(thm)],[51825:[bind(A,$thf( tc_Nat_Onat @ c_Groups_Oone__class_Oone )),bind(B,$thf( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc ))]]) ).

thf(52740,plain,
    tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ c_Nat_OSuc @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ),
    inference(rewrite,[status(thm)],[51826,1603,2249]) ).

thf(716,axiom,
    tc_Nat_Onat @ class_Groups_Omonoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).

thf(3886,plain,
    tc_Nat_Onat @ class_Groups_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

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

thf(1713,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( ( B @ ( C @ c_Groups_Oabs__class_Oabs ) )
          = ( A @ ( C @ c_Groups_Oabs__class_Oabs ) ) )
       => ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(9333,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Int_Oint @ class_Rings_Omult__zero )
       != ( B @ class_Rings_Omult__zero ) )
      | ~ $true
      | ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(paramod_ordered,[status(thm)],[3703,1357]) ).

thf(9334,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Int_Oint @ class_Rings_Omult__zero )
       != ( B @ class_Rings_Omult__zero ) )
      | ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(simp,[status(thm)],[9333]) ).

thf(9335,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ),
    inference(pattern_uni,[status(thm)],[9334:[bind(A,$thf( A )),bind(B,$thf( tc_Int_Oint ))]]) ).

thf(863,axiom,
    tc_Nat_Onat @ class_Rings_Olinordered__semiring__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).

thf(4345,plain,
    tc_Nat_Onat @ class_Rings_Olinordered__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).

thf(319,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 @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__power) ).

thf(2502,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 @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Oone__class_Oone @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(218,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
       => ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult) ).

thf(2127,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( B @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) )
       => ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(392,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 @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__neg) ).

thf(2810,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 @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(1136,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/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__zero) ).

thf(5204,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)],[1136]) ).

thf(790,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/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).

thf(4129,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)],[790]) ).

thf(433,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__assoc) ).

thf(2966,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(655,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/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__self) ).

thf(3701,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)],[655]) ).

thf(827,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/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).

thf(4242,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)],[827]) ).

thf(402,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Ominus )
     => ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus ) ) @ hAPP ) )
        = ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__apply) ).

thf(2847,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( E @ class_Groups_Ominus )
     => ( ( A @ ( B @ ( C @ ( E @ ( D @ tc_fun ) @ c_Groups_Ominus__class_Ominus ) ) @ hAPP ) )
        = ( A @ ( B @ hAPP ) @ ( A @ ( C @ hAPP ) @ ( E @ c_Groups_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(563,axiom,
    tc_Int_Oint @ class_Rings_Oordered__cancel__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).

thf(3411,plain,
    tc_Int_Oint @ class_Rings_Oordered__cancel__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(683,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/sandbox2/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).

thf(3772,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)],[683]) ).

thf(80,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Orderings_Oord )
     => ( B @ ( A @ tc_fun ) @ class_Orderings_Oord ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).

thf(1550,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Orderings_Oord )
     => ( B @ ( A @ tc_fun ) @ class_Orderings_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(518,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ c_Groups_Oone__class_Oone @ ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).

thf(3259,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( C @ c_Groups_Oone__class_Oone @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
         => ( C @ c_Groups_Oone__class_Oone @ ( A @ c_Nat_OSuc @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(769,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/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).

thf(4066,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)],[769]) ).

thf(694,axiom,
    tc_Complex_Ocomplex @ class_Groups_Ocancel__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).

thf(3817,plain,
    tc_Complex_Ocomplex @ class_Groups_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).

thf(1499,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ),
    inference(cnf,[status(esa)],[1498]) ).

thf(1500,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
      = ( A @ ( B @ c_Nat_OSuc @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ),
    inference(lifteq,[status(thm)],[1499]) ).

thf(515,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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__eq__mult) ).

thf(3245,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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(1097,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/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__cancel) ).

thf(5060,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)],[1097]) ).

thf(883,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/sandbox2/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).

thf(4410,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)],[883]) ).

thf(965,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/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__le__zero) ).

thf(4659,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)],[965]) ).

thf(980,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/sandbox2/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).

thf(4713,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)],[980]) ).

thf(407,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).

thf(2864,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)],[407]) ).

thf(670,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/sandbox2/benchmark/theBenchmark.p',fact_sgn__less) ).

thf(3740,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)],[670]) ).

thf(1429,plain,
    ~ ? [A: $i] :
        ( ( A @ c_Nat_OSuc )
        = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(miniscope,[status(thm)],[1428]) ).

thf(1430,plain,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(cnf,[status(esa)],[1429]) ).

thf(1431,plain,
    ! [A: $i] :
      ( ( A @ c_Nat_OSuc )
     != ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ),
    inference(lifteq,[status(thm)],[1430]) ).

thf(464,axiom,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
          = ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
      <=> ( B
          = ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).

thf(3076,plain,
    ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
      ( ( D @ ( E @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
     => ( ( ( B
            = ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
         => ( ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
            = ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) )
        & ( ( ( B @ ( C @ ( E @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) )
            = ( A @ ( C @ ( D @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) )
         => ( B
            = ( A @ ( C @ ( E @ ( D @ ( tc_Nat_Onat @ c_Groups_Ominus__class_Ominus ) ) @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(164,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/sandbox2/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).

thf(1902,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)],[164]) ).

thf(55358,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
       != ( B @ ( B @ ( 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 )
       != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ),
    inference(paramod_ordered,[status(thm)],[49036,4425]) ).

thf(55359,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) @ ( A @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) )
     != ( B @ ( B @ ( 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(simp,[status(thm)],[55358]) ).

thf(55438,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
       != B )
      | ( A
       != ( B @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) ) )
      | ( tc_Int_Oint != tc_Int_Oint ) ),
    inference(simp,[status(thm)],[55359]) ).

thf(55458,plain,
    ! [A: $i] :
      ( ( A @ ( tc_Int_Oint @ c_Groups_Oone__class_Oone @ ( tc_Int_Oint @ c_Groups_Oplus__class_Oplus ) ) @ ( tc_Int_Oint @ c_Groups_Ouminus__class_Ouminus ) )
     != A ),
    inference(simp,[status(thm)],[55438]) ).

thf(978,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
    <=> ( ( A
          = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
        | ( B
         != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__zpower__abs__iff) ).

thf(4691,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
          | ( B
           != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) )
       => ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) ) )
      & ( ( A @ ( B @ ( tc_Int_Oint @ c_Groups_Oabs__class_Oabs ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero @ ( tc_Int_Oint @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A
            = ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
          | ( B
           != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).

thf(98,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Oring__1__no__zero__divisors )
     => ( ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
          = ( 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/sandbox2/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).

thf(1621,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 @ hAPP ) @ hAPP ) )
            = ( B @ c_Groups_Oone__class_Oone ) ) )
        & ( ( ( A @ ( A @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
            = ( 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)],[98]) ).

thf(776,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/sandbox2/benchmark/theBenchmark.p',fact_divide__neg__pos) ).

thf(4088,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)],[776]) ).

thf(1210,axiom,
    tc_RealDef_Oreal @ class_Groups_Oordered__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).

thf(5344,plain,
    tc_RealDef_Oreal @ class_Groups_Oordered__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).

thf(970,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
     => ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__imp__le) ).

thf(4674,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) )
     => ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( 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)],[970]) ).

thf(621,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).

thf(3580,plain,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Olinordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(920,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Olinordered__idom )
     => ( A @ tc_Polynomial_Opoly @ class_Rings_Oordered__ring__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring__abs) ).

thf(4520,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)],[920]) ).

thf(176,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 @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).

thf(1962,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 @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(408,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing) ).

thf(2866,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( D @ c_Groups_Oone__class_Oone @ ( D @ c_Orderings_Oord__class_Oless ) ) )
         => ( B @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(152,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).

thf(1848,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(1415,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Groups_Oabs__class_Oabs ) @ ( A @ ( B @ c_Groups_Osgn__class_Osgn ) @ ( B @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = A )
      | ~ ( B @ class_Rings_Olinordered__idom ) ),
    inference(cnf,[status(esa)],[1414]) ).

thf(1416,plain,
    ! [B: $i,A: $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 @ hAPP ) @ hAPP ) )
        = A ) ),
    inference(lifteq,[status(thm)],[1415]) ).

thf(749,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/sandbox2/benchmark/theBenchmark.p',fact_gt__half__sum) ).

thf(4002,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)],[749]) ).

thf(720,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/sandbox2/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).

thf(3901,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)],[720]) ).

thf(447,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 @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff1) ).

thf(3013,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 @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(15002,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_Groups_Ozero__class_Ozero )
     != ( tc_Int_Oint @ c_Groups_Ozero__class_Ozero ) )
    | ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
     != v_mazh )
    | ( v_cs____ != v_da____ )
    | ( tc_Int_Oint != tc_RealDef_Oreal ) ),
    inference(paramod_ordered,[status(thm)],[1280,14585]) ).

thf(15003,plain,
    ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly )
     != tc_Int_Oint )
    | ( ( tc_Int_Oint @ c_Groups_Oone__class_Oone )
     != v_mazh )
    | ( v_cs____ != v_da____ )
    | ( tc_Int_Oint != tc_RealDef_Oreal ) ),
    inference(simp,[status(thm)],[15002]) ).

thf(606,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/sandbox2/benchmark/theBenchmark.p',fact_frac__less) ).

thf(3528,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)],[606]) ).

thf(1018,axiom,
    tc_Nat_Onat @ class_Groups_Ocancel__comm__monoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).

thf(4826,plain,
    tc_Nat_Onat @ class_Groups_Ocancel__comm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).

thf(414,axiom,
    ! [A: $i] :
      ( ( A @ class_Rings_Ocomm__semiring__1 )
     => ( A @ tc_Polynomial_Opoly @ class_Groups_Omonoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).

thf(2879,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)],[414]) ).

thf(1006,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
        <=> ( B = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).

thf(4779,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Orderings_Olinorder )
     => ( ~ ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( ( B = A )
           => ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) ) )
          & ( ( A @ ( B @ ( C @ c_Orderings_Oord__class_Oless__eq ) ) )
           => ( B = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).

thf(1084,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/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).

thf(5029,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)],[1084]) ).

thf(960,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/sandbox2/benchmark/theBenchmark.p',fact_zabs__def) ).

thf(4642,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)],[960]) ).

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

thf(3227,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( B @ ( A @ ( C @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(173,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__ring__strict )
     => ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).

thf(1944,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 @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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)],[173]) ).

thf(1184,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oord )
     => ( ( C = B )
       => ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord__eq__le__trans) ).

thf(5307,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Oord )
     => ( ( C = B )
       => ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).

thf(415,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Rings_Odvd__class_Odvd ) ) )
       => ( A
          = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__left) ).

thf(2881,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Rings_Ocomm__semiring__1 )
     => ( ( A @ ( B @ c_Groups_Ozero__class_Ozero @ ( B @ c_Rings_Odvd__class_Odvd ) ) )
       => ( A
          = ( B @ c_Groups_Ozero__class_Ozero ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(636,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/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).

thf(3626,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)],[636]) ).

thf(1186,axiom,
    tc_RealDef_Oreal @ class_Rings_Olinordered__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).

thf(5312,plain,
    tc_RealDef_Oreal @ class_Rings_Olinordered__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).

thf(1262,axiom,
    tc_RealDef_Oreal @ class_Groups_Oordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).

thf(5458,plain,
    tc_RealDef_Oreal @ class_Groups_Oordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262]) ).

thf(241,axiom,
    ! [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_Oone__class_Oone ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__pos) ).

thf(2206,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_Oone__class_Oone ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(109,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zpower) ).

thf(1681,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( A @ ( B @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
      = ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( tc_Int_Oint @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(417,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/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__mono) ).

thf(2887,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)],[417]) ).

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

thf(4949,plain,
    tc_Nat_Onat @ class_Rings_Osemiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).

thf(1000,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/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).

thf(4767,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)],[1000]) ).

thf(363,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 @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).

thf(2690,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 @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) )
        = ( A @ ( B @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(1463,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( 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 @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
      | ~ ( C @ class_Rings_Olinordered__semiring__strict ) ),
    inference(cnf,[status(esa)],[1462]) ).

thf(1128,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__field )
     => ? [C: $i] :
        ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( B @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide_Obounded) ).

thf(5183,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_RealVector_Oreal__normed__field )
     => ? [C: $i] :
        ! [D: $i] : ( C @ ( D @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( B @ c_Rings_Oinverse__class_Odivide ) ) @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).

thf(86,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( B @ c_Nat_OSuc @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ c_Nat_OSuc @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__base) ).

thf(1565,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Rings_Olinordered__semidom )
     => ( ( B @ c_Nat_OSuc @ ( A @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( B @ c_Nat_OSuc @ ( C @ ( D @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
       => ( ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(1247,axiom,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).

thf(5436,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).

thf(994,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/sandbox2/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).

thf(4752,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)],[994]) ).

thf(270,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 @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono1) ).

thf(2297,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 @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(576,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Opreorder )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).

thf(3443,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ class_Orderings_Opreorder )
     => ( ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) )
       => ( ( A @ ( B @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
         => ( A @ ( C @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(343,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 @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__divide__eq) ).

thf(2615,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 @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( A @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(43575,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       != ( v_mazh @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      | ~ $true
      | ~ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(paramod_ordered,[status(thm)],[5270,15663]) ).

thf(43576,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) )
       != ( v_mazh @ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( tc_RealDef_Oreal @ c_Orderings_Oord__class_Oless__eq ) ) ) )
      | ~ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[43575]) ).

thf(43647,plain,
    ! [A: $i] :
      ( ( A != v_mazh )
      | ( A
       != ( tc_Nat_Onat @ c_Groups_Oone__class_Oone ) )
      | ( tc_RealDef_Oreal != tc_RealDef_Oreal )
      | ~ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[43576]) ).

thf(43701,plain,
    ( ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone )
     != v_mazh )
    | ~ ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( v_da____ @ ( tc_Nat_Onat @ c_Rings_Odvd__class_Odvd ) ) ) ),
    inference(simp,[status(thm)],[43647]) ).

thf(1044,axiom,
    tc_Int_Oint @ class_Groups_Oab__semigroup__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).

thf(4908,plain,
    tc_Int_Oint @ class_Groups_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).

thf(457,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono) ).

thf(3052,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 @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( E @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( E @ c_Orderings_Oord__class_Oless ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(1029,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/sandbox2/benchmark/theBenchmark.p',fact_real__sgn__eq) ).

thf(4863,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)],[1029]) ).

thf(534,axiom,
    ! [A: $i,B: $i] :
      ( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ hBOOL )
     => ( ( A @ ( B @ hAPP ) @ hBOOL )
       => ? [C: $i] :
            ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ hAPP ) @ hBOOL )
            & ! [D: $i] :
                ( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
               => ~ ( D @ ( B @ hAPP ) @ hBOOL ) )
            & ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__least__nat__less) ).

thf(3316,plain,
    ! [A: $i,B: $i] :
      ( ~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( B @ hAPP ) @ hBOOL )
     => ( ( A @ ( B @ hAPP ) @ hBOOL )
       => ? [C: $i] :
            ( ( tc_Nat_Onat @ c_Groups_Oone__class_Oone @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus ) ) @ ( B @ hAPP ) @ hBOOL )
            & ! [D: $i] :
                ( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq ) ) )
               => ~ ( D @ ( B @ hAPP ) @ hBOOL ) )
            & ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(232,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
      <=> ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__abs__iff) ).

thf(2170,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__idom )
     => ( ( ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
         => ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) )
        & ( ( A @ ( C @ c_Groups_Oabs__class_Oabs ) @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) )
         => ( A @ ( B @ ( C @ c_Rings_Odvd__class_Odvd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(397,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ class_Power_Opower )
     => ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Oone__class_Oone ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0) ).

thf(2834,plain,
    ! [A: $i,B: $i] :
      ( ( B @ class_Power_Opower )
     => ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( B @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) )
        = ( B @ c_Groups_Oone__class_Oone ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(238,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power) ).

thf(2191,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ class_Rings_Olinordered__semidom )
     => ( ( B @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) )
       => ( A @ ( B @ ( C @ c_Power_Opower__class_Opower @ hAPP ) @ hAPP ) @ ( C @ c_Groups_Ozero__class_Ozero @ ( C @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

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

thf(2106,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 @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(615,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/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).

thf(3553,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)],[615]) ).

thf(1179,axiom,
    tc_RealDef_Oreal @ class_Groups_Ocancel__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).

thf(5293,plain,
    tc_RealDef_Oreal @ class_Groups_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).

thf(1468,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( C @ ( A @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( A @ ( D @ c_Groups_Ozero__class_Ozero @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( B @ ( C @ ( D @ c_Orderings_Oord__class_Oless__eq ) ) )
      | ~ ( D @ class_Rings_Oordered__semiring ) ),
    inference(cnf,[status(esa)],[1467]) ).

thf(314,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 @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff2) ).

thf(2470,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 @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless ) ) )
         => ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( F @ c_Orderings_Oord__class_Oless ) ) ) )
        & ( ( A @ ( D @ ( B @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( D @ ( E @ ( F @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( 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 @ hAPP ) @ hAPP ) @ ( F @ c_Groups_Oplus__class_Oplus ) ) @ ( C @ ( F @ c_Orderings_Oord__class_Oless ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(166,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).

thf(1912,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 @ hAPP ) @ hAPP ) )
        = ( A @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ c_Groups_Otimes__class_Otimes @ hAPP ) @ hAPP ) @ ( D @ c_Groups_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(2979,plain,
    ( ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero )
   != ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone ) ),
    inference(polarity_switch,[status(thm)],[2978]) ).

thf(2980,plain,
    ( ( tc_RealDef_Oreal @ c_Groups_Oone__class_Oone )
   != ( tc_RealDef_Oreal @ c_Groups_Ozero__class_Ozero ) ),
    inference(lifteq,[status(thm)],[2979]) ).

thf(82441,plain,
    $false,
    inference(e,[status(thm)],[5437,4188,3883,1469,1633,4169,5320,4290,1982,4877,1501,2452,15170,4560,1879,5422,1337,2744,4835,4450,2341,3008,5593,2131,4909,4262,2072,5260,4899,1559,21439,3666,1729,6285,2463,1899,1840,14585,1315,2499,4992,5131,2280,4904,3172,4166,2250,3681,4376,5242,3910,4960,4603,3498,1533,21570,1305,3382,1486,5444,4043,3534,2117,1596,5141,2808,1522,3762,2644,3813,3230,25304,5069,2395,3549,1443,5000,3417,3460,1422,2248,5224,2282,1591,2114,5405,2837,1269,1437,4487,4592,4403,3429,4418,2686,3648,4011,3365,3446,3338,4279,3781,4650,19653,3313,25078,1354,5412,1497,1705,3017,4543,5425,1426,3217,3530,23438,4090,1655,5361,1756,22970,4026,3044,5288,4528,3175,1275,5316,5257,4638,5146,1872,1327,3693,3826,21857,3414,4294,4435,3577,3717,5192,4762,1458,4941,1835,5195,3730,2082,39017,4156,2531,1482,5024,3836,4343,3236,3629,5227,2723,2972,5252,3766,2432,5393,2763,2227,1576,13915,4079,1441,4266,4618,3088,1601,1386,10698,4030,1724,1475,2400,1529,59281,25940,2957,55637,3820,2328,2039,5284,3495,3061,5188,3776,3744,5289,2356,1409,4238,1287,19267,4546,3938,7277,4348,25499,4743,5306,4866,2735,4563,1985,4422,1760,4956,4415,3342,5274,5064,50772,3617,49845,1860,1264,2217,1323,3148,21354,1511,2274,3485,15663,1826,1313,1279,5130,3410,3749,5182,2562,47907,4766,1462,4428,1545,21220,32229,4862,5127,1319,1609,2635,1773,4390,4771,2533,4967,4756,1379,3385,5256,2403,21491,1514,4179,5193,4492,5397,4622,5323,1347,1398,4317,3312,3657,57072,4368,15161,3951,2024,1641,4383,1815,2989,5076,4507,48998,1875,6983,4258,2893,4724,46958,5156,1383,2950,2237,4988,5433,1302,2794,2324,3887,3966,3199,4173,3934,4903,4443,4072,24000,4454,4600,3295,4733,2259,1334,3527,3438,1864,3973,1978,3569,2540,5311,3923,5135,3093,4115,2335,5457,2777,5360,4556,5259,1283,3771,4810,4162,1843,3537,2861,5096,5375,5370,1351,2639,2750,3559,3378,5045,5059,4055,5448,5353,3685,1886,3808,3036,4364,2371,1394,3157,1526,5321,2137,20963,28747,2002,3955,15210,3870,3606,4588,5328,4628,3184,2884,3435,3582,3011,5406,3459,3301,2646,3852,5438,5167,5034,1915,2641,1604,3899,5174,3097,4893,2910,4589,4407,4888,1438,3720,5443,2164,47299,5142,4557,5416,2737,1311,3054,4031,2621,28208,4059,5334,2061,3550,5281,1636,2264,1387,3261,17936,2428,1355,4499,22052,41352,5206,2673,5049,3735,4016,3972,2249,3603,2596,3867,5002,4989,1676,5455,4252,25123,2969,4344,3989,4128,3239,3233,3371,3884,3154,3134,5754,1370,3814,2986,5396,23148,4661,25212,2396,3682,3471,3286,4140,1920,4585,1819,9301,3282,2958,3948,3958,4295,1938,5391,2873,3980,19273,3269,4849,4192,3403,3090,1555,2332,3314,3137,5177,3556,21751,4385,49220,5021,1296,3877,4553,3600,1687,3546,5038,3144,3535,1787,4417,3028,3050,2344,3763,1281,2741,1392,3667,4732,2112,4080,3931,3033,3408,1740,4680,5330,3799,2769,3445,5066,3731,4957,2157,2709,5362,4883,5313,4123,2245,5189,3467,3782,1541,3482,5053,2515,2100,1270,1851,5098,2377,5270,5238,4512,2685,4974,3862,21325,5345,2841,1328,14941,2359,4486,4789,4048,1498,39217,4525,1425,3102,5428,3704,4930,1719,4227,2858,8636,5373,3746,4109,5687,2268,4219,5497,3001,4898,1397,4263,5031,4983,1292,1414,33237,2085,56064,1419,1567,4676,2460,4320,3141,4951,2877,4518,3326,5166,1964,49807,3407,3210,4721,1461,4425,56049,3728,2868,4389,4421,2455,4750,4545,5337,4744,5213,2108,1446,3723,2666,36348,3555,2978,2649,3242,4508,1552,3390,4717,4231,3409,2766,4953,3920,7333,3703,5063,1324,2285,2504,5317,4846,3611,47491,1263,2450,3654,1588,2536,3126,1451,5374,2845,3059,1266,3354,4068,2387,1831,4970,9498,5234,1668,1974,21243,4540,24412,49792,4120,1874,5305,3109,3074,4069,3083,3162,4223,3215,5245,3454,1333,3755,1318,3802,2203,4288,4765,20766,1563,1466,2408,2529,3824,5112,1434,4184,39522,3225,1779,9094,4567,49071,3279,4889,3592,1846,5434,50517,16825,3321,5447,2368,5419,3639,20120,1895,2189,1616,5249,2662,4004,1996,4308,2729,3660,5327,18968,1483,5048,4562,3289,2602,4577,3111,4269,2235,2144,4921,15427,2413,3130,8641,4685,2904,22396,1698,2556,4116,2253,2149,23365,3257,3890,4874,5278,49788,1273,5230,4256,1747,12119,1548,3738,1301,4340,3375,3523,2734,4599,4365,3396,4453,1631,5043,5241,4786,4144,49036,1833,2727,3768,2938,10700,4465,5271,5239,4946,3213,2225,3504,4283,1784,4494,28207,3255,3811,5395,2791,3609,4159,8470,2981,4309,3472,2489,2393,1752,1652,13395,3758,3945,16323,4677,17931,1388,4801,4122,1535,39004,19659,1701,3590,23245,3868,4758,4769,2134,21909,3599,2193,4186,5363,3340,15428,2166,2457,3416,3304,14942,3719,3170,1428,3223,13197,1503,5185,19269,4978,3118,5033,4127,1371,4837,1312,49530,15160,3330,3208,5331,3663,4672,2935,4822,2442,5190,5207,14183,3487,4060,5449,5158,45349,1464,2474,1638,4245,3532,17860,7529,2721,5671,5244,24720,1524,3419,2257,4139,2896,4773,3160,4388,4929,15700,3996,3631,1853,3764,9614,24484,2415,5103,2637,5325,4914,26188,2955,1492,1603,2299,3106,1542,4586,2839,4958,5407,2945,5346,5093,2856,4176,3500,49533,56855,10696,2180,4203,4635,5035,48240,4569,1993,2780,4181,4332,2593,4296,5180,2664,1381,2974,4990,2812,2632,4420,4445,2605,1557,4009,2129,2625,4462,4911,2261,5439,3932,1909,5286,2446,4277,5392,1838,1325,5318,3298,4652,56090,3971,1344,1293,2278,2553,3150,4684,2842,1952,3838,1445,20617,2797,1435,4918,2999,2069,3539,2418,4832,5340,5057,23059,5254,49907,21296,2365,1474,2350,2725,22331,2051,2481,3917,15933,5516,5248,3806,24299,2064,4362,3674,4827,2288,4703,4304,1726,4954,5326,5139,1694,2693,2984,4481,3490,4473,4084,4331,4426,1758,5528,3576,2652,1420,1684,3975,1472,4688,26258,5763,5133,2005,1413,3881,4741,2239,1809,5424,2952,4441,4136,2096,13168,3427,1467,4886,4260,5025,2271,3206,4052,4319,3146,4879,4292,1509,1990,3048,4859,3292,2899,4812,47593,4986,4168,15895,3849,5414,4045,5452,5229,1770,3913,25213,2012,26078,4641,2821,1267,4377,2831,5446,2513,15308,3640,1598,4360,5294,5602,5250,3842,4937,5388,18974,1743,21251,4950,4534,22546,2732,3462,1531,4324,43447,2850,1484,2160,35263,21237,4522,49917,4549,5276,1763,1538,1336,5277,2354,3019,2747,2569,4437,3642,4346,4240,2092,1987,5420,1716,5418,1432,4190,3818,28524,1452,3114,2700,25405,21554,4020,4145,13149,2276,2219,1980,5203,4132,2322,4982,3623,14480,3412,3359,2044,1738,5450,3652,4959,3493,49837,4611,1284,1797,3071,4819,4217,2675,5319,1358,1934,2948,2411,40955,3488,24633,1543,4802,1766,49810,2558,5223,4133,4436,2543,3356,4748,1955,16367,2145,1485,1506,5453,1749,1427,3388,1504,4235,2511,4267,2030,1272,5100,4795,2584,4257,4671,3398,4111,4414,4587,4945,22469,4656,15805,3188,57927,3056,4730,33430,2875,26033,3168,3284,2760,1421,3400,3478,3433,3946,3620,59277,3452,23360,1918,4138,3457,1316,3757,4851,4727,2088,2870,4165,1817,42334,2347,1412,43011,1781,40614,2209,3625,3725,2997,1448,4102,4006,2110,4463,5332,44397,1866,45117,2707,2174,5272,2406,1508,3220,28245,2971,2608,5394,4881,4823,3662,5258,1276,1590,5315,2443,1385,2594,1721,1341,2098,1481,4683,4791,3991,5228,2026,4834,5243,3859,4451,4261,3085,1491,5164,2041,2066,2162,2183,9211,1442,4372,5336,3420,2009,4182,3978,5304,3181,7256,4602,5408,46419,3430,4591,4774,5109,1440,2330,49842,55842,1607,4404,3351,3993,1513,2902,5119,2294,2036,1309,3645,4306,4927,2930,4917,1512,3907,48959,21265,4523,3521,2815,5527,4579,5247,2142,3379,2374,4039,1348,2302,2683,48242,3705,1280,4014,4114,5129,4472,2385,46327,2155,15705,2255,2983,3865,4254,4811,22761,3733,3601,2233,3882,1395,3987,4719,5430,2522,3100,1593,3464,1380,4491,19272,4663,3496,3469,5041,3822,3328,51057,3177,5339,3323,3030,5215,21436,3805,3897,4565,4777,4350,45050,1495,5404,1657,4895,4286,3277,2186,4281,21702,4210,9271,5019,4024,2572,5413,2704,3479,1410,4193,2619,2021,5322,1346,2783,5324,5275,3974,4118,2467,4484,4239,52740,3886,1713,9335,4345,2502,2127,2810,1352,5204,4129,47754,2966,3701,4242,2847,1384,3411,3772,21804,1550,4987,1357,4506,3259,4066,3817,1500,3965,1923,3245,5060,4410,4659,4713,2864,3740,1431,3076,1902,55458,4691,1505,1621,4088,5344,4674,3580,4520,1962,2866,1848,1416,4002,1417,3901,3013,3526,15003,1331,3528,4826,4655,2879,5155,4779,5029,4642,3227,1944,5307,2881,3626,5312,5458,2206,1681,2887,4949,4767,2690,1463,5183,1565,5261,5436,21391,1490,4752,2297,3443,2615,43701,4908,3052,4863,3316,2170,2834,2191,1449,2106,3553,5293,15722,1468,2470,1912,2980]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWW237+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.16/0.42  % Computer : n005.cluster.edu
% 0.16/0.42  % Model    : x86_64 x86_64
% 0.16/0.42  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42  % Memory   : 8046.5625MB
% 0.16/0.42  % OS       : Linux 6.8.0-71-generic
% 0.16/0.42  % CPULimit : 300
% 0.16/0.42  % WCLimit  : 300
% 0.16/0.42  % DateTime : Sat Sep 26 15:30:31 UTC 2026
% 0.16/0.42  % CPUTime  : 
% 0.16/0.42  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.93/1.00  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.89/1.54  % [INFO] 	 Parsing done (534ms). 
% 2.89/1.56  % [INFO] 	 Running in sequential loop mode. 
% 3.91/1.94  % [INFO] 	 eprover registered as external prover. 
% 3.91/1.95  % [INFO] 	 Scanning for conjecture ... 
% 4.65/2.18  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1288 axioms. Running axiom selection ... 
% 6.71/2.66  % [INFO] 	 Axiom selection finished. Selected 1260 axioms (removed 28 axioms). 
% 9.04/3.28  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 9.45/3.34  % [INFO] 	 Type checking passed. 
% 9.45/3.35  % [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 ... 
% 243.31/69.67  % External prover 'e' found a proof!
% 243.31/69.67  % [INFO] 	 Killing All external provers ... 
% 243.31/69.67  % Time passed: 69108ms (effective reasoning time: 68112ms)
% 243.31/69.67  % 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)>
% 243.31/69.69  % Axioms used in derivation (1260): fact_zero__le__divide__iff, fact_dvd_Oord__less__eq__trans, fact_xt1_I1_J, fact_le__SucI, arity_fun__Orderings_Oorder, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_power__abs, fact_dvd_Oless__trans, fact_incr__mult__lemma, fact_zle__refl, fact_neg__le__0__iff__le, arity_Complex__Ocomplex__Rings_Odvd, fact_add__le__less__mono, fact_mult__strict__left__mono__neg, fact_order__le__neq__trans, fact_Nat_Oadd__0__right, fact_one__dvd, fact_right__inverse__eq, fact_real__squared__diff__one__factored, arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra, arity_Polynomial__Opoly__Rings_Osemiring__0, fact_abs__of__pos, fact_real__le__refl, fact_abs__le__D2, arity_Complex__Ocomplex__Rings_Oidom, fact_nat_Osimps_I3_J, arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_mult__right__le__imp__le, fact_zdvd__antisym__abs, fact_real__less__def, arity_Nat__Onat__Groups_Ocancel__semigroup__add, fact_real__le__trans, fact_neg__le__divide__eq, fact_power__strict__decreasing, arity_Complex__Ocomplex__Groups_Omonoid__add, arity_Int__Oint__Rings_Ocomm__semiring, fact_pos__add__strict, arity_Int__Oint__Rings_Osemiring, fact_mult__poly__0__right, arity_RealDef__Oreal__Orderings_Oord, fact_add__strict__right__mono, arity_Int__Oint__Orderings_Olinorder, fact_mult__1__left, fact_diff__0__eq__0, fact_minus__mult__left, fact_neg__divide__le__eq, fact_dvd__mult__cancel__left, fact_zdvd__not__zless, fact_neg__equal__0__iff__equal, fact_inf__period_I4_J, fact_dvdI, fact_abs__minus__commute, fact_abs__if, fact_le__eq__less__or__eq, fact_minus__mult__right, fact_xt1_I4_J, arity_RealDef__Oreal__Groups_Ozero, fact_trans__less__add1, fact_q__pos__lemma, fact_add__poly__code_I2_J, fact_abs__ge__self, arity_RealDef__Oreal__Rings_Oordered__comm__semiring, arity_Complex__Ocomplex__Groups_Oab__group__add, fact_order, fact_diff__0__right, fact_mult__less__cancel__left__disj, fact_nat__add__left__commute, fact_real__mult__left__cancel, fact_mult__nonpos__nonpos, fact_dvd_Oeq__iff, fact_order__le__less__trans, fact_mult__left_Ominus, arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors, fact_real__sgn__eq, fact_zdvd__antisym__nonneg, fact_power__inject__base, fact_norm__power, arity_Nat__Onat__Rings_Ono__zero__divisors, fact_nat__less__cases, fact_divide__nonpos__neg, fact_one__is__add, arity_Int__Oint__Rings_Olinordered__semiring__strict, arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add, fact_termination__basic__simps_I5_J, arity_Polynomial__Opoly__Rings_Ocomm__semiring__0, fact_norm__mult__less, fact_odd__nonzero, fact_mult_Opos__bounded, fact_dvd_Oorder__trans, fact_norm__diff__triangle__ineq, fact_zminus__zminus, fact_mult__nonneg__nonpos, fact_poly__eq__0__iff__dvd, fact_less__imp__le__nat, fact_combine__common__factor, fact_le__imp__0__less, fact_n__less__m__mult__n, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J, fact_Suc__mono, fact_add__less__mono, fact_real__0__less__add__iff, fact_mult__eq__0__iff, fact_pow__divides__pow__int, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J, arity_RealDef__Oreal__Groups_Ominus, arity_Nat__Onat__Orderings_Oorder, fact_mult__right__less__imp__less, fact_dvd__triv__right, fact_add__leD1, fact_abs__eq__mult, fact_split__mult__neg__le, fact_dvd_Oless__asym_H, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, fact_unity__coeff__ex, fact_abs__div__pos, fact_zero__less__power, arity_Nat__Onat__Rings_Ocomm__semiring__0, fact_psize__eq__0__iff, arity_Nat__Onat__Groups_Oordered__comm__monoid__add, fact_less__nat__zero__code, arity_RealDef__Oreal__Rings_Osemiring__0, arity_RealDef__Oreal__Rings_Olinordered__ring, fact_linorder__not__le, fact_poly__bound__exists, arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le, fact_mult__le__less__imp__less, fact_zadd__commute, arity_Nat__Onat__Groups_Omonoid__mult, fact_power__increasing, fact_diff__Suc__less, fact_real__add__le__0__iff, fact_mult__0, fact_abs__triangle__ineq2__sym, fact_order__less__asym_H, fact_mult__poly__0__left, arity_Polynomial__Opoly__Rings_Olinordered__ring__strict, fact_order__eq__refl, fact_linorder__antisym__conv2, fact_abs__poly__def, fact_mult__mono, fact_linorder__neqE, fact_field__power__not__zero, arity_RealDef__Oreal__Rings_Oidom, fact_Suc__le__mono, fact_dvd_Oless__imp__not__less, fact_norm__add__less, arity_Nat__Onat__Rings_Ozero__neq__one, fact_poly__zero, fact_divide_Obounded, fact_eq__neg__iff__add__eq__0, arity_Polynomial__Opoly__Groups_Oab__semigroup__mult, fact_zero__le__zpower__abs, fact_add__right__imp__eq, fact_realpow__two__diff, arity_Complex__Ocomplex__Groups_Oab__semigroup__mult, arity_Polynomial__Opoly__Rings_Oidom, fact_mult_Ononneg__bounded, fact_nat__add__right__cancel, fact_neg__le__iff__le, fact_gr0__conv__Suc, arity_Polynomial__Opoly__Groups_Ominus, arity_RealDef__Oreal__Groups_Omonoid__add, fact_neg__0__less__iff__less, fact_zdvd__mult__cancel, fact_abs__diff__triangle__ineq, fact_leI, fact_dvd_Oord__eq__less__trans, fact_mult__le__mono2, fact_Suc__diff__diff, fact_le__neq__implies__less, arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add, arity_Polynomial__Opoly__Rings_Ocomm__ring, fact_zle__linear, fact_pow__divides__pow__nat, fact_zero__le__one, fact_poly__add, arity_RealDef__Oreal__Rings_Ocomm__ring__1, fact_nat__add__left__cancel__less, fact_le__minus__iff, fact_pos__le__divide__eq, fact_mult_Oadd__right, fact_mult_Ominus__right, fact_le__add__iff2, fact_mult__eq__self__implies__10, fact_minus__pCons, fact_mult__left__le__imp__le, fact_divide__pos__neg, fact_minus__add__cancel, fact_add__pos__nonneg, arity_Int__Oint__Orderings_Oord, arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add, fact_order__1, fact_int__0__less__1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_linorder__antisym__conv3, fact_add__strict__increasing2, fact_order__less__imp__not__eq, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J, fact_linorder__neqE__linordered__idom, fact_mult__left_Ononneg__bounded, fact_mult__imp__le__div__pos, fact_abs__of__neg, arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero, arity_Polynomial__Opoly__Rings_Olinordered__semidom, fact_abs__triangle__ineq2, fact_divide__right__mono, fact_add__le__imp__le__left, fact_add__nonneg__eq__0__iff, fact_real__mult__commute, fact_dvd__power__le, arity_Complex__Ocomplex__Rings_Ocomm__semiring__1, arity_Polynomial__Opoly__Orderings_Olinorder, fact_synthetic__div__correct_H, fact_neg__less__0__iff__less, fact_zadd__left__mono, fact_sum__squares__le__zero__iff, fact_divide__1, fact_mult__strict__left__mono, arity_Int__Oint__Rings_Olinordered__semiring__1__strict, fact_mult__right_Ozero, fact_mult__le__cancel__left__neg, fact_sum__squares__ge__zero, fact_add__increasing2, fact_pow__divides__eq__nat, arity_RealDef__Oreal__Fields_Ofield__inverse__zero, fact_dvd__reduce, fact_zero__le__mult__iff, arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero, fact_linorder__antisym__conv1, arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add, arity_RealDef__Oreal__Groups_Oabs__if, fact_divide__le__eq, fact_synthetic__div__0, arity_Int__Oint__Groups_Ozero, fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J, fact_mult_Ozero__left, fact_power__commutes, fact_poly__0, fact_add__mono, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, arity_Int__Oint__Rings_Olinordered__ring, fact_add__0__iff, fact_le__funD, fact_add__right__mono, arity_Polynomial__Opoly__Orderings_Oord, fact_abs__add__one__gt__zero, arity_Int__Oint__Groups_Ocancel__comm__monoid__add, fact_one__less__power, fact_power__strict__increasing, fact_power__one__over, fact_one__le__power, fact_even__less__0__iff, fact_self__quotient__aux1, fact_sgn__neg, arity_Int__Oint__Groups_Ocomm__monoid__add, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, arity_RealDef__Oreal__Groups_Omonoid__mult, fact_add__0__left, fact_gr0I, fact_sgn__minus, fact_le__fun__def, fact_minus__add, fact_divide__eq__imp, arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add, fact_norm__triangle__ineq3, fact_power__minus, fact_nat__dvd__not__less, fact_real__mult__assoc, arity_Nat__Onat__Rings_Osemiring__0, fact_rabs__ratiotest__lemma, arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict, fact_mult__eq__1__iff, arity_Nat__Onat__Rings_Oordered__comm__semiring, fact_power__eq__0__iff, fact_divide__add__eq__iff, fact_nat__mult__1__right, fact_divide__strict__left__mono__neg, arity_Complex__Ocomplex__Rings_Osemiring__0, fact_order__less__imp__not__less, fact_less__eq__nat_Osimps_I1_J, fact_compl__mono, fact_zero__le__power__abs, fact_ord__less__eq__trans, arity_Int__Oint__Groups_Oordered__ab__group__add, fact_mult__right_Odiff, fact_le__iff__add, fact_one__reorient, fact_minus__less__iff, arity_fun__Groups_Ouminus, fact_xt1_I9_J, fact_less__add__eq__less, fact_minus__mult__commute, fact_linorder__less__linear, arity_Polynomial__Opoly__Groups_Omonoid__add, fact_mult__left_Odiff, fact_eq__iff__diff__eq__0, fact_add__lessD1, fact_add__le__mono1, arity_Int__Oint__Rings_Oidom, arity_Complex__Ocomplex__Fields_Ofield, arity_Polynomial__Opoly__Int_Oring__char__0, fact_lessI, fact_zero__le__square, fact_dvd_Oantisym__conv, fact_zero__reorient, arity_RealDef__Oreal__Rings_Olinordered__idom, fact_termination__basic__simps_I4_J, fact_dvd__0__right, fact_synthetic__div__pCons, fact_zadd__zless__mono, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_mult__less__mono1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J, fact_poly__mult, fact_split__mult__pos__le, fact_minus__le__iff, fact_dvd__mult__cancel2, fact_nat_Oinject, fact_mult__left__le__one__le, arity_Polynomial__Opoly__Power_Opower, fact_mult__left_Obounded, arity_Int__Oint__Rings_Oring__no__zero__divisors, fact_not__add__less2, fact_dvd__trans, fact_less__or__eq__imp__le, fact_rcis__mult, fact_Suc__less__SucD, fact_dvd_Oeq__refl, fact_power__strict__mono, arity_Polynomial__Opoly__Groups_Osgn__if, fact_sgn__zero, arity_Int__Oint__Rings_Oordered__cancel__semiring, fact_real__add__minus__iff, fact_incr__lemma, arity_RealDef__Oreal__Groups_Ocancel__semigroup__add, fact_minus__divide__divide, fact_zadd__strict__right__mono, arity_Complex__Ocomplex__RealVector_Oreal__field, fact_complex__mod__triangle__sub, fact_q__neg__lemma, fact_minus__apply, fact_zdvd__reduce, fact_add__0__right, fact_mult__pos__neg, fact_power__gt1__lemma, fact_pos__less__divide__eq, fact_dvd_Oord__eq__le__trans, fact_nat__eq__add__iff2, fact_zdvd1__eq, arity_Polynomial__Opoly__Rings_Oring__1, fact_Suc__leI, fact_add__neg__nonpos, fact_unique__quotient__lemma__neg, arity_RealDef__Oreal__Rings_Ozero__neq__one, fact_sgn__mult, fact_mult__pos__neg2, fact_power__Suc2, fact_convex__bound__lt, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, fact_zadd__assoc, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_real__0__le__divide__iff, arity_Nat__Onat__Orderings_Opreorder, fact_dvd__abs__iff, arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs, fact_Suc__n__not__le__n, arity_RealDef__Oreal__RealVector_Oreal__normed__algebra, fact_not__less__less__Suc__eq, fact_diff__def, fact_dvd__mult2, arity_RealDef__Oreal__RealVector_Oreal__field, fact_nat__mult__1, fact_mult__right__mono__neg, fact_diff__pCons, fact_abs__minus__add__cancel, fact_zpower__zadd__distrib, fact_divide__strict__right__mono__neg, fact_le__add2, fact_minus__divide__right, fact_abs__eq__0, fact_dvd_Oless__imp__neq, fact_diff__self, fact_minus__nat_Odiff__0, fact_pos__zmult__eq__1__iff, arity_Int__Oint__Groups_Ocancel__semigroup__add, arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_pos__divide__le__eq, fact_order__antisym, fact_xt1_I10_J, fact_less__irrefl__nat, fact_mult_Oprod__diff__prod, fact_zle__diff1__eq, fact_Suc__lessD, fact_order__less__imp__not__eq2, fact_sgn__less, arity_Int__Oint__Power_Opower, fact_divide_Ononneg__bounded, fact_diff__0, fact_add__left__imp__eq, arity_Int__Oint__Rings_Osemiring__0, fact_trans__less__add2, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_zpower__zpower, fact_add__leD2, fact_mult__mono_H, fact_real__add__mult__distrib, arity_Nat__Onat__Rings_Ocomm__semiring__1, fact_abs__ge__minus__self, fact_order__refl, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, fact_dvd__pos__nat, arity_Nat__Onat__Power_Opower, fact_ab__semigroup__mult__class_Omult__ac_I1_J, fact_not__less0, arity_Int__Oint__Groups_Ouminus, fact_less__Suc__eq__le, arity_Nat__Onat__Groups_Ocancel__comm__monoid__add, fact_nat__diff__split, fact_norm__one, fact_zadd__0, fact_add__frac__eq, fact_divide__left__mono__neg, fact_real__zero__not__eq__one, fact_xt1_I5_J, fact_abs__of__nonneg, arity_RealDef__Oreal__Rings_Omult__zero, arity_Complex__Ocomplex__Groups_Oab__semigroup__add, arity_Complex__Ocomplex__Fields_Ofield__inverse__zero, fact_divide__left__mono, fact_dvd_Oless__asym, fact_divide_Ominus, arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add, fact_real__mult__right__cancel, fact_not__less__eq, fact_nat_Osimps_I2_J, fact_mult__divide__mult__cancel__left, fact_zero__le__double__add__iff__zero__le__single__add, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, arity_Int__Oint__Groups_Oab__semigroup__mult, fact_mult__left__less__imp__less, fact_pCons__0__0, fact_sgn__poly__def, fact_neg__less__iff__less, arity_Complex__Ocomplex__Rings_Osemiring, fact_less__zeroE, fact_termination__basic__simps_I2_J, fact_minus__zero, arity_Complex__Ocomplex__Groups_Ogroup__add, fact_not__one__less__zero, fact_reduce__poly__simple, fact_abs__diff__less__iff, fact_zero__less__norm__iff, fact_one__le__mult__iff, arity_RealDef__Oreal__Rings_Olinordered__semiring, arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, fact_complex__mod__minus__le__complex__mod, fact_norm__le__zero__iff, fact_mult__imp__div__pos__less, fact_mult__le__cancel1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J, fact_nat__neq__iff, fact_nat__1__eq__mult__iff, fact_diff__mult__distrib2, fact_dvd_Ole__less, arity_Nat__Onat__Groups_Ominus, fact_abs__le__D1, fact_eq__add__iff1, arity_Int__Oint__Groups_Ocancel__ab__semigroup__add, fact_add__left__cancel, arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add, fact_add__pCons, fact_neg__less__nonneg, fact_zmult__assoc, fact_nat__add__left__cancel__le, fact_less__imp__neq, arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict, fact_xt1_I8_J, fact_power__less__imp__less__base, fact_less__eq__real__def, fact_norm__triangle__ineq4, fact_add__mult__distrib2, arity_Polynomial__Opoly__Orderings_Oorder, fact_less__not__refl3, arity_Complex__Ocomplex__Rings_Ozero__neq__one, fact_sgn__sgn, arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult, fact_abs__real__def, fact_norm__eq__zero, fact_add__right__cancel, fact_mult__strict__mono_H, fact_nat__one__le__power, fact_one__less__mult, fact_poly__pCons, fact_nat__diff__split__asm, fact_zle__antisym, fact_nat__mult__dvd__cancel__disj, fact_dvd_Oorder__refl, fact_abs__less__iff, fact_mult__nonneg__nonneg, fact_add__less__cancel__left, fact_zero__less__mult__pos2, fact_dvd__mult, fact_frac__le, arity_Int__Oint__Rings_Oordered__ring__abs, fact_frac__eq__eq, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_abs__not__less__zero, fact_abs__sgn, arity_Complex__Ocomplex__Rings_Ocomm__semiring, arity_Int__Oint__Rings_Oordered__semiring, fact_dvd_Oord__le__eq__trans, arity_Complex__Ocomplex__RealVector_Oreal__normed__field, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J, fact_xt1_I3_J, fact_double__zero__sym, fact_divide__pos__pos, fact_neg__0__equal__iff__equal, arity_Polynomial__Opoly__Rings_Oordered__comm__semiring, fact_divide__neg__neg, fact_complex__mod__rcis, fact_mult__left__mono, fact_abs__zmult__eq__1, fact_mult__left_Oadd, fact_real__minus__mult__self__le, fact_mult__imp__less__div__pos, fact_add__divide__eq__iff, fact_double__compl, fact_zminus__zadd__distrib, fact_norm__power__ineq, fact_norm__ge__zero, fact_zmult__1, fact_mult__left_Ozero, fact_one__neq__zero, fact_left__minus, fact_norm__divide, fact_divide__neg__pos, arity_RealDef__Oreal__Fields_Olinordered__field, fact_right__minus, fact_power__decreasing, fact_le__add__iff1, fact_mult__dvd__mono, fact_poly__1, fact_less__Suc__eq__0__disj, fact_norm__minus__commute, fact_divide__nonneg__pos, fact_le__Suc__eq, fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J, arity_RealDef__Oreal__Orderings_Opreorder, fact_less__add__iff2, arity_Polynomial__Opoly__Rings_Oring, fact_add__strict__mono, fact_diff__divide__eq__iff, fact_norm__diff__ineq, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, fact_frac__less, arity_Polynomial__Opoly__Groups_Oab__group__add, fact_le__imp__power__dvd, fact_nat__mult__le__cancel1, arity_RealDef__Oreal__Orderings_Oorder, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, arity_Int__Oint__Rings_Olinordered__semidom, fact_equation__minus__iff, fact_le__funE, fact_nat__diff__add__eq2, arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add, arity_RealDef__Oreal__Orderings_Olinorder, fact_mult__neg__pos, arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult, fact_diff__int__def__symmetric, arity_Nat__Onat__Groups_Ocomm__monoid__add, fact_Suc__mult__less__cancel1, fact_mult__right_Obounded, arity_Polynomial__Opoly__Groups_Oab__semigroup__add, fact_less__antisym, fact_not__real__square__gt__zero, fact_add__num__frac, fact_order__neq__le__trans, fact_not__one__le__zero, arity_Polynomial__Opoly__Rings_Olinordered__idom, fact_Suc__le__eq, arity_Int__Oint__Groups_Ogroup__add, fact_add__diff__cancel, arity_fun__Lattices_Oboolean__algebra, fact_mult__cancel2, arity_Polynomial__Opoly__Groups_Ouminus, fact_poly__minus, arity_RealDef__Oreal__Rings_Ocomm__semiring, arity_Polynomial__Opoly__Rings_Oordered__semiring, arity_RealDef__Oreal__RealVector_Oreal__normed__vector, arity_Int__Oint__Rings_Ocomm__ring, arity_Nat__Onat__Rings_Ocomm__semiring, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_mult__less__le__imp__less, fact_nat__mult__assoc, arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, arity_Polynomial__Opoly__Rings_Oordered__ring__abs, fact_diff__int__def, arity_Nat__Onat__Groups_Omonoid__add, fact_power__add, fact_sgn__0__0, fact_diff__add__cancel, arity_Complex__Ocomplex__Rings_Oring, fact_zmult__commute, fact_divide__nonpos__pos, arity_Nat__Onat__Orderings_Oord, fact_equal__neg__zero, fact_power__Suc__less__one, arity_fun__Orderings_Opreorder, fact_not__sum__squares__lt__zero, fact_order__2, arity_Polynomial__Opoly__Groups_Oordered__ab__group__add, fact_real__sgn__pos, fact_real__mult__1, fact_less__eq__Suc__le, fact_divide__eq__eq, fact_mult__nonneg__nonpos2, fact_less__add__Suc2, arity_Polynomial__Opoly__Groups_Omonoid__mult, fact_dvd__power__same, fact_less__imp__diff__less, arity_RealDef__Oreal__Rings_Oordered__cancel__semiring, fact_uminus__apply, fact_mult_Ominus__left, arity_RealDef__Oreal__Rings_Odivision__ring, fact_nat__mult__eq__cancel1, arity_Int__Oint__Rings_Oring__1__no__zero__divisors, fact_abs__ge__zero, fact_pCons__eq__iff, fact_dvd_Oless__not__sym, arity_Int__Oint__Groups_Oab__group__add, fact_ord__le__eq__trans, fact_abs__idempotent, arity_RealDef__Oreal__Rings_Oring, fact_comm__mult__strict__left__mono, fact_linorder__neq__iff, fact_minus__minus, fact_dvd__mult__cancel1, fact_th0, fact_minus__add__distrib, arity_RealDef__Oreal__Rings_Osemiring, fact_power__inject__exp, fact_dvd__if__abs__eq, arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add, arity_Complex__Ocomplex__Groups_Oone, fact_add__is__1, arity_Nat__Onat__Groups_Oordered__ab__semigroup__add, fact_less__minus__iff, fact_dvd__refl, fact_zero__less__power__nat__eq, fact_power__Suc__less, fact_rcis__zero__mod, fact_linorder__neqE__nat, fact_mult__less__mono2, fact_not__less__iff__gr__or__eq, fact_diffs0__imp__equal, arity_Complex__Ocomplex__Groups_Ocomm__monoid__add, fact_dvd__diff, fact_nonzero__divide__eq__eq, arity_RealDef__Oreal__Rings_Ocomm__ring, fact_divide__less__0__iff, fact_norm__not__less__zero, arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add, arity_Nat__Onat__Groups_Ozero, fact_pCons__eq__0__iff, fact_real__mult__le__cancel__iff1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_abs__of__nonpos, fact_nat__mult__less__cancel1, fact_zadd__left__commute, fact_order__less__le, arity_Complex__Ocomplex__Rings_Oring__1, fact_dvd_Oneq__le__trans, arity_Nat__Onat__Groups_Ocomm__monoid__mult, fact_mult_Ozero__right, fact_abs__triangle__ineq3, fact_power__divide, fact_sgn__times, fact_zless__le, fact_mult__right_Oadd, arity_RealDef__Oreal__Int_Oring__char__0, fact_unique__quotient__lemma, fact_frac__less2, fact_dvd__add, fact_one__poly__def, fact_order__root, arity_Complex__Ocomplex__Groups_Ouminus, arity_Complex__Ocomplex__Rings_Odivision__ring, fact_power__le__imp__le__exp, fact_power__one__right, fact_add__nonneg__pos, fact_mult__less__cancel__right__disj, arity_RealDef__Oreal__Groups_Oab__semigroup__add, fact_add__less__cancel__right, fact_Suc__mult__cancel1, fact_mult__strict__right__mono, fact_add__nonpos__nonpos, arity_Int__Oint__Groups_Omonoid__mult, arity_RealDef__Oreal__Rings_Olinordered__semiring__strict, fact_mult__poly__add__left, fact_Suc__le__lessD, arity_RealDef__Oreal__Rings_Oordered__ring, fact_add__increasing, fact_not__add__less1, fact_xt1_I12_J, fact_norm__zero, arity_Int__Oint__Int_Oring__char__0, fact_abs__power__minus, fact_power__increasing__iff, arity_RealDef__Oreal__Groups_Oordered__ab__group__add, fact_zless__imp__add1__zle, fact_mult__le__cancel__left__pos, fact_mult_Oadd__left, fact_zero__less__double__add__iff__zero__less__single__add, fact_times__divide__eq__right, fact_zero__le__power, fact_Suc__neq__Zero, arity_Polynomial__Opoly__Rings_Omult__zero, fact_le__divide__eq, arity_RealDef__Oreal__RealVector_Oreal__normed__field, fact_real__mult__less__iff1, fact_nat__le__add__iff2, arity_RealDef__Oreal__Rings_Olinordered__ring__strict, fact_Suc__inject, arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors, arity_fun__Orderings_Oord, fact_norm__mult, fact_minus__dvd__iff, fact_divide__right__mono__neg, fact_ext, fact_order__less__not__sym, fact_diff__poly__code_I2_J, fact_crossproduct__noteq, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, arity_Nat__Onat__Rings_Olinordered__semiring, fact_zle__trans, fact_le__imp__neg__le, arity_Polynomial__Opoly__Rings_Ocomm__semiring__1, fact_calculation, fact_less__add__iff1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, arity_Complex__Ocomplex__Rings_Ocomm__ring__1, arity_RealDef__Oreal__Groups_Osgn__if, fact_nat__power__less__imp__less, fact_linorder__le__less__linear, fact_abs__one, fact_nat__lt__two__imp__zero__or__one, fact_power__strict__increasing__iff, fact_divide__le__0__iff, fact_eq__divide__imp, fact_abs__minus__le__zero, fact_diff__less__Suc, fact_add__eq__self__zero, fact_real__abs__def, fact_abs__leI, arity_Int__Oint__Rings_Omult__zero, fact_real__le__antisym, arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs, fact_dvd_Oless__imp__le, fact_mult__le__mono, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_zminus__0, fact_mult__le__0__iff, fact_le__iff__diff__le__0, fact_divide__self__if, fact_mult__is__0, fact_nat__add__left__cancel, fact_uminus__dvd__conv_I2_J, fact_divide_Ozero, fact_mult__le__cancel2, fact_norm__triangle__ineq, fact_dvd__imp__le, fact_less__le__not__le, fact_nat__mult__dvd__cancel1, arity_Nat__Onat__Orderings_Olinorder, fact_n__not__Suc__n, fact_nat__le__linear, fact_linorder__le__cases, fact_mult__zero__right, arity_Int__Oint__Rings_Oring, fact_divide__zero, fact_order__less__le__trans, fact_power__less__imp__less__exp, arity_Nat__Onat__Rings_Omult__zero, arity_Int__Oint__Groups_Oordered__comm__monoid__add, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_add__Suc, fact_sum__squares__gt__zero__iff, fact_diff__divide__distrib, arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1, arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add, fact_abs__le__interval__iff, arity_Int__Oint__Groups_Oordered__ab__group__add__abs, arity_RealDef__Oreal__Groups_Ocomm__monoid__add, fact_abs__mult, arity_RealDef__Oreal__Rings_Ocomm__semiring__1, fact_dvd__1__left, fact_diff__eq__diff__less, arity_Polynomial__Opoly__Rings_Ozero__neq__one, fact_add__mult__distrib, fact_less__minus__self__iff, fact_power__dvd__imp__le, fact_not__leE, arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict, fact_add__strict__left__mono, fact_leD, fact_abs__divide, fact_nat__le__add__iff1, fact_mult__less__cancel1, fact_order__less__asym, fact_dvd__triv__left, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_nat__0__less__mult__iff, fact_abs__dvd__iff, arity_RealDef__Oreal__Rings_Ono__zero__divisors, fact_add__gr__0, arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict, fact_zdiff__zmult__distrib2, fact_mult__divide__mult__cancel__right, fact_zero__less__zpower__abs__iff, fact_minus__unique, fact_poly__power, fact_diff__less__mono2, fact_dvd_Oless__imp__not__eq, fact_divide__zero__left, arity_Nat__Onat__Rings_Oordered__cancel__semiring, fact_diff__mult__distrib, fact_int__0__neq__1, fact_Suc__eq__plus1__left, arity_Complex__Ocomplex__Rings_Ono__zero__divisors, arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add, fact_mult__strict__mono, fact_Suc__leD, fact_power__0, fact_power__0__left, fact_add_Ocomm__neutral, fact_real__divide__square__eq, fact_power__Suc, fact_add__less__imp__less__right, fact_le__Suc__ex__iff, arity_Nat__Onat__Rings_Odvd, arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le, arity_RealDef__Oreal__Rings_Oring__no__zero__divisors, fact_zdiff__zmult__distrib, fact_Zero__not__Suc, fact_dvd__mult__right, fact_gcd__lcm__complete__lattice__nat_Otop__greatest, arity_RealDef__Oreal__Rings_Olinordered__semiring__1, fact_field__le__mult__one__interval, fact_norm__sgn, arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le, fact_zero__less__one, fact_power__le__dvd, fact_neg__equal__zero, fact_mult__right_Ononneg__bounded, fact_power__mult, 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_pCons_Ohyps, fact_norm__ratiotest__lemma, fact_pos__divide__less__eq, arity_Int__Oint__Groups_Osgn__if, fact_realpow__pos__nth, fact_mult__Suc, fact_xt1_I6_J, fact_le__minus__self__iff, fact_diff__frac__eq, arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors, fact_abs__mult__less, fact_sgn__1__neg, fact_h, arity_Nat__Onat__Rings_Oordered__semiring, fact_linorder__linear, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_mult__zero__left, fact_abs__sum__triangle__ineq, fact_less__trans__Suc, arity_Int__Oint__Groups_Oordered__ab__semigroup__add, fact_left__add__mult__distrib, fact_add__scale__eq__noteq, 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_le__add1, fact_mult__cancel1, fact_trans__le__add2, fact_zdvd__mono, fact_abs__le__zero__iff, fact_mult__right__le__one__le, fact_mult__right_Opos__bounded, arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra, arity_RealDef__Oreal__Groups_Oone, fact_linorder__not__less, fact_Suc__mult__le__cancel1, fact_mult__diff__mult, arity_RealDef__Oreal__Groups_Ouminus, fact_add__less__imp__less__left, fact_divide_Oadd, fact_ab__diff__minus, fact_le__imp__less__Suc, fact_sgn__zero__iff, fact_mult__right__mono, conj_1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J, arity_Int__Oint__Rings_Olinordered__semiring, fact_nonzero__minus__divide__divide, fact_abs__zero, fact_less__add__Suc1, fact_ab__left__minus, fact_sgn0, fact_add__neg__neg, arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict, fact_less__fun__def, fact_One__nat__def, fact_minus__diff__eq, fact_comm__semiring__class_Odistrib, fact_square__eq__iff, fact_zero__less__abs__iff, fact_abs__add__abs, fact_nonzero__minus__divide__right, fact_add__is__0, fact_nat__diff__add__eq1, fact_termination__basic__simps_I3_J, fact_divide__diff__eq__iff, arity_Int__Oint__Rings_Oordered__ring, fact_abs__le__iff, fact_times__divide__times__eq, fact_sgn__pos, fact_dvd__imp__le__int, fact_abs__triangle__ineq4, fact_xt1_I2_J, fact__0960_A_060_Acmod_Ac_096, fact_abs__minus__cancel, arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add, fact_add__0, arity_Polynomial__Opoly__Rings_Oordered__ring, fact_diff__minus__eq__add, fact_power__mono, fact_mult__le__mono1, fact_diff__self__eq__0, fact_add__eq__0__iff, fact_minus__poly__code_I2_J, fact_neg__equal__iff__equal, fact_compl__eq__compl__iff, arity_Polynomial__Opoly__Rings_Olinordered__semiring__1, arity_RealDef__Oreal__Groups_Ocomm__monoid__mult, arity_Polynomial__Opoly__Rings_Osemiring, fact_uminus__dvd__conv_I1_J, fact_Zero__neq__Suc, fact_add__pos__pos, arity_Nat__Onat__Groups_Oab__semigroup__mult, fact_add__nonneg__nonneg, fact_nat__eq__add__iff1, arity_RealDef__Oreal__Power_Opower, fact_Suc__eq__plus1, arity_RealDef__Oreal__Groups_Oab__group__add, fact_dvd__mult__cancel, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J, arity_Int__Oint__Rings_Olinordered__idom, arity_Int__Oint__Rings_Ocomm__semiring__1, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_self__quotient__aux2, arity_RealDef__Oreal__Rings_Olinordered__semidom, fact_sgn__greater, fact_realpow__two__disj, arity_RealDef__Oreal__Rings_Odvd, arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1, fact_mult__nonpos__nonneg, fact_order__eq__iff, arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict, fact_dvd__minus__iff, arity_Nat__Onat__Groups_Oab__semigroup__add, fact_power__mult__distrib, arity_Int__Oint__Rings_Oordered__comm__semiring, fact_zdvd__mult__cancel1, fact_mult__pos__pos, fact_sgn__real__def, fact_zmult__zless__mono2, fact_comm__mult__left__mono, fact_Suc__pred, arity_Int__Oint__Groups_Oab__semigroup__add, fact_nat__dvd__1__iff__1, fact_divide__less__eq, arity_Int__Oint__Groups_Oone, fact_decr__lemma, 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_power__Suc__0, fact_nat__mult__eq__1__iff, fact_not__less__eq__eq, fact_n__less__n__mult__m, fact_mult__right_Ominus, fact_less__not__refl, fact_double__add__le__zero__iff__single__add__le__zero, fact_mult__less__cancel__left__neg, fact_zabs__def, fact_ord__eq__less__trans, fact_sgn__if, fact_less__1__mult, fact_compl__le__compl__iff, fact_cs0, fact_le0, fact_power__one, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J, fact_poly__diff, arity_Int__Oint__Orderings_Oorder, fact_minus__mult__minus, fact_ex__least__nat__less, fact_crossproduct__eq, fact_square__eq__1__iff, fact_dvd_Oantisym, fact_neg__less__divide__eq, fact_le__trans, arity_Int__Oint__Groups_Oabs__if, fact_inf__period_I3_J, arity_fun__Groups_Ominus, fact_gr__implies__not0, fact_mult__strict__right__mono__neg, fact_dvd_Ole__neq__trans, fact_abs__triangle__ineq, arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add, fact_less__add__one, arity_Nat__Onat__Rings_Olinordered__semiring__strict, fact_mult__less__imp__less__right, fact_zero__neq__one, fact_norm__mult__ineq, fact_diff__eq__diff__less__eq, fact_divide__strict__left__mono, fact_add__leE, fact_mult_Odiff__left, fact_add__less__le__mono, fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J, arity_Polynomial__Opoly__Orderings_Opreorder, fact_dvd__antisym, fact_zsgn__def, fact_real__two__squares__add__zero__iff, fact_power__less__power__Suc, arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero, arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors, fact_cs0_H, fact_int__one__le__iff__zero__less, fact_power__eq__imp__eq__base, fact_less__Suc__eq, fact_nat__add__commute, arity_Int__Oint__Rings_Ono__zero__divisors, fact_add__poly__code_I1_J, 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, arity_Int__Oint__Rings_Odvd, fact_neg__0__le__iff__le, fact_zmult__zminus, fact_zdiv__mono2__lemma, arity_Polynomial__Opoly__Groups_Ogroup__add, fact_sgn__one, arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add, arity_RealDef__Oreal__Rings_Oring__1, fact_add1__zle__eq, fact_pCons_Oprems, fact_plus__nat_Oadd__0, arity_Complex__Ocomplex__Rings_Ocomm__ring, fact_less__divide__eq, fact_mult_Ocomm__neutral, fact_real__add__left__mono, fact_add__strict__increasing, arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_add__nonpos__neg, fact_c0, fact_pow__divides__eq__int, arity_RealDef__Oreal__Rings_Oordered__semiring, fact_le__SucE, fact_dvd_Oless__le__trans, fact_nat__mult__commute, fact_nat__power__eq__Suc__0__iff, fact_divide_Odiff, fact_mult_Obounded, fact_zero__less__Suc, arity_Polynomial__Opoly__Rings_Olinordered__semiring, fact_eq__imp__le, arity_Complex__Ocomplex__Int_Oring__char__0, arity_Int__Oint__Rings_Olinordered__semiring__1, fact_neg__divide__less__eq, fact_minus__le__self__iff, fact_diff__eq__diff__eq, fact_order__le__imp__less__or__eq, fact_real__mult__order, fact_dvd_Oless__le, fact_le__less__Suc__eq, fact_real__norm__def, fact_nonzero__abs__divide, fact_Suc__n__not__n, fact_zdvd__period, fact_le__antisym, fact_zadd__0__right, fact_add__divide__distrib, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, arity_Int__Oint__Rings_Olinordered__comm__semiring__strict, fact_abs__mult__pos, fact_lemma__MVT, arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring, arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le, arity_Polynomial__Opoly__Rings_Ocomm__ring__1, fact_order__antisym__conv, fact_neq0__conv, fact_add__frac__num, fact_minus__equation__iff, fact_mult__left_Opos__bounded, fact_mult__left__mono__neg, 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_trans__le__add1, fact_zero__less__mult__pos, arity_Polynomial__Opoly__Rings_Odvd, arity_Polynomial__Opoly__Rings_Ocomm__semiring, arity_Int__Oint__Groups_Ominus, 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_mult__Suc__right, fact_zdvd__zdiffD, fact_realpow__pos__nth__unique, fact_zdvd__imp__le, fact_dvd__0__left, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J, fact_zle__add1__eq__le, fact_dvd__1__iff__1, fact_mult__1__right, fact_zero__less__two, fact_gcd__lcm__complete__lattice__nat_Obot__least, arity_Polynomial__Opoly__Groups_Ozero, fact_add__le__imp__le__right, fact_order__less__irrefl, conj_0, fact_dvd__iff__poly__eq__0, fact_less__Suc0, fact_order__le__less, fact_dvd_Ole__less__trans, fact_convex__bound__le, fact_divide__nonneg__neg, arity_Nat__Onat__Rings_Osemiring, fact_mult__less__imp__less__left, arity_Polynomial__Opoly__Groups_Oabs__if, fact_less__iff__Suc__add, fact_order__less__imp__le, fact_termination__basic__simps_I1_J, fact_real__0__le__add__iff, fact_order__less__trans, fact_mult__less__cancel2, fact_divide_Opos__bounded, fact_abs__mult__self, fact_real__mult__less__mono2, fact_sum__squares__eq__zero__iff, fact_abs__norm__cancel, fact_nat__zero__less__power__iff, fact_zabs__less__one__iff, arity_Int__Oint__Rings_Ocomm__ring__1, fact_add__le__mono, arity_Int__Oint__Groups_Olinordered__ab__group__add, fact_nat__mult__eq__cancel__disj, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, arity_Nat__Onat__Groups_Oone, fact_add__imp__eq, arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, fact_power__gt1, fact_le__square, fact_zadd__zmult__distrib, fact_zadd__zminus__inverse2, fact_ab__semigroup__add__class_Oadd__ac_I1_J, fact_diff__Suc__Suc, fact_dvd__mult__left, arity_RealDef__Oreal__Groups_Oab__semigroup__mult, arity_Int__Oint__Rings_Ozero__neq__one, arity_RealDef__Oreal__Fields_Ofield, fact_dvd_Ole__imp__less__or__eq, fact_power__0__Suc, fact_minus__poly__code_I1_J, fact_nat__less__le, arity_Complex__Ocomplex__RealVector_Oreal__normed__vector, fact_no__zero__divisors, fact_sgn__1__pos, fact_less__iff__diff__less__0, fact_less__SucE, fact_gt__half__sum, fact_le__cube, fact_zless__add1__eq, fact_linorder__cases, fact_xt1_I11_J, fact_add__less__mono1, fact_add__le__cancel__left, fact_eq__divide__eq, fact_divisors__zero, arity_Polynomial__Opoly__Rings_Olinordered__ring, fact_nonzero__norm__divide, 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_real__le__linear, arity_Complex__Ocomplex__Power_Opower, fact_ord__eq__le__trans, fact_nonzero__eq__divide__eq, fact_realpow__Suc__le__self, 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_odd__less__0, fact_dvd_Oless__imp__not__eq2, fact_norm__triangle__ineq2, arity_Int__Oint__Groups_Omonoid__add, fact_add__Suc__shift, fact_dvd__mult__cancel__right, fact_xt1_I7_J, fact_power__le__imp__le__base, arity_Int__Oint__Orderings_Opreorder, fact_less__half__sum, arity_Int__Oint__Rings_Ocomm__semiring__0, fact_less__SucI, fact_Suc__not__Zero, arity_Complex__Ocomplex__Groups_Ozero, fact_order__trans, fact_dvd__power, arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add, fact_not__square__less__zero, fact_Suc__lessI, fact_add__Suc__right, arity_Complex__Ocomplex__Groups_Ominus, fact_mult__1, fact_less__bin__lemma, arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add, arity_Int__Oint__Rings_Olinordered__ring__strict, fact_mult_Odiff__right, fact_zdiv__mono2__neg__lemma, fact_real__sgn__def, arity_Complex__Ocomplex__Rings_Ocomm__semiring__0, fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J, fact_divide__self, fact_nonzero__power__divide
% 243.31/69.69  % No. of inferences in proof: 3434
% 243.31/69.69  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 69108 ms resp. 68112 ms w/o parsing
% 249.29/70.63  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 249.29/70.66  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------