ConnectPP---0.7.2.THM-Prf.s

%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : SWW232+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n011.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 : Thu Sep 24 09:04:56 AM UTC 2026

% Result   : Theorem 150.25s 150.52s
% Output   : Proof 150.36s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_ext,axiom,
    ! [V_g_2,V_f_2] :
      ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
     => V_f_2 = V_g_2 ),
    file('theBenchmark.p',fact_ext) ).

fof(fact_H,axiom,
    v_cs____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    file('theBenchmark.p',fact_H) ).

fof(fact_pCons_Oprems,axiom,
    c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    file('theBenchmark.p',fact_pCons_Oprems) ).

fof(fact_pCons_Ohyps,axiom,
    ! [V_a,V_d] :
      ( v_cs____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
     => ? [B_r] :
        ! [B_z] :
          ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_r,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z))
         => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_d,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,V_a,v_cs____)),B_z))) ) ),
    file('theBenchmark.p',fact_pCons_Ohyps) ).

fof(fact_assms,axiom,
    v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    file('theBenchmark.p',fact_assms) ).

fof(fact_norm__triangle__ineq,axiom,
    ! [V_y,V_x,T_a] :
      ( class_RealVector_Oreal__normed__vector(T_a)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ),
    file('theBenchmark.p',fact_norm__triangle__ineq) ).

fof(fact_order__refl,axiom,
    ! [V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x) ),
    file('theBenchmark.p',fact_order__refl) ).

fof(fact_poly__add,axiom,
    ! [V_x,V_q,V_p,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ),
    file('theBenchmark.p',fact_poly__add) ).

fof(fact_add__pCons,axiom,
    ! [V_q,V_b,V_p,V_a,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q)) = c_Polynomial_OpCons(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) ),
    file('theBenchmark.p',fact_add__pCons) ).

fof(fact_real__add__left__mono,axiom,
    ! [V_z,V_y,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y)) ),
    file('theBenchmark.p',fact_real__add__left__mono) ).

fof(fact_add__le__cancel__right,axiom,
    ! [V_b_2,V_ca_2,V_ab_2,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))
      <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2) ) ),
    file('theBenchmark.p',fact_add__le__cancel__right) ).

fof(fact_add__le__cancel__left,axiom,
    ! [V_b_2,V_ab_2,V_ca_2,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))
      <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2) ) ),
    file('theBenchmark.p',fact_add__le__cancel__left) ).

fof(fact_add__right__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
       => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ),
    file('theBenchmark.p',fact_add__right__mono) ).

fof(fact_add__left__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
       => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)) ) ),
    file('theBenchmark.p',fact_add__left__mono) ).

fof(fact_add__mono,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
         => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ),
    file('theBenchmark.p',fact_add__mono) ).

fof(fact_norm__zero,axiom,
    ! [T_a] :
      ( class_RealVector_Oreal__normed__vector(T_a)
     => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    file('theBenchmark.p',fact_norm__zero) ).

fof(fact_pCons__0__0,axiom,
    ! [T_a] :
      ( class_Groups_Ozero(T_a)
     => c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
    file('theBenchmark.p',fact_pCons__0__0) ).

fof(fact_poly__0,axiom,
    ! [V_x,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_poly__0) ).

fof(fact_add__poly__code_I1_J,axiom,
    ! [V_q,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = V_q ),
    file('theBenchmark.p',fact_add__poly__code_I1_J) ).

fof(fact_zero__reorient,axiom,
    ! [V_x_2,T_a] :
      ( class_Groups_Ozero(T_a)
     => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
      <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_zero__reorient) ).

fof(fact_add__poly__code_I2_J,axiom,
    ! [V_p,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ),
    file('theBenchmark.p',fact_add__poly__code_I2_J) ).

fof(fact_norm__eq__zero,axiom,
    ! [V_x_2,T_a] :
      ( class_RealVector_Oreal__normed__vector(T_a)
     => ( c_RealVector_Onorm__class_Onorm(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
      <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_norm__eq__zero) ).

fof(fact_pCons__eq__0__iff,axiom,
    ! [V_pa_2,V_ab_2,T_a] :
      ( class_Groups_Ozero(T_a)
     => ( c_Polynomial_OpCons(T_a,V_ab_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
      <=> ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
          & V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_pCons__eq__0__iff) ).

fof(fact_add_Ocomm__neutral,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
    file('theBenchmark.p',fact_add_Ocomm__neutral) ).

fof(fact_add__0__right,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Omonoid__add(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
    file('theBenchmark.p',fact_add__0__right) ).

fof(fact_double__zero__sym,axiom,
    ! [V_ab_2,T_a] :
      ( class_Groups_Olinordered__ab__group__add(T_a)
     => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2)
      <=> V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_double__zero__sym) ).

fof(fact_add__0,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ),
    file('theBenchmark.p',fact_add__0) ).

fof(fact_add__0__left,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Omonoid__add(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ),
    file('theBenchmark.p',fact_add__0__left) ).

fof(fact_norm__le__zero__iff,axiom,
    ! [V_x_2,T_a] :
      ( class_RealVector_Oreal__normed__vector(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_norm__le__zero__iff) ).

fof(fact_poly__zero,axiom,
    ! [V_pa_2,T_a] :
      ( ( class_Rings_Oidom(T_a)
        & class_Int_Oring__char__0(T_a) )
     => ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
      <=> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
    file('theBenchmark.p',fact_poly__zero) ).

fof(fact_add__nonpos__nonpos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
         => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
    file('theBenchmark.p',fact_add__nonpos__nonpos) ).

fof(fact_add__increasing2,axiom,
    ! [V_a,V_b,V_c,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
         => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
    file('theBenchmark.p',fact_add__increasing2) ).

fof(fact_add__increasing,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
         => c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
    file('theBenchmark.p',fact_add__increasing) ).

fof(fact_add__nonneg__eq__0__iff,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)
         => ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
          <=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
              & V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ),
    file('theBenchmark.p',fact_add__nonneg__eq__0__iff) ).

fof(fact_add__nonneg__nonneg,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
         => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ),
    file('theBenchmark.p',fact_add__nonneg__nonneg) ).

fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
    ! [V_ab_2,T_a] :
      ( class_Groups_Olinordered__ab__group__add(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2),c_Groups_Ozero__class_Ozero(T_a))
      <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
    file('theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).

fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
    ! [V_ab_2,T_a] :
      ( class_Groups_Olinordered__ab__group__add(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2))
      <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) ) ),
    file('theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).

fof(fact_linorder__le__cases,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
       => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ),
    file('theBenchmark.p',fact_linorder__le__cases) ).

fof(fact_le__funE,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
      ( class_Orderings_Oord(T_b)
     => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
       => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_le__funE) ).

fof(fact_xt1_I6_J,axiom,
    ! [V_z,V_x,V_y,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
         => c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x) ) ) ),
    file('theBenchmark.p',fact_xt1_I6_J) ).

fof(fact_xt1_I5_J,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
         => V_x = V_y ) ) ),
    file('theBenchmark.p',fact_xt1_I5_J) ).

fof(fact_order__trans,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
         => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z) ) ) ),
    file('theBenchmark.p',fact_order__trans) ).

fof(fact_order__antisym,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
         => V_x = V_y ) ) ),
    file('theBenchmark.p',fact_order__antisym) ).

fof(fact_xt1_I4_J,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
       => ( V_b = V_c
         => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ),
    file('theBenchmark.p',fact_xt1_I4_J) ).

fof(fact_ord__le__eq__trans,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Orderings_Oord(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
       => ( V_b = V_c
         => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ),
    file('theBenchmark.p',fact_ord__le__eq__trans) ).

fof(fact_xt1_I3_J,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( V_a = V_b
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b)
         => c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ),
    file('theBenchmark.p',fact_xt1_I3_J) ).

fof(fact_ord__eq__le__trans,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Orderings_Oord(T_a)
     => ( V_a = V_b
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
         => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ),
    file('theBenchmark.p',fact_ord__eq__le__trans) ).

fof(fact_order__antisym__conv,axiom,
    ! [V_x_2,V_y_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
        <=> V_x_2 = V_y_2 ) ) ),
    file('theBenchmark.p',fact_order__antisym__conv) ).

fof(fact_le__funD,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
      ( class_Orderings_Oord(T_b)
     => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
       => c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_le__funD) ).

fof(fact_order__eq__refl,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( V_x = V_y
       => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
    file('theBenchmark.p',fact_order__eq__refl) ).

fof(fact_order__eq__iff,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( V_x_2 = V_y_2
      <=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
          & c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) ) ),
    file('theBenchmark.p',fact_order__eq__iff) ).

fof(fact_linorder__linear,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
        | c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
    file('theBenchmark.p',fact_linorder__linear) ).

fof(fact_le__fun__def,axiom,
    ! [V_g_2,V_f_2,T_a,T_b] :
      ( class_Orderings_Oord(T_b)
     => ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
      <=> ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)) ) ),
    file('theBenchmark.p',fact_le__fun__def) ).

fof(fact_complex__mod__triangle__sub,axiom,
    ! [V_z,V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_w,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))),
    file('theBenchmark.p',fact_complex__mod__triangle__sub) ).

fof(fact_add__right__imp__eq,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Groups_Ocancel__semigroup__add(T_a)
     => ( c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
       => V_b = V_c ) ),
    file('theBenchmark.p',fact_add__right__imp__eq) ).

fof(fact_add__imp__eq,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Ocancel__ab__semigroup__add(T_a)
     => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
       => V_b = V_c ) ),
    file('theBenchmark.p',fact_add__imp__eq) ).

fof(fact_add__left__imp__eq,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Ocancel__semigroup__add(T_a)
     => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
       => V_b = V_c ) ),
    file('theBenchmark.p',fact_add__left__imp__eq) ).

fof(fact_add__right__cancel,axiom,
    ! [V_ca_2,V_ab_2,V_b_2,T_a] :
      ( class_Groups_Ocancel__semigroup__add(T_a)
     => ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2)
      <=> V_b_2 = V_ca_2 ) ),
    file('theBenchmark.p',fact_add__right__cancel) ).

fof(fact_add__left__cancel,axiom,
    ! [V_ca_2,V_b_2,V_ab_2,T_a] :
      ( class_Groups_Ocancel__semigroup__add(T_a)
     => ( c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_b_2) = c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ca_2)
      <=> V_b_2 = V_ca_2 ) ),
    file('theBenchmark.p',fact_add__left__cancel) ).

fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oab__semigroup__add(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ),
    file('theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).

fof(fact_real__le__antisym,axiom,
    ! [V_w,V_z] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
       => V_z = V_w ) ),
    file('theBenchmark.p',fact_real__le__antisym) ).

fof(fact_real__le__trans,axiom,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k)
       => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k) ) ),
    file('theBenchmark.p',fact_real__le__trans) ).

fof(fact_real__le__linear,axiom,
    ! [V_w,V_z] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w) ),
    file('theBenchmark.p',fact_real__le__linear) ).

fof(fact_real__le__refl,axiom,
    ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w),
    file('theBenchmark.p',fact_real__le__refl) ).

fof(fact_pCons__eq__iff,axiom,
    ! [V_q_2,V_b_2,V_pa_2,V_ab_2,T_a] :
      ( class_Groups_Ozero(T_a)
     => ( c_Polynomial_OpCons(T_a,V_ab_2,V_pa_2) = c_Polynomial_OpCons(T_a,V_b_2,V_q_2)
      <=> ( V_pa_2 = V_q_2
          & V_ab_2 = V_b_2 ) ) ),
    file('theBenchmark.p',fact_pCons__eq__iff) ).

fof(fact_poly__eq__iff,axiom,
    ! [V_q_2,V_pa_2,T_a] :
      ( ( class_Rings_Oidom(T_a)
        & class_Int_Oring__char__0(T_a) )
     => ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,V_q_2)
      <=> V_pa_2 = V_q_2 ) ),
    file('theBenchmark.p',fact_poly__eq__iff) ).

fof(fact_add__le__imp__le__left,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
       => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ),
    file('theBenchmark.p',fact_add__le__imp__le__left) ).

fof(fact_add__le__imp__le__right,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
       => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ),
    file('theBenchmark.p',fact_add__le__imp__le__right) ).

fof(fact_order__root,axiom,
    ! [V_ab_2,V_pa_2,T_a] :
      ( class_Rings_Oidom(T_a)
     => ( hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_ab_2) = c_Groups_Ozero__class_Ozero(T_a)
      <=> ( c_Polynomial_Oorder(T_a,V_ab_2,V_pa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
    file('theBenchmark.p',fact_order__root) ).

fof(fact_double__eq__0__iff,axiom,
    ! [V_ab_2,T_a] :
      ( class_Groups_Olinordered__ab__group__add(T_a)
     => ( c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a)
      <=> V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_double__eq__0__iff) ).

fof(fact_add__0__iff,axiom,
    ! [V_ab_2,V_b_2,T_a] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
     => ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2)
      <=> V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_add__0__iff) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

fof(fact_poly__rec__pCons,axiom,
    ! [V_pa_2,V_ab_2,T_a,V_z_2,V_f_2,T_b] :
      ( class_Groups_Ozero(T_b)
     => ( hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2) = V_z_2
       => c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_ab_2,V_pa_2)) = hAPP(hAPP(hAPP(V_f_2,V_ab_2),V_pa_2),c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pa_2)) ) ),
    file('theBenchmark.p',fact_poly__rec__pCons) ).

fof(fact_poly__rec_Osimps,axiom,
    ! [V_pa_2,V_ab_2,V_f_2,V_z_2,T_a,T_b] :
      ( class_Groups_Ozero(T_b)
     => c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_ab_2,V_pa_2)) = hAPP(hAPP(hAPP(V_f_2,V_ab_2),V_pa_2),c_If(T_a,c_fequal(V_pa_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2,c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pa_2))) ),
    file('theBenchmark.p',fact_poly__rec_Osimps) ).

fof(fact_poly__minimum__modulus__disc,axiom,
    ! [V_p,V_r] :
    ? [B_z] :
    ! [B_w] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_w),V_r)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),B_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),B_w))) ),
    file('theBenchmark.p',fact_poly__minimum__modulus__disc) ).

fof(fact_offset__poly__single,axiom,
    ! [V_h,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ),
    file('theBenchmark.p',fact_offset__poly__single) ).

fof(fact_poly__rec__0,axiom,
    ! [T_a,V_z_2,V_f_2,T_b] :
      ( class_Groups_Ozero(T_b)
     => ( hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2) = V_z_2
       => c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))) = V_z_2 ) ),
    file('theBenchmark.p',fact_poly__rec__0) ).

fof(fact_synthetic__div__pCons,axiom,
    ! [V_c,V_p,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => c_Polynomial_Osynthetic__div(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_c) = c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)) ),
    file('theBenchmark.p',fact_synthetic__div__pCons) ).

fof(fact_poly__offset__poly,axiom,
    ! [V_x,V_h,V_p,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => hAPP(c_Polynomial_Opoly(T_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),V_x) = hAPP(c_Polynomial_Opoly(T_a,V_p),c_Groups_Oplus__class_Oplus(T_a,V_h,V_x)) ),
    file('theBenchmark.p',fact_poly__offset__poly) ).

fof(fact_synthetic__div__0,axiom,
    ! [V_c,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => c_Polynomial_Osynthetic__div(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_c) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
    file('theBenchmark.p',fact_synthetic__div__0) ).

fof(fact_norm__ge__zero,axiom,
    ! [V_x,T_a] :
      ( class_RealVector_Oreal__normed__vector(T_a)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)) ),
    file('theBenchmark.p',fact_norm__ge__zero) ).

fof(fact_offset__poly__eq__0__iff,axiom,
    ! [V_h_2,V_pa_2,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_pa_2,V_h_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
      <=> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
    file('theBenchmark.p',fact_offset__poly__eq__0__iff) ).

fof(fact_offset__poly__0,axiom,
    ! [V_h,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
    file('theBenchmark.p',fact_offset__poly__0) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
    ! [V_c,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
    ! [V_d,V_c,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
    ! [V_d,V_c,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).

fof(fact_psize__eq__0__iff,axiom,
    ! [V_pa_2,T_a] :
      ( class_Groups_Ozero(T_a)
     => ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      <=> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
    file('theBenchmark.p',fact_psize__eq__0__iff) ).

fof(fact_le0,axiom,
    ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n),
    file('theBenchmark.p',fact_le0) ).

fof(fact_synthetic__div__correct,axiom,
    ! [V_c,V_p,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,c_Polynomial_Osynthetic__div(T_a,V_p,V_c))) = c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)) ),
    file('theBenchmark.p',fact_synthetic__div__correct) ).

fof(fact_synthetic__div__unique,axiom,
    ! [V_r,V_q,V_c,V_p,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,V_q)) = c_Polynomial_OpCons(T_a,V_r,V_q)
       => ( V_q = c_Polynomial_Osynthetic__div(T_a,V_p,V_c)
          & V_r = hAPP(c_Polynomial_Opoly(T_a,V_p),V_c) ) ) ),
    file('theBenchmark.p',fact_synthetic__div__unique) ).

fof(fact_monom__0,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ozero(T_a)
     => c_Polynomial_Omonom(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ),
    file('theBenchmark.p',fact_monom__0) ).

fof(fact_norm__diff__triangle__ineq,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_RealVector_Oreal__normed__vector(T_a)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d)))) ),
    file('theBenchmark.p',fact_norm__diff__triangle__ineq) ).

fof(fact_offset__poly__pCons,axiom,
    ! [V_h,V_p,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))) ),
    file('theBenchmark.p',fact_offset__poly__pCons) ).

fof(fact_offset__poly__eq__0__lemma,axiom,
    ! [V_a,V_p,V_c,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
       => V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
    file('theBenchmark.p',fact_offset__poly__eq__0__lemma) ).

fof(fact_poly__pCons,axiom,
    ! [V_x,V_p,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ),
    file('theBenchmark.p',fact_poly__pCons) ).

fof(fact_less__eq__nat_Osimps_I1_J,axiom,
    ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n),
    file('theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).

fof(fact_le__refl,axiom,
    ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n),
    file('theBenchmark.p',fact_le__refl) ).

fof(fact_le__square,axiom,
    ! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)),
    file('theBenchmark.p',fact_le__square) ).

fof(fact_le__add2,axiom,
    ! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
    file('theBenchmark.p',fact_le__add2) ).

fof(fact_le__add1,axiom,
    ! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)),
    file('theBenchmark.p',fact_le__add1) ).

fof(fact_le__cube,axiom,
    ! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))),
    file('theBenchmark.p',fact_le__cube) ).

fof(fact_diff__le__self,axiom,
    ! [V_n,V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m),
    file('theBenchmark.p',fact_diff__le__self) ).

fof(fact_le__iff__add,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
    <=> ? [B_k] : V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k) ),
    file('theBenchmark.p',fact_le__iff__add) ).

fof(fact_nat__le__linear,axiom,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
    file('theBenchmark.p',fact_nat__le__linear) ).

fof(fact_diff__diff__right,axiom,
    ! [V_i,V_j,V_k] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j) ),
    file('theBenchmark.p',fact_diff__diff__right) ).

fof(fact_le__diff__conv,axiom,
    ! [V_i_2,V_k_2,V_j_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)) ),
    file('theBenchmark.p',fact_le__diff__conv) ).

fof(fact_nat__add__left__cancel__le,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ),
    file('theBenchmark.p',fact_nat__add__left__cancel__le) ).

fof(fact_mult__monom,axiom,
    ! [V_n,V_b,V_m,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,V_a,V_m)),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) ),
    file('theBenchmark.p',fact_mult__monom) ).

fof(fact_eq__imp__le,axiom,
    ! [V_n,V_m] :
      ( V_m = V_n
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
    file('theBenchmark.p',fact_eq__imp__le) ).

fof(fact_trans__le__add1,axiom,
    ! [V_m,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ),
    file('theBenchmark.p',fact_trans__le__add1) ).

fof(fact_trans__le__add2,axiom,
    ! [V_m,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ),
    file('theBenchmark.p',fact_trans__le__add2) ).

fof(fact_le__add__diff,axiom,
    ! [V_m,V_n,V_k] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k)) ),
    file('theBenchmark.p',fact_le__add__diff) ).

fof(fact_add__le__mono1,axiom,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ),
    file('theBenchmark.p',fact_add__le__mono1) ).

fof(fact_mult__le__mono1,axiom,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)) ),
    file('theBenchmark.p',fact_mult__le__mono1) ).

fof(fact_mult__le__mono2,axiom,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)) ),
    file('theBenchmark.p',fact_mult__le__mono2) ).

fof(fact_diff__le__mono2,axiom,
    ! [V_l,V_n,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)) ),
    file('theBenchmark.p',fact_diff__le__mono2) ).

fof(fact_diff__le__mono,axiom,
    ! [V_l,V_n,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l)) ),
    file('theBenchmark.p',fact_diff__le__mono) ).

fof(fact_diff__diff__cancel,axiom,
    ! [V_n,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_n)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = V_i ),
    file('theBenchmark.p',fact_diff__diff__cancel) ).

fof(fact_le__add__diff__inverse,axiom,
    ! [V_m,V_n] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ),
    file('theBenchmark.p',fact_le__add__diff__inverse) ).

fof(fact_add__diff__assoc,axiom,
    ! [V_i,V_j,V_k] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) ),
    file('theBenchmark.p',fact_add__diff__assoc) ).

fof(fact_le__diff__conv2,axiom,
    ! [V_i_2,V_j_2,V_k_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_j_2)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) ) ),
    file('theBenchmark.p',fact_le__diff__conv2) ).

fof(fact_le__add__diff__inverse2,axiom,
    ! [V_m,V_n] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) = V_m ),
    file('theBenchmark.p',fact_le__add__diff__inverse2) ).

fof(fact_le__imp__diff__is__add,axiom,
    ! [V_k_2,V_j_2,V_i_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
     => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_k_2
      <=> V_j_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2) ) ),
    file('theBenchmark.p',fact_le__imp__diff__is__add) ).

fof(fact_diff__add__assoc,axiom,
    ! [V_i,V_j,V_k] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) ),
    file('theBenchmark.p',fact_diff__add__assoc) ).

fof(fact_add__diff__assoc2,axiom,
    ! [V_i,V_j,V_k] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k) ),
    file('theBenchmark.p',fact_add__diff__assoc2) ).

fof(fact_diff__add__assoc2,axiom,
    ! [V_i,V_j,V_k] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i) ),
    file('theBenchmark.p',fact_diff__add__assoc2) ).

fof(fact_le__trans,axiom,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k) ) ),
    file('theBenchmark.p',fact_le__trans) ).

fof(fact_le__antisym,axiom,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
       => V_m = V_n ) ),
    file('theBenchmark.p',fact_le__antisym) ).

fof(fact_add__le__mono,axiom,
    ! [V_l,V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)) ) ),
    file('theBenchmark.p',fact_add__le__mono) ).

fof(fact_mult__le__mono,axiom,
    ! [V_l,V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l)) ) ),
    file('theBenchmark.p',fact_mult__le__mono) ).

fof(fact_eq__diff__iff,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
       => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)
        <=> V_m_2 = V_n_2 ) ) ),
    file('theBenchmark.p',fact_eq__diff__iff) ).

fof(fact_Nat_Odiff__diff__eq,axiom,
    ! [V_n,V_m,V_k] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_m)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
       => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ) ),
    file('theBenchmark.p',fact_Nat_Odiff__diff__eq) ).

fof(fact_le__diff__iff,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))
        <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ) ),
    file('theBenchmark.p',fact_le__diff__iff) ).

fof(fact_add__leD2,axiom,
    ! [V_n,V_k,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ),
    file('theBenchmark.p',fact_add__leD2) ).

fof(fact_add__leD1,axiom,
    ! [V_n,V_k,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
    file('theBenchmark.p',fact_add__leD1) ).

fof(fact_add__leE,axiom,
    ! [V_n,V_k,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)
     => ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
         => ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ),
    file('theBenchmark.p',fact_add__leE) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
    ! [V_ry,V_rx,V_ly,V_lx,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
    ! [V_ry,V_rx,V_ly,V_lx,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
    ! [V_ry,V_rx,V_ly,V_lx,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry))) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
    ! [V_rx,V_ly,V_lx,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
    ! [V_rx,V_ly,V_lx,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
    ! [V_ry,V_rx,V_lx,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
    ! [V_ry,V_rx,V_lx,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).

fof(fact_mult_Oprod__diff__prod,axiom,
    ! [V_b,V_a,V_y,V_x,T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))) ),
    file('theBenchmark.p',fact_mult_Oprod__diff__prod) ).

fof(fact_mult__diff__mult,axiom,
    ! [V_b,V_a,V_y,V_x,T_a] :
      ( class_Rings_Oring(T_a)
     => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)) ),
    file('theBenchmark.p',fact_mult__diff__mult) ).

fof(fact_diff__eq__diff__eq,axiom,
    ! [V_db_2,V_ca_2,V_b_2,V_ab_2,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => ( c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_db_2)
       => ( V_ab_2 = V_b_2
        <=> V_ca_2 = V_db_2 ) ) ),
    file('theBenchmark.p',fact_diff__eq__diff__eq) ).

fof(fact_diff__monom,axiom,
    ! [V_b,V_n,V_a,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_n) ),
    file('theBenchmark.p',fact_diff__monom) ).

fof(fact_monom__eq__iff,axiom,
    ! [V_b_2,V_n_2,V_ab_2,T_a] :
      ( class_Groups_Ozero(T_a)
     => ( c_Polynomial_Omonom(T_a,V_ab_2,V_n_2) = c_Polynomial_Omonom(T_a,V_b_2,V_n_2)
      <=> V_ab_2 = V_b_2 ) ),
    file('theBenchmark.p',fact_monom__eq__iff) ).

fof(fact_mult__left_Odiff,axiom,
    ! [V_ya,V_y,V_x,T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),V_ya) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)) ),
    file('theBenchmark.p',fact_mult__left_Odiff) ).

fof(fact_mult_Odiff__left,axiom,
    ! [V_b,V_a_H,V_a,T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H)),V_b) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)) ),
    file('theBenchmark.p',fact_mult_Odiff__left) ).

fof(fact_smult__diff__left,axiom,
    ! [V_p,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__ring(T_a)
     => c_Polynomial_Osmult(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_p) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_b,V_p)) ),
    file('theBenchmark.p',fact_smult__diff__left) ).

fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oab__semigroup__mult(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).

fof(fact_mult__smult__left,axiom,
    ! [V_q,V_p,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Osmult(T_a,V_a,V_p)),V_q) = c_Polynomial_Osmult(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) ),
    file('theBenchmark.p',fact_mult__smult__left) ).

fof(fact_mult__right_Odiff,axiom,
    ! [V_y,V_x,V_xa,T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)) ),
    file('theBenchmark.p',fact_mult__right_Odiff) ).

fof(fact_mult_Odiff__right,axiom,
    ! [V_b_H,V_b,V_a,T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)) ),
    file('theBenchmark.p',fact_mult_Odiff__right) ).

fof(fact_smult__diff__right,axiom,
    ! [V_q,V_p,V_a,T_a] :
      ( class_Rings_Ocomm__ring(T_a)
     => c_Polynomial_Osmult(T_a,V_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_a,V_q)) ),
    file('theBenchmark.p',fact_smult__diff__right) ).

fof(fact_smult__smult,axiom,
    ! [V_p,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => c_Polynomial_Osmult(T_a,V_a,c_Polynomial_Osmult(T_a,V_b,V_p)) = c_Polynomial_Osmult(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_p) ),
    file('theBenchmark.p',fact_smult__smult) ).

fof(fact_smult__monom,axiom,
    ! [V_n,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => c_Polynomial_Osmult(T_a,V_a,c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_n) ),
    file('theBenchmark.p',fact_smult__monom) ).

fof(fact_mult__smult__right,axiom,
    ! [V_q,V_a,V_p,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_Osmult(T_a,V_a,V_q)) = c_Polynomial_Osmult(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) ),
    file('theBenchmark.p',fact_mult__smult__right) ).

fof(fact_diff__pCons,axiom,
    ! [V_q,V_b,V_p,V_a,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q)) = c_Polynomial_OpCons(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)) ),
    file('theBenchmark.p',fact_diff__pCons) ).

fof(fact_norm__mult,axiom,
    ! [V_y,V_x,T_a] :
      ( class_RealVector_Oreal__normed__div__algebra(T_a)
     => c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)) ),
    file('theBenchmark.p',fact_norm__mult) ).

fof(fact_smult__pCons,axiom,
    ! [V_p,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => c_Polynomial_Osmult(T_a,V_a,c_Polynomial_OpCons(T_a,V_b,V_p)) = c_Polynomial_OpCons(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Polynomial_Osmult(T_a,V_a,V_p)) ),
    file('theBenchmark.p',fact_smult__pCons) ).

fof(fact_poly__diff,axiom,
    ! [V_x,V_q,V_p,T_a] :
      ( class_Rings_Ocomm__ring(T_a)
     => hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ),
    file('theBenchmark.p',fact_poly__diff) ).

fof(fact_poly__smult,axiom,
    ! [V_x,V_p,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Osmult(T_a,V_a,V_p)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)) ),
    file('theBenchmark.p',fact_poly__smult) ).

fof(fact_diffs0__imp__equal,axiom,
    ! [V_n,V_m] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => V_m = V_n ) ),
    file('theBenchmark.p',fact_diffs0__imp__equal) ).

fof(fact_diff__is__0__eq_H,axiom,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_diff__is__0__eq_H) ).

fof(fact_diff__is__0__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ),
    file('theBenchmark.p',fact_diff__is__0__eq) ).

fof(fact_diff__add__0,axiom,
    ! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_diff__add__0) ).

fof(fact_diff__self__eq__0,axiom,
    ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_diff__self__eq__0) ).

fof(fact_minus__nat_Odiff__0,axiom,
    ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
    file('theBenchmark.p',fact_minus__nat_Odiff__0) ).

fof(fact_diff__0__eq__0,axiom,
    ! [V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_diff__0__eq__0) ).

fof(fact_poly__mult,axiom,
    ! [V_x,V_q,V_p,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ),
    file('theBenchmark.p',fact_poly__mult) ).

fof(fact_mult__cancel2,axiom,
    ! [V_n_2,V_k_2,V_m_2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)
    <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_m_2 = V_n_2 ) ),
    file('theBenchmark.p',fact_mult__cancel2) ).

fof(fact_mult__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
    <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_m_2 = V_n_2 ) ),
    file('theBenchmark.p',fact_mult__cancel1) ).

fof(fact_mult__is__0,axiom,
    ! [V_n_2,V_m_2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_mult__is__0) ).

fof(fact_mult__0__right,axiom,
    ! [V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_mult__0__right) ).

fof(fact_mult__0,axiom,
    ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_mult__0) ).

fof(fact_norm__triangle__ineq2,axiom,
    ! [V_b,V_a,T_a] :
      ( class_RealVector_Oreal__normed__vector(T_a)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ),
    file('theBenchmark.p',fact_norm__triangle__ineq2) ).

fof(fact_norm__mult__ineq,axiom,
    ! [V_y,V_x,T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))) ),
    file('theBenchmark.p',fact_norm__mult__ineq) ).

fof(fact_diff__0__right,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
    file('theBenchmark.p',fact_diff__0__right) ).

fof(fact_diff__self,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => c_Groups_Ominus__class_Ominus(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_diff__self) ).

fof(fact_eq__iff__diff__eq__0,axiom,
    ! [V_b_2,V_ab_2,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => ( V_ab_2 = V_b_2
      <=> c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_eq__iff__diff__eq__0) ).

fof(fact_right__minus__eq,axiom,
    ! [V_b_2,V_ab_2,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => ( c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
      <=> V_ab_2 = V_b_2 ) ),
    file('theBenchmark.p',fact_right__minus__eq) ).

fof(fact_diff__eq__diff__less__eq,axiom,
    ! [V_db_2,V_ca_2,V_b_2,V_ab_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_db_2)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2)
        <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2,V_db_2) ) ) ),
    file('theBenchmark.p',fact_diff__eq__diff__less__eq) ).

fof(fact_add__diff__cancel,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a ),
    file('theBenchmark.p',fact_add__diff__cancel) ).

fof(fact_diff__add__cancel,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a ),
    file('theBenchmark.p',fact_diff__add__cancel) ).

fof(fact_mult_Ozero__left,axiom,
    ! [V_b,T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_mult_Ozero__left) ).

fof(fact_mult__left_Ozero,axiom,
    ! [V_y,T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_mult__left_Ozero) ).

fof(fact_mult_Ozero__right,axiom,
    ! [V_a,T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_mult_Ozero__right) ).

fof(fact_mult__right_Ozero,axiom,
    ! [V_x,T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_mult__right_Ozero) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).

fof(fact_norm__minus__commute,axiom,
    ! [V_b,V_a,T_a] :
      ( class_RealVector_Oreal__normed__vector(T_a)
     => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)) ),
    file('theBenchmark.p',fact_norm__minus__commute) ).

fof(fact_mult__left_Oadd,axiom,
    ! [V_ya,V_y,V_x,T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),V_ya) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)) ),
    file('theBenchmark.p',fact_mult__left_Oadd) ).

fof(fact_mult_Oadd__left,axiom,
    ! [V_b,V_a_H,V_a,T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H)),V_b) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b)) ),
    file('theBenchmark.p',fact_mult_Oadd__left) ).

fof(fact_mult__right_Oadd,axiom,
    ! [V_y,V_x,V_xa,T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)) ),
    file('theBenchmark.p',fact_mult__right_Oadd) ).

fof(fact_mult_Oadd__right,axiom,
    ! [V_b_H,V_b,V_a,T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H)) ),
    file('theBenchmark.p',fact_mult_Oadd__right) ).

fof(fact_crossproduct__eq,axiom,
    ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
     => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))
      <=> ( V_y_2 = V_z_2
          | V_w_2 = V_x_2 ) ) ),
    file('theBenchmark.p',fact_crossproduct__eq) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
    ! [V_b,V_m,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_m) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).

fof(fact_crossproduct__noteq,axiom,
    ! [V_db_2,V_ca_2,V_b_2,V_ab_2,T_a] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
     => ( ( V_ca_2 != V_db_2
          & V_ab_2 != V_b_2 )
      <=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_db_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_db_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)) ) ),
    file('theBenchmark.p',fact_crossproduct__noteq) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Oplus__class_Oplus(T_a,V_y,V_z)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).

fof(fact_diff__poly__code_I2_J,axiom,
    ! [V_p,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ),
    file('theBenchmark.p',fact_diff__poly__code_I2_J) ).

fof(fact_real__mult__left__cancel,axiom,
    ! [V_b_2,V_ab_2,V_ca_2] :
      ( V_ca_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_ab_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_b_2)
      <=> V_ab_2 = V_b_2 ) ),
    file('theBenchmark.p',fact_real__mult__left__cancel) ).

fof(fact_real__mult__right__cancel,axiom,
    ! [V_b_2,V_ab_2,V_ca_2] :
      ( V_ca_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ab_2),V_ca_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_ca_2)
      <=> V_ab_2 = V_b_2 ) ),
    file('theBenchmark.p',fact_real__mult__right__cancel) ).

fof(fact_smult__0__right,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => c_Polynomial_Osmult(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
    file('theBenchmark.p',fact_smult__0__right) ).

fof(fact_real__add__mult__distrib,axiom,
    ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z1,V_z2)),V_w) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_w)),
    file('theBenchmark.p',fact_real__add__mult__distrib) ).

fof(fact_mult__poly__0__left,axiom,
    ! [V_q,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
    file('theBenchmark.p',fact_mult__poly__0__left) ).

fof(fact_mult__poly__0__right,axiom,
    ! [V_p,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
    file('theBenchmark.p',fact_mult__poly__0__right) ).

fof(fact_smult__add__right,axiom,
    ! [V_q,V_p,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => c_Polynomial_Osmult(T_a,V_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_a,V_q)) ),
    file('theBenchmark.p',fact_smult__add__right) ).

fof(fact_mult__poly__add__left,axiom,
    ! [V_r,V_q,V_p,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_r) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),V_r)) ),
    file('theBenchmark.p',fact_mult__poly__add__left) ).

fof(fact_mult__pCons__right,axiom,
    ! [V_q,V_a,V_p,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ),
    file('theBenchmark.p',fact_mult__pCons__right) ).

fof(fact_mult__pCons__left,axiom,
    ! [V_q,V_p,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,V_p)),V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_q),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))) ),
    file('theBenchmark.p',fact_mult__pCons__left) ).

fof(fact_le__iff__diff__le__0,axiom,
    ! [V_b_2,V_ab_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2)
      <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ),
    file('theBenchmark.p',fact_le__iff__diff__le__0) ).

fof(fact_add__scale__eq__noteq,axiom,
    ! [V_d,V_c,V_b,V_a,V_r,T_a] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
     => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
       => ( ( V_c != V_d
            & V_a = V_b )
         => c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != c_Groups_Oplus__class_Oplus(T_a,V_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)) ) ) ),
    file('theBenchmark.p',fact_add__scale__eq__noteq) ).

fof(fact_real__le__eq__diff,axiom,
    ! [V_y_2,V_x_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    file('theBenchmark.p',fact_real__le__eq__diff) ).

fof(fact_smult__0__left,axiom,
    ! [V_p,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => c_Polynomial_Osmult(T_a,c_Groups_Ozero__class_Ozero(T_a),V_p) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
    file('theBenchmark.p',fact_smult__0__left) ).

fof(fact_smult__eq__0__iff,axiom,
    ! [V_pa_2,V_ab_2,T_a] :
      ( class_Rings_Oidom(T_a)
     => ( c_Polynomial_Osmult(T_a,V_ab_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
      <=> ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
          | V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_smult__eq__0__iff) ).

fof(fact_real__two__squares__add__zero__iff,axiom,
    ! [V_y_2,V_x_2] :
      ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    <=> ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        & V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    file('theBenchmark.p',fact_real__two__squares__add__zero__iff) ).

fof(fact_synthetic__div__unique__lemma,axiom,
    ! [V_a,V_p,V_c,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => ( c_Polynomial_Osmult(T_a,V_c,V_p) = c_Polynomial_OpCons(T_a,V_a,V_p)
       => V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
    file('theBenchmark.p',fact_synthetic__div__unique__lemma) ).

fof(fact_smult__add__left,axiom,
    ! [V_p,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => c_Polynomial_Osmult(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_p) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_b,V_p)) ),
    file('theBenchmark.p',fact_smult__add__left) ).

fof(fact_monom__eq__0,axiom,
    ! [V_n,T_a] :
      ( class_Groups_Ozero(T_a)
     => c_Polynomial_Omonom(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
    file('theBenchmark.p',fact_monom__eq__0) ).

fof(fact_monom__eq__0__iff,axiom,
    ! [V_n_2,V_ab_2,T_a] :
      ( class_Groups_Ozero(T_a)
     => ( c_Polynomial_Omonom(T_a,V_ab_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
      <=> V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_monom__eq__0__iff) ).

fof(fact_add__monom,axiom,
    ! [V_b,V_n,V_a,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_n) ),
    file('theBenchmark.p',fact_add__monom) ).

fof(fact_norm__diff__ineq,axiom,
    ! [V_b,V_a,T_a] :
      ( class_RealVector_Oreal__normed__vector(T_a)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))) ),
    file('theBenchmark.p',fact_norm__diff__ineq) ).

fof(fact_norm__triangle__ineq4,axiom,
    ! [V_b,V_a,T_a] :
      ( class_RealVector_Oreal__normed__vector(T_a)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b))) ),
    file('theBenchmark.p',fact_norm__triangle__ineq4) ).

fof(fact_add__eq__self__zero,axiom,
    ! [V_n,V_m] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_m
     => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_add__eq__self__zero) ).

fof(fact_add__is__0,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_add__is__0) ).

fof(fact_le__0__eq,axiom,
    ! [V_n_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_le__0__eq) ).

fof(fact_Nat_Oadd__0__right,axiom,
    ! [V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
    file('theBenchmark.p',fact_Nat_Oadd__0__right) ).

fof(fact_plus__nat_Oadd__0,axiom,
    ! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n,
    file('theBenchmark.p',fact_plus__nat_Oadd__0) ).

fof(fact_norm__ratiotest__lemma,axiom,
    ! [V_y,V_x,V_c,T_a] :
      ( class_RealVector_Oreal__normed__vector(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
       => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_RealVector_Onorm__class_Onorm(T_a,V_y)))
         => V_x = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_norm__ratiotest__lemma) ).

fof(fact_le__add__iff1,axiom,
    ! [V_db_2,V_b_2,V_ca_2,V_e_2,V_ab_2,T_a] :
      ( class_Rings_Oordered__ring(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2))
      <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2)),V_e_2),V_ca_2),V_db_2) ) ),
    file('theBenchmark.p',fact_le__add__iff1) ).

fof(fact_le__add__iff2,axiom,
    ! [V_db_2,V_b_2,V_ca_2,V_e_2,V_ab_2,T_a] :
      ( class_Rings_Oordered__ring(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2))
      <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_ab_2)),V_e_2),V_db_2)) ) ),
    file('theBenchmark.p',fact_le__add__iff2) ).

fof(fact_sum__squares__le__zero__iff,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))
      <=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
          & V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_sum__squares__le__zero__iff) ).

fof(fact_sum__squares__ge__zero,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__ring(T_a)
     => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))) ),
    file('theBenchmark.p',fact_sum__squares__ge__zero) ).

fof(fact_complex__mod__triangle__ineq2,axiom,
    ! [V_a,V_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_b,V_a)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_b)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_a)),
    file('theBenchmark.p',fact_complex__mod__triangle__ineq2) ).

fof(fact_eq__add__iff2,axiom,
    ! [V_db_2,V_b_2,V_ca_2,V_e_2,V_ab_2,T_a] :
      ( class_Rings_Oring(T_a)
     => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2)
      <=> V_ca_2 = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_ab_2)),V_e_2),V_db_2) ) ),
    file('theBenchmark.p',fact_eq__add__iff2) ).

fof(fact_eq__add__iff1,axiom,
    ! [V_db_2,V_b_2,V_ca_2,V_e_2,V_ab_2,T_a] :
      ( class_Rings_Oring(T_a)
     => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2)
      <=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2)),V_e_2),V_ca_2) = V_db_2 ) ),
    file('theBenchmark.p',fact_eq__add__iff1) ).

fof(fact_sum__squares__eq__zero__iff,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_a)
      <=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
          & V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_sum__squares__eq__zero__iff) ).

fof(fact_zero__le__square,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__ring(T_a)
     => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) ),
    file('theBenchmark.p',fact_zero__le__square) ).

fof(fact_nat__add__commute,axiom,
    ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),
    file('theBenchmark.p',fact_nat__add__commute) ).

fof(fact_nat__add__left__commute,axiom,
    ! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z)),
    file('theBenchmark.p',fact_nat__add__left__commute) ).

fof(fact_add__mult__distrib2,axiom,
    ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
    file('theBenchmark.p',fact_add__mult__distrib2) ).

fof(fact_diff__add__inverse2,axiom,
    ! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n) = V_m,
    file('theBenchmark.p',fact_diff__add__inverse2) ).

fof(fact_diff__add__inverse,axiom,
    ! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_n) = V_m,
    file('theBenchmark.p',fact_diff__add__inverse) ).

fof(fact_nat__add__assoc,axiom,
    ! [V_k,V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)),
    file('theBenchmark.p',fact_nat__add__assoc) ).

fof(fact_diff__diff__left,axiom,
    ! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)),
    file('theBenchmark.p',fact_diff__diff__left) ).

fof(fact_add__mult__distrib,axiom,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
    file('theBenchmark.p',fact_add__mult__distrib) ).

fof(fact_nat__add__left__cancel,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)
    <=> V_m_2 = V_n_2 ),
    file('theBenchmark.p',fact_nat__add__left__cancel) ).

fof(fact_nat__add__right__cancel,axiom,
    ! [V_n_2,V_k_2,V_m_2] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)
    <=> V_m_2 = V_n_2 ),
    file('theBenchmark.p',fact_nat__add__right__cancel) ).

fof(fact_diff__cancel,axiom,
    ! [V_n,V_m,V_k] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),
    file('theBenchmark.p',fact_diff__cancel) ).

fof(fact_diff__cancel2,axiom,
    ! [V_n,V_k,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),
    file('theBenchmark.p',fact_diff__cancel2) ).

fof(fact_nat__mult__commute,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),
    file('theBenchmark.p',fact_nat__mult__commute) ).

fof(fact_diff__mult__distrib2,axiom,
    ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
    file('theBenchmark.p',fact_diff__mult__distrib2) ).

fof(fact_nat__mult__assoc,axiom,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
    file('theBenchmark.p',fact_nat__mult__assoc) ).

fof(fact_diff__commute,axiom,
    ! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j),
    file('theBenchmark.p',fact_diff__commute) ).

fof(fact_diff__mult__distrib,axiom,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
    file('theBenchmark.p',fact_diff__mult__distrib) ).

fof(fact_real__mult__assoc,axiom,
    ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_z3)),
    file('theBenchmark.p',fact_real__mult__assoc) ).

fof(fact_real__mult__commute,axiom,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z),
    file('theBenchmark.p',fact_real__mult__commute) ).

fof(fact_le__Suc__ex__iff,axiom,
    ! [V_l_2,V_k_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2)
    <=> ? [B_n] : V_l_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n) ),
    file('theBenchmark.p',fact_le__Suc__ex__iff) ).

fof(fact_divisors__zero,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Ono__zero__divisors(T_a)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
       => ( V_b = c_Groups_Ozero__class_Ozero(T_a)
          | V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_divisors__zero) ).

fof(fact_no__zero__divisors,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Ono__zero__divisors(T_a)
     => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
       => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_no__zero__divisors) ).

fof(fact_mult__eq__0__iff,axiom,
    ! [V_b_2,V_ab_2,T_a] :
      ( class_Rings_Oring__no__zero__divisors(T_a)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
      <=> ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a)
          | V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_mult__eq__0__iff) ).

fof(fact_mult__zero__right,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Omult__zero(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_mult__zero__right) ).

fof(fact_mult__zero__left,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Omult__zero(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_mult__zero__left) ).

fof(fact_comm__semiring__class_Odistrib,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_comm__semiring__class_Odistrib) ).

fof(fact_combine__common__factor,axiom,
    ! [V_c,V_b,V_e,V_a,T_a] :
      ( class_Rings_Osemiring(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e),V_c)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_e),V_c) ),
    file('theBenchmark.p',fact_combine__common__factor) ).

fof(fact_split__mult__neg__le,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oordered__cancel__semiring(T_a)
     => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
            & c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
          | ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
            & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )
       => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ),
    file('theBenchmark.p',fact_split__mult__neg__le) ).

fof(fact_split__mult__pos__le,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oordered__ring(T_a)
     => ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
            & c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
          | ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
            & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )
       => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ),
    file('theBenchmark.p',fact_split__mult__pos__le) ).

fof(fact_mult__mono,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Rings_Oordered__semiring(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
         => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
           => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
             => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ),
    file('theBenchmark.p',fact_mult__mono) ).

fof(fact_mult__mono_H,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Rings_Oordered__semiring(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
         => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
           => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
             => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ),
    file('theBenchmark.p',fact_mult__mono_H) ).

fof(fact_mult__left__mono__neg,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Rings_Oordered__ring(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
         => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ),
    file('theBenchmark.p',fact_mult__left__mono__neg) ).

fof(fact_mult__right__mono__neg,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Rings_Oordered__ring(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
         => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ),
    file('theBenchmark.p',fact_mult__right__mono__neg) ).

fof(fact_comm__mult__left__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Oordered__comm__semiring(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
         => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ),
    file('theBenchmark.p',fact_comm__mult__left__mono) ).

fof(fact_mult__left__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Oordered__semiring(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
         => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ),
    file('theBenchmark.p',fact_mult__left__mono) ).

fof(fact_mult__right__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Oordered__semiring(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
         => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ),
    file('theBenchmark.p',fact_mult__right__mono) ).

fof(fact_mult__nonpos__nonpos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oordered__ring(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
         => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_mult__nonpos__nonpos) ).

fof(fact_mult__nonpos__nonneg,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oordered__cancel__semiring(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
       => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
         => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
    file('theBenchmark.p',fact_mult__nonpos__nonneg) ).

fof(fact_mult__nonneg__nonpos2,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oordered__cancel__semiring(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
         => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
    file('theBenchmark.p',fact_mult__nonneg__nonpos2) ).

fof(fact_mult__nonneg__nonpos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oordered__cancel__semiring(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
         => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
    file('theBenchmark.p',fact_mult__nonneg__nonpos) ).

fof(fact_mult__nonneg__nonneg,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oordered__cancel__semiring(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
         => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_mult__nonneg__nonneg) ).

fof(fact_mult__le__0__iff,axiom,
    ! [V_b_2,V_ab_2,T_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))
      <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
            & c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) )
          | ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
            & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) ) ) ) ),
    file('theBenchmark.p',fact_mult__le__0__iff) ).

fof(fact_zero__le__mult__iff,axiom,
    ! [V_b_2,V_ab_2,T_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_b_2))
      <=> ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
            & c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) )
          | ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
            & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) ) ) ) ),
    file('theBenchmark.p',fact_zero__le__mult__iff) ).

fof(fact_nat__le__add__iff1,axiom,
    ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2),V_n_2) ) ),
    file('theBenchmark.p',fact_nat__le__add__iff1) ).

fof(fact_nat__diff__add__eq1,axiom,
    ! [V_n,V_m,V_u,V_i,V_j] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_i)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j)),V_u),V_m),V_n) ),
    file('theBenchmark.p',fact_nat__diff__add__eq1) ).

fof(fact_nat__eq__add__iff1,axiom,
    ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
     => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)
      <=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2) = V_n_2 ) ),
    file('theBenchmark.p',fact_nat__eq__add__iff1) ).

fof(fact_nat__le__add__iff2,axiom,
    ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_nat__le__add__iff2) ).

fof(fact_nat__diff__add__eq2,axiom,
    ! [V_n,V_m,V_u,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u),V_n)) ),
    file('theBenchmark.p',fact_nat__diff__add__eq2) ).

fof(fact_nat__eq__add__iff2,axiom,
    ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
     => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)
      <=> V_m_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2) ) ),
    file('theBenchmark.p',fact_nat__eq__add__iff2) ).

fof(fact_pcompose__pCons,axiom,
    ! [V_q,V_p,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => c_Polynomial_Opcompose(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),c_Polynomial_Opcompose(T_a,V_p,V_q))) ),
    file('theBenchmark.p',fact_pcompose__pCons) ).

fof(fact_pcompose__0,axiom,
    ! [V_q,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => c_Polynomial_Opcompose(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
    file('theBenchmark.p',fact_pcompose__0) ).

fof(fact_poly__pcompose,axiom,
    ! [V_x,V_q,V_p,T_a] :
      ( class_Rings_Ocomm__semiring__0(T_a)
     => hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Opcompose(T_a,V_p,V_q)),V_x) = hAPP(c_Polynomial_Opoly(T_a,V_p),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ),
    file('theBenchmark.p',fact_poly__pcompose) ).

fof(fact_nat__mult__eq__cancel__disj,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
    <=> ( V_m_2 = V_n_2
        | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).

fof(fact_left__add__mult__distrib,axiom,
    ! [V_k,V_j,V_u,V_i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j)),V_u),V_k),
    file('theBenchmark.p',fact_left__add__mult__distrib) ).

fof(fact_termination__basic__simps_I3_J,axiom,
    ! [V_z,V_y,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ),
    file('theBenchmark.p',fact_termination__basic__simps_I3_J) ).

fof(fact_termination__basic__simps_I4_J,axiom,
    ! [V_y,V_z,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_z)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ),
    file('theBenchmark.p',fact_termination__basic__simps_I4_J) ).

fof(fact_Deriv_Oadd__diff__add,axiom,
    ! [V_d,V_b,V_c,V_a,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d)) ),
    file('theBenchmark.p',fact_Deriv_Oadd__diff__add) ).

fof(fact_mult_Ononneg__bounded,axiom,
    ! [T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => ? [B_K] :
          ( ! [B_a,B_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ),
    file('theBenchmark.p',fact_mult_Ononneg__bounded) ).

fof(fact_mult__right_Ononneg__bounded,axiom,
    ! [V_x,T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => ? [B_K] :
          ( ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ),
    file('theBenchmark.p',fact_mult__right_Ononneg__bounded) ).

fof(fact_mult__left_Ononneg__bounded,axiom,
    ! [V_y,T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => ? [B_K] :
          ( ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ),
    file('theBenchmark.p',fact_mult__left_Ononneg__bounded) ).

fof(fact_mult_Obounded,axiom,
    ! [T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => ? [B_K] :
        ! [B_a,B_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K)) ),
    file('theBenchmark.p',fact_mult_Obounded) ).

fof(fact_mult__right_Obounded,axiom,
    ! [V_x,T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => ? [B_K] :
        ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)) ),
    file('theBenchmark.p',fact_mult__right_Obounded) ).

fof(fact_mult__left_Obounded,axiom,
    ! [V_y,T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => ? [B_K] :
        ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K)) ),
    file('theBenchmark.p',fact_mult__left_Obounded) ).

fof(fact_mult__eq__if,axiom,
    ! [V_n,V_m] :
      ( ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) )
      & ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_mult__eq__if) ).

fof(fact_nat__less__add__iff1,axiom,
    ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
      <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2),V_n_2) ) ),
    file('theBenchmark.p',fact_nat__less__add__iff1) ).

fof(fact_nat__less__add__iff2,axiom,
    ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
      <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_nat__less__add__iff2) ).

fof(fact_less__zeroE,axiom,
    ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_less__zeroE) ).

fof(fact_less__1__mult,axiom,
    ! [V_n,V_m,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)
       => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)
         => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n)) ) ) ),
    file('theBenchmark.p',fact_less__1__mult) ).

fof(fact_linorder__neqE__linordered__idom,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( V_x != V_y
       => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
         => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ),
    file('theBenchmark.p',fact_linorder__neqE__linordered__idom) ).

fof(fact_less__add__one,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))) ),
    file('theBenchmark.p',fact_less__add__one) ).

fof(fact_zero__less__one,axiom,
    ! [T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ),
    file('theBenchmark.p',fact_zero__less__one) ).

fof(fact_not__one__less__zero,axiom,
    ! [T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ),
    file('theBenchmark.p',fact_not__one__less__zero) ).

fof(fact_poly__1,axiom,
    ! [V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_poly__1) ).

fof(fact_linorder__cases,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
       => ( V_x != V_y
         => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ),
    file('theBenchmark.p',fact_linorder__cases) ).

fof(fact_order__less__asym,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
       => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ),
    file('theBenchmark.p',fact_order__less__asym) ).

fof(fact_xt1_I10_J,axiom,
    ! [V_z,V_x,V_y,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
       => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
         => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ),
    file('theBenchmark.p',fact_xt1_I10_J) ).

fof(fact_order__less__trans,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
       => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
         => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ),
    file('theBenchmark.p',fact_order__less__trans) ).

fof(fact_xt1_I2_J,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
       => ( V_b = V_c
         => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ),
    file('theBenchmark.p',fact_xt1_I2_J) ).

fof(fact_ord__less__eq__trans,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Orderings_Oord(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
       => ( V_b = V_c
         => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ),
    file('theBenchmark.p',fact_ord__less__eq__trans) ).

fof(fact_xt1_I1_J,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( V_a = V_b
       => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_b)
         => c_Orderings_Oord__class_Oless(T_a,V_c,V_a) ) ) ),
    file('theBenchmark.p',fact_xt1_I1_J) ).

fof(fact_ord__eq__less__trans,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Orderings_Oord(T_a)
     => ( V_a = V_b
       => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
         => c_Orderings_Oord__class_Oless(T_a,V_a,V_c) ) ) ),
    file('theBenchmark.p',fact_ord__eq__less__trans) ).

fof(fact_xt1_I9_J,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
       => ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ),
    file('theBenchmark.p',fact_xt1_I9_J) ).

fof(fact_order__less__asym_H,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
       => ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ),
    file('theBenchmark.p',fact_order__less__asym_H) ).

fof(fact_order__less__imp__not__eq2,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
       => V_y != V_x ) ),
    file('theBenchmark.p',fact_order__less__imp__not__eq2) ).

fof(fact_order__less__imp__not__eq,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
       => V_x != V_y ) ),
    file('theBenchmark.p',fact_order__less__imp__not__eq) ).

fof(fact_order__less__imp__not__less,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
       => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ),
    file('theBenchmark.p',fact_order__less__imp__not__less) ).

fof(fact_order__less__not__sym,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
       => ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ),
    file('theBenchmark.p',fact_order__less__not__sym) ).

fof(fact_less__imp__neq,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
       => V_x != V_y ) ),
    file('theBenchmark.p',fact_less__imp__neq) ).

fof(fact_linorder__neqE,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( V_x != V_y
       => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
         => c_Orderings_Oord__class_Oless(T_a,V_y,V_x) ) ) ),
    file('theBenchmark.p',fact_linorder__neqE) ).

fof(fact_linorder__antisym__conv3,axiom,
    ! [V_x_2,V_y_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
       => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
        <=> V_x_2 = V_y_2 ) ) ),
    file('theBenchmark.p',fact_linorder__antisym__conv3) ).

fof(fact_linorder__less__linear,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
        | V_x = V_y
        | c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ),
    file('theBenchmark.p',fact_linorder__less__linear) ).

fof(fact_one__reorient,axiom,
    ! [V_x_2,T_a] :
      ( class_Groups_Oone(T_a)
     => ( c_Groups_Oone__class_Oone(T_a) = V_x_2
      <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ),
    file('theBenchmark.p',fact_one__reorient) ).

fof(fact_not__less__iff__gr__or__eq,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
      <=> ( V_x_2 = V_y_2
          | c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ),
    file('theBenchmark.p',fact_not__less__iff__gr__or__eq) ).

fof(fact_linorder__neq__iff,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( V_x_2 != V_y_2
      <=> ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
          | c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) ) ),
    file('theBenchmark.p',fact_linorder__neq__iff) ).

fof(fact_order__less__irrefl,axiom,
    ! [V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_x) ),
    file('theBenchmark.p',fact_order__less__irrefl) ).

fof(fact_norm__one,axiom,
    ! [T_a] :
      ( class_RealVector_Oreal__normed__algebra__1(T_a)
     => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    file('theBenchmark.p',fact_norm__one) ).

fof(fact_nat__less__cases,axiom,
    ! [V_P_2,V_n_2,V_m_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
       => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
     => ( ( V_m_2 = V_n_2
         => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
       => ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
           => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
         => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ),
    file('theBenchmark.p',fact_nat__less__cases) ).

fof(fact_less__not__refl3,axiom,
    ! [V_t,V_s] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)
     => V_s != V_t ),
    file('theBenchmark.p',fact_less__not__refl3) ).

fof(fact_less__not__refl2,axiom,
    ! [V_m,V_n] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
     => V_m != V_n ),
    file('theBenchmark.p',fact_less__not__refl2) ).

fof(fact_less__irrefl__nat,axiom,
    ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n),
    file('theBenchmark.p',fact_less__irrefl__nat) ).

fof(fact_linorder__neqE__nat,axiom,
    ! [V_y,V_x] :
      ( V_x != V_y
     => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x) ) ),
    file('theBenchmark.p',fact_linorder__neqE__nat) ).

fof(fact_nat__neq__iff,axiom,
    ! [V_n_2,V_m_2] :
      ( V_m_2 != V_n_2
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ),
    file('theBenchmark.p',fact_nat__neq__iff) ).

fof(fact_less__not__refl,axiom,
    ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n),
    file('theBenchmark.p',fact_less__not__refl) ).

fof(fact_zero__less__two,axiom,
    ! [T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))) ),
    file('theBenchmark.p',fact_zero__less__two) ).

fof(fact_one__poly__def,axiom,
    ! [T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ),
    file('theBenchmark.p',fact_one__poly__def) ).

fof(fact_xt1_I8_J,axiom,
    ! [V_z,V_x,V_y,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
       => ( c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
         => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ),
    file('theBenchmark.p',fact_xt1_I8_J) ).

fof(fact_order__le__less__trans,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
       => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
         => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ),
    file('theBenchmark.p',fact_order__le__less__trans) ).

fof(fact_xt1_I7_J,axiom,
    ! [V_z,V_x,V_y,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
         => c_Orderings_Oord__class_Oless(T_a,V_z,V_x) ) ) ),
    file('theBenchmark.p',fact_xt1_I7_J) ).

fof(fact_order__less__le__trans,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
         => c_Orderings_Oord__class_Oless(T_a,V_x,V_z) ) ) ),
    file('theBenchmark.p',fact_order__less__le__trans) ).

fof(fact_xt1_I11_J,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
       => ( V_a != V_b
         => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ),
    file('theBenchmark.p',fact_xt1_I11_J) ).

fof(fact_order__le__neq__trans,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
       => ( V_a != V_b
         => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
    file('theBenchmark.p',fact_order__le__neq__trans) ).

fof(fact_order__le__imp__less__or__eq,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
       => ( V_x = V_y
          | c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ) ),
    file('theBenchmark.p',fact_order__le__imp__less__or__eq) ).

fof(fact_linorder__antisym__conv2,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
       => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
        <=> V_x_2 = V_y_2 ) ) ),
    file('theBenchmark.p',fact_linorder__antisym__conv2) ).

fof(fact_order__less__imp__le,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
       => c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
    file('theBenchmark.p',fact_order__less__imp__le) ).

fof(fact_leD,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
       => ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ),
    file('theBenchmark.p',fact_leD) ).

fof(fact_xt1_I12_J,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( V_a != V_b
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
         => c_Orderings_Oord__class_Oless(T_a,V_b,V_a) ) ) ),
    file('theBenchmark.p',fact_xt1_I12_J) ).

fof(fact_order__neq__le__trans,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( V_a != V_b
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
         => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
    file('theBenchmark.p',fact_order__neq__le__trans) ).

fof(fact_linorder__antisym__conv1,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
        <=> V_x_2 = V_y_2 ) ) ),
    file('theBenchmark.p',fact_linorder__antisym__conv1) ).

fof(fact_not__leE,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
       => c_Orderings_Oord__class_Oless(T_a,V_x,V_y) ) ),
    file('theBenchmark.p',fact_not__leE) ).

fof(fact_leI,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
       => c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ),
    file('theBenchmark.p',fact_leI) ).

fof(fact_order__le__less,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
      <=> ( V_x_2 = V_y_2
          | c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) ) ),
    file('theBenchmark.p',fact_order__le__less) ).

fof(fact_less__le__not__le,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Orderings_Opreorder(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
      <=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
          & c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) ) ),
    file('theBenchmark.p',fact_less__le__not__le) ).

fof(fact_order__less__le,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
      <=> ( V_x_2 != V_y_2
          & c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) ) ),
    file('theBenchmark.p',fact_order__less__le) ).

fof(fact_linorder__le__less__linear,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
        | c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
    file('theBenchmark.p',fact_linorder__le__less__linear) ).

fof(fact_linorder__not__le,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
      <=> c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ),
    file('theBenchmark.p',fact_linorder__not__le) ).

fof(fact_linorder__not__less,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
      <=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ),
    file('theBenchmark.p',fact_linorder__not__less) ).

fof(fact_one__neq__zero,axiom,
    ! [T_a] :
      ( class_Rings_Ozero__neq__one(T_a)
     => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_one__neq__zero) ).

fof(fact_zero__neq__one,axiom,
    ! [T_a] :
      ( class_Rings_Ozero__neq__one(T_a)
     => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_zero__neq__one) ).

fof(fact_add__less__imp__less__left,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
       => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ),
    file('theBenchmark.p',fact_add__less__imp__less__left) ).

fof(fact_add__less__imp__less__right,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
       => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ),
    file('theBenchmark.p',fact_add__less__imp__less__right) ).

fof(fact_add__strict__mono,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
       => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
         => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ),
    file('theBenchmark.p',fact_add__strict__mono) ).

fof(fact_add__strict__left__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
       => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)) ) ),
    file('theBenchmark.p',fact_add__strict__left__mono) ).

fof(fact_add__strict__right__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
       => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ),
    file('theBenchmark.p',fact_add__strict__right__mono) ).

fof(fact_add__less__cancel__left,axiom,
    ! [V_b_2,V_ab_2,V_ca_2,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))
      <=> c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2) ) ),
    file('theBenchmark.p',fact_add__less__cancel__left) ).

fof(fact_add__less__cancel__right,axiom,
    ! [V_b_2,V_ca_2,V_ab_2,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))
      <=> c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2) ) ),
    file('theBenchmark.p',fact_add__less__cancel__right) ).

fof(fact_diff__eq__diff__less,axiom,
    ! [V_db_2,V_ca_2,V_b_2,V_ab_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2) = c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_db_2)
       => ( c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2)
        <=> c_Orderings_Oord__class_Oless(T_a,V_ca_2,V_db_2) ) ) ),
    file('theBenchmark.p',fact_diff__eq__diff__less) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).

fof(fact_mult_Ocomm__neutral,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ocomm__monoid__mult(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
    file('theBenchmark.p',fact_mult_Ocomm__neutral) ).

fof(fact_mult__1__right,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ),
    file('theBenchmark.p',fact_mult__1__right) ).

fof(fact_mult__1,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ocomm__monoid__mult(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ),
    file('theBenchmark.p',fact_mult__1) ).

fof(fact_mult__1__left,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ),
    file('theBenchmark.p',fact_mult__1__left) ).

fof(fact_gr0I,axiom,
    ! [V_n] :
      ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
    file('theBenchmark.p',fact_gr0I) ).

fof(fact_gr__implies__not0,axiom,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
     => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_gr__implies__not0) ).

fof(fact_less__nat__zero__code,axiom,
    ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_less__nat__zero__code) ).

fof(fact_neq0__conv,axiom,
    ! [V_n_2] :
      ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ),
    file('theBenchmark.p',fact_neq0__conv) ).

fof(fact_not__less0,axiom,
    ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_not__less0) ).

fof(fact_add__lessD1,axiom,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k) ),
    file('theBenchmark.p',fact_add__lessD1) ).

fof(fact_less__add__eq__less,axiom,
    ! [V_n,V_m,V_l,V_k] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
     => ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ),
    file('theBenchmark.p',fact_less__add__eq__less) ).

fof(fact_add__less__mono,axiom,
    ! [V_l,V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)) ) ),
    file('theBenchmark.p',fact_add__less__mono) ).

fof(fact_add__less__mono1,axiom,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)) ),
    file('theBenchmark.p',fact_add__less__mono1) ).

fof(fact_trans__less__add2,axiom,
    ! [V_m,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)) ),
    file('theBenchmark.p',fact_trans__less__add2) ).

fof(fact_trans__less__add1,axiom,
    ! [V_m,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)) ),
    file('theBenchmark.p',fact_trans__less__add1) ).

fof(fact_nat__add__left__cancel__less,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ),
    file('theBenchmark.p',fact_nat__add__left__cancel__less) ).

fof(fact_not__add__less2,axiom,
    ! [V_i,V_j] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i),
    file('theBenchmark.p',fact_not__add__less2) ).

fof(fact_not__add__less1,axiom,
    ! [V_j,V_i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i),
    file('theBenchmark.p',fact_not__add__less1) ).

fof(fact_termination__basic__simps_I2_J,axiom,
    ! [V_y,V_z,V_x] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ),
    file('theBenchmark.p',fact_termination__basic__simps_I2_J) ).

fof(fact_termination__basic__simps_I1_J,axiom,
    ! [V_z,V_y,V_x] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ),
    file('theBenchmark.p',fact_termination__basic__simps_I1_J) ).

fof(fact_nat__less__le,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
    <=> ( V_m_2 != V_n_2
        & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ),
    file('theBenchmark.p',fact_nat__less__le) ).

fof(fact_le__eq__less__or__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
    <=> ( V_m_2 = V_n_2
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ),
    file('theBenchmark.p',fact_le__eq__less__or__eq) ).

fof(fact_less__imp__le__nat,axiom,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
    file('theBenchmark.p',fact_less__imp__le__nat) ).

fof(fact_le__neq__implies__less,axiom,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
     => ( V_m != V_n
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ),
    file('theBenchmark.p',fact_le__neq__implies__less) ).

fof(fact_less__or__eq__imp__le,axiom,
    ! [V_n,V_m] :
      ( ( V_m = V_n
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) )
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
    file('theBenchmark.p',fact_less__or__eq__imp__le) ).

fof(fact_termination__basic__simps_I5_J,axiom,
    ! [V_y,V_x] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y) ),
    file('theBenchmark.p',fact_termination__basic__simps_I5_J) ).

fof(fact_diff__less__mono2,axiom,
    ! [V_l,V_n,V_m] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)) ) ),
    file('theBenchmark.p',fact_diff__less__mono2) ).

fof(fact_less__imp__diff__less,axiom,
    ! [V_n,V_k,V_j] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k) ),
    file('theBenchmark.p',fact_less__imp__diff__less) ).

fof(fact_nat__mult__eq__1__iff,axiom,
    ! [V_n_2,V_m_2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    <=> ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        & V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__mult__eq__1__iff) ).

fof(fact_nat__mult__1__right,axiom,
    ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n,
    file('theBenchmark.p',fact_nat__mult__1__right) ).

fof(fact_nat__1__eq__mult__iff,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
    <=> ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        & V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__1__eq__mult__iff) ).

fof(fact_nat__mult__1,axiom,
    ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n,
    file('theBenchmark.p',fact_nat__mult__1) ).

fof(fact_smult__1__left,axiom,
    ! [V_p,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => c_Polynomial_Osmult(T_a,c_Groups_Oone__class_Oone(T_a),V_p) = V_p ),
    file('theBenchmark.p',fact_smult__1__left) ).

fof(fact_convex__bound__lt,axiom,
    ! [V_v,V_u,V_y,V_a,V_x,T_a] :
      ( class_Rings_Olinordered__semiring__1__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_x,V_a)
       => ( c_Orderings_Oord__class_Oless(T_a,V_y,V_a)
         => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
           => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
             => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
               => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a) ) ) ) ) ) ),
    file('theBenchmark.p',fact_convex__bound__lt) ).

fof(fact_not__square__less__zero,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__ring(T_a)
     => ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) ),
    file('theBenchmark.p',fact_not__square__less__zero) ).

fof(fact_mult__less__cancel__right__disj,axiom,
    ! [V_b_2,V_ca_2,V_ab_2,T_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))
      <=> ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_ab_2)
            & c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) )
          | ( c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2)
            & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) ) ) ) ),
    file('theBenchmark.p',fact_mult__less__cancel__right__disj) ).

fof(fact_mult__less__cancel__left__disj,axiom,
    ! [V_b_2,V_ab_2,V_ca_2,T_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
      <=> ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_ab_2)
            & c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) )
          | ( c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2)
            & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) ) ) ) ),
    file('theBenchmark.p',fact_mult__less__cancel__left__disj) ).

fof(fact_mult__less__cancel__left__pos,axiom,
    ! [V_b_2,V_ab_2,V_ca_2,T_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
       => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
        <=> c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2) ) ) ),
    file('theBenchmark.p',fact_mult__less__cancel__left__pos) ).

fof(fact_mult__pos__pos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
       => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
         => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_mult__pos__pos) ).

fof(fact_mult__pos__neg,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
       => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
         => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
    file('theBenchmark.p',fact_mult__pos__neg) ).

fof(fact_mult__pos__neg2,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
       => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
         => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
    file('theBenchmark.p',fact_mult__pos__neg2) ).

fof(fact_zero__less__mult__pos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
       => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
         => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ),
    file('theBenchmark.p',fact_zero__less__mult__pos) ).

fof(fact_zero__less__mult__pos2,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))
       => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
         => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b) ) ) ),
    file('theBenchmark.p',fact_zero__less__mult__pos2) ).

fof(fact_mult__less__cancel__left__neg,axiom,
    ! [V_b_2,V_ab_2,V_ca_2,T_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
       => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
        <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,V_ab_2) ) ) ),
    file('theBenchmark.p',fact_mult__less__cancel__left__neg) ).

fof(fact_mult__neg__pos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
       => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
         => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
    file('theBenchmark.p',fact_mult__neg__pos) ).

fof(fact_mult__neg__neg,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
       => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
         => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_mult__neg__neg) ).

fof(fact_mult__strict__right__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
       => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
         => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ),
    file('theBenchmark.p',fact_mult__strict__right__mono) ).

fof(fact_mult__strict__left__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
       => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
         => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ),
    file('theBenchmark.p',fact_mult__strict__left__mono) ).

fof(fact_comm__mult__strict__left__mono,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__comm__semiring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
       => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
         => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ),
    file('theBenchmark.p',fact_comm__mult__strict__left__mono) ).

fof(fact_mult__strict__right__mono__neg,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
       => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
         => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ),
    file('theBenchmark.p',fact_mult__strict__right__mono__neg) ).

fof(fact_mult__strict__left__mono__neg,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
       => ( c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
         => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ),
    file('theBenchmark.p',fact_mult__strict__left__mono__neg) ).

fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
    ! [V_ab_2,T_a] :
      ( class_Groups_Olinordered__ab__group__add(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2))
      <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) ) ),
    file('theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).

fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
    ! [V_ab_2,T_a] :
      ( class_Groups_Olinordered__ab__group__add(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2),c_Groups_Ozero__class_Ozero(T_a))
      <=> c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
    file('theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).

fof(fact_add__pos__pos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
       => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
         => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ),
    file('theBenchmark.p',fact_add__pos__pos) ).

fof(fact_add__neg__neg,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
       => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
         => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
    file('theBenchmark.p',fact_add__neg__neg) ).

fof(fact_even__less__0__iff,axiom,
    ! [V_ab_2,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2),c_Groups_Ozero__class_Ozero(T_a))
      <=> c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
    file('theBenchmark.p',fact_even__less__0__iff) ).

fof(fact_pos__add__strict,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
       => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
         => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
    file('theBenchmark.p',fact_pos__add__strict) ).

fof(fact_add__le__less__mono,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
       => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
         => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ),
    file('theBenchmark.p',fact_add__le__less__mono) ).

fof(fact_add__less__le__mono,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
         => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ) ) ),
    file('theBenchmark.p',fact_add__less__le__mono) ).

fof(fact_less__iff__diff__less__0,axiom,
    ! [V_b_2,V_ab_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2)
      <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) ),
    file('theBenchmark.p',fact_less__iff__diff__less__0) ).

fof(fact_not__one__le__zero,axiom,
    ! [T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)) ),
    file('theBenchmark.p',fact_not__one__le__zero) ).

fof(fact_zero__le__one,axiom,
    ! [T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)) ),
    file('theBenchmark.p',fact_zero__le__one) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
    ! [V_m,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,V_m,V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_m) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
    ! [V_a,V_m,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
    ! [V_m,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).

fof(fact_add__gr__0,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) ) ),
    file('theBenchmark.p',fact_add__gr__0) ).

fof(fact_nat__mult__eq__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
      <=> V_m_2 = V_n_2 ) ),
    file('theBenchmark.p',fact_nat__mult__eq__cancel1) ).

fof(fact_nat__mult__less__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
      <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ),
    file('theBenchmark.p',fact_nat__mult__less__cancel1) ).

fof(fact_nat__0__less__mult__iff,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) ) ),
    file('theBenchmark.p',fact_nat__0__less__mult__iff) ).

fof(fact_mult__less__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) ) ),
    file('theBenchmark.p',fact_mult__less__cancel1) ).

fof(fact_mult__less__cancel2,axiom,
    ! [V_n_2,V_k_2,V_m_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) ) ),
    file('theBenchmark.p',fact_mult__less__cancel2) ).

fof(fact_mult__less__mono1,axiom,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)) ) ),
    file('theBenchmark.p',fact_mult__less__mono1) ).

fof(fact_mult__less__mono2,axiom,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)) ) ),
    file('theBenchmark.p',fact_mult__less__mono2) ).

fof(fact_zero__less__diff,axiom,
    ! [V_m_2,V_n_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ),
    file('theBenchmark.p',fact_zero__less__diff) ).

fof(fact_diff__less,axiom,
    ! [V_m,V_n] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m) ) ),
    file('theBenchmark.p',fact_diff__less) ).

fof(fact_add__diff__inverse,axiom,
    ! [V_n,V_m] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
     => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ),
    file('theBenchmark.p',fact_add__diff__inverse) ).

fof(fact_less__diff__conv,axiom,
    ! [V_k_2,V_j_2,V_i_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) ),
    file('theBenchmark.p',fact_less__diff__conv) ).

fof(fact_diff__less__mono,axiom,
    ! [V_c,V_b,V_a] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c,V_a)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c)) ) ),
    file('theBenchmark.p',fact_diff__less__mono) ).

fof(fact_less__diff__iff,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
       => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))
        <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ) ),
    file('theBenchmark.p',fact_less__diff__iff) ).

fof(fact_mult__eq__self__implies__10,axiom,
    ! [V_n,V_m] :
      ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
     => ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_mult__eq__self__implies__10) ).

fof(fact_mult__le__cancel__left__pos,axiom,
    ! [V_b_2,V_ab_2,V_ca_2,T_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
        <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2) ) ) ),
    file('theBenchmark.p',fact_mult__le__cancel__left__pos) ).

fof(fact_mult__le__cancel__left__neg,axiom,
    ! [V_b_2,V_ab_2,V_ca_2,T_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
       => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
        <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_ab_2) ) ) ),
    file('theBenchmark.p',fact_mult__le__cancel__left__neg) ).

fof(fact_mult__strict__mono,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
       => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
         => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
           => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
             => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ),
    file('theBenchmark.p',fact_mult__strict__mono) ).

fof(fact_mult__strict__mono_H,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
       => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
         => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
           => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
             => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ),
    file('theBenchmark.p',fact_mult__strict__mono_H) ).

fof(fact_mult__less__le__imp__less,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
         => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
           => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
             => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ),
    file('theBenchmark.p',fact_mult__less__le__imp__less) ).

fof(fact_mult__le__less__imp__less,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
       => ( c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
         => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
           => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
             => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ),
    file('theBenchmark.p',fact_mult__le__less__imp__less) ).

fof(fact_mult__right__less__imp__less,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Rings_Olinordered__semiring(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
       => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
         => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
    file('theBenchmark.p',fact_mult__right__less__imp__less) ).

fof(fact_mult__less__imp__less__right,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
       => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
         => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
    file('theBenchmark.p',fact_mult__less__imp__less__right) ).

fof(fact_mult__left__less__imp__less,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Rings_Olinordered__semiring(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
       => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
         => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
    file('theBenchmark.p',fact_mult__left__less__imp__less) ).

fof(fact_mult__less__imp__less__left,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
       => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
         => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
    file('theBenchmark.p',fact_mult__less__imp__less__left) ).

fof(fact_mult__right__le__imp__le,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
       => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
         => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ),
    file('theBenchmark.p',fact_mult__right__le__imp__le) ).

fof(fact_mult__left__le__imp__le,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Rings_Olinordered__semiring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
       => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
         => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ),
    file('theBenchmark.p',fact_mult__left__le__imp__le) ).

fof(fact_add__nonpos__neg,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
       => ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
         => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
    file('theBenchmark.p',fact_add__nonpos__neg) ).

fof(fact_add__neg__nonpos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
         => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
    file('theBenchmark.p',fact_add__neg__nonpos) ).

fof(fact_add__strict__increasing2,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
       => ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
         => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
    file('theBenchmark.p',fact_add__strict__increasing2) ).

fof(fact_add__strict__increasing,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
         => c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
    file('theBenchmark.p',fact_add__strict__increasing) ).

fof(fact_add__nonneg__pos,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
       => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
         => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ),
    file('theBenchmark.p',fact_add__nonneg__pos) ).

fof(fact_add__pos__nonneg,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__comm__monoid__add(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
         => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ),
    file('theBenchmark.p',fact_add__pos__nonneg) ).

fof(fact_not__sum__squares__lt__zero,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__ring(T_a)
     => ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a)) ),
    file('theBenchmark.p',fact_not__sum__squares__lt__zero) ).

fof(fact_sum__squares__gt__zero__iff,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Rings_Olinordered__ring__strict(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))
      <=> ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_sum__squares__gt__zero__iff) ).

fof(fact_mult__right__le__one__le,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
         => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
           => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),V_x) ) ) ) ),
    file('theBenchmark.p',fact_mult__right__le__one__le) ).

fof(fact_mult__left__le__one__le,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
         => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
           => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x) ) ) ) ),
    file('theBenchmark.p',fact_mult__left__le__one__le) ).

fof(fact_less__add__iff2,axiom,
    ! [V_db_2,V_b_2,V_ca_2,V_e_2,V_ab_2,T_a] :
      ( class_Rings_Oordered__ring(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2))
      <=> c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_ab_2)),V_e_2),V_db_2)) ) ),
    file('theBenchmark.p',fact_less__add__iff2) ).

fof(fact_less__add__iff1,axiom,
    ! [V_db_2,V_b_2,V_ca_2,V_e_2,V_ab_2,T_a] :
      ( class_Rings_Oordered__ring(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2))
      <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2)),V_e_2),V_ca_2),V_db_2) ) ),
    file('theBenchmark.p',fact_less__add__iff1) ).

fof(fact_real__squared__diff__one__factored,axiom,
    ! [V_x,T_a] :
      ( class_Rings_Oring__1(T_a)
     => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))) ),
    file('theBenchmark.p',fact_real__squared__diff__one__factored) ).

fof(fact_nat__mult__le__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ),
    file('theBenchmark.p',fact_nat__mult__le__cancel1) ).

fof(fact_mult__le__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ),
    file('theBenchmark.p',fact_mult__le__cancel1) ).

fof(fact_mult__le__cancel2,axiom,
    ! [V_n_2,V_k_2,V_m_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ),
    file('theBenchmark.p',fact_mult__le__cancel2) ).

fof(fact_nat__diff__split__asm,axiom,
    ! [V_b_2,V_ab_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ab_2,V_b_2)))
    <=> ~ ( ? [B_d] :
              ( ~ hBOOL(hAPP(V_P_2,B_d))
              & V_ab_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d) )
          | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ab_2,V_b_2) ) ) ),
    file('theBenchmark.p',fact_nat__diff__split__asm) ).

fof(fact_nat__diff__split,axiom,
    ! [V_b_2,V_ab_2,V_P_2] :
      ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ab_2,V_b_2)))
    <=> ( ! [B_d] :
            ( V_ab_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)
           => hBOOL(hAPP(V_P_2,B_d)) )
        & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ab_2,V_b_2)
         => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('theBenchmark.p',fact_nat__diff__split) ).

fof(fact_convex__bound__le,axiom,
    ! [V_v,V_u,V_y,V_a,V_x,T_a] :
      ( class_Rings_Olinordered__semiring__1(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_a)
         => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
           => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
             => ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
               => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a) ) ) ) ) ) ),
    file('theBenchmark.p',fact_convex__bound__le) ).

fof(fact_synthetic__div__correct_H,axiom,
    ! [V_p,V_c,T_a] :
      ( class_Rings_Ocomm__ring__1(T_a)
     => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_c),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)),c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) = V_p ),
    file('theBenchmark.p',fact_synthetic__div__correct_H) ).

fof(fact_pos__poly__pCons,axiom,
    ! [V_pa_2,V_ab_2,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_ab_2,V_pa_2))
      <=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2)
            & V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
          | c_Polynomial_Opos__poly(T_a,V_pa_2) ) ) ),
    file('theBenchmark.p',fact_pos__poly__pCons) ).

fof(fact_ex__least__nat__less,axiom,
    ! [V_n_2,V_P_2] :
      ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
     => ( hBOOL(hAPP(V_P_2,V_n_2))
       => ? [B_k] :
            ( hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B_k,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
            & ! [B_i] :
                ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i,B_k)
               => ~ hBOOL(hAPP(V_P_2,B_i)) )
            & c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k,V_n_2) ) ) ),
    file('theBenchmark.p',fact_ex__least__nat__less) ).

fof(fact_realpow__minus__mult,axiom,
    ! [V_x,V_n,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n) ) ),
    file('theBenchmark.p',fact_realpow__minus__mult) ).

fof(fact_le__mult__natfloor,axiom,
    ! [V_b,V_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_b)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(V_a)),c_RComplete_Onatfloor(V_b)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_le__mult__natfloor) ).

fof(fact_add__eq__if,axiom,
    ! [V_n,V_m] :
      ( ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) )
      & ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_n ) ),
    file('theBenchmark.p',fact_add__eq__if) ).

fof(fact_lessI,axiom,
    ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)),
    file('theBenchmark.p',fact_lessI) ).

fof(fact_Suc__mono,axiom,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) ),
    file('theBenchmark.p',fact_Suc__mono) ).

fof(fact_zero__less__Suc,axiom,
    ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)),
    file('theBenchmark.p',fact_zero__less__Suc) ).

fof(fact_less__poly__def,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)
      <=> c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_less__poly__def) ).

fof(fact_natfloor__one,axiom,
    c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    file('theBenchmark.p',fact_natfloor__one) ).

fof(fact_n__not__Suc__n,axiom,
    ! [V_n] : V_n != c_Nat_OSuc(V_n),
    file('theBenchmark.p',fact_n__not__Suc__n) ).

fof(fact_Suc__n__not__n,axiom,
    ! [V_n] : c_Nat_OSuc(V_n) != V_n,
    file('theBenchmark.p',fact_Suc__n__not__n) ).

fof(fact_nat_Oinject,axiom,
    ! [V_nat_H_2,V_nat_2] :
      ( c_Nat_OSuc(V_nat_2) = c_Nat_OSuc(V_nat_H_2)
    <=> V_nat_2 = V_nat_H_2 ),
    file('theBenchmark.p',fact_nat_Oinject) ).

fof(fact_Suc__inject,axiom,
    ! [V_y,V_x] :
      ( c_Nat_OSuc(V_x) = c_Nat_OSuc(V_y)
     => V_x = V_y ),
    file('theBenchmark.p',fact_Suc__inject) ).

fof(fact_smult__minus__left,axiom,
    ! [V_p,V_a,T_a] :
      ( class_Rings_Ocomm__ring(T_a)
     => c_Polynomial_Osmult(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_p) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p)) ),
    file('theBenchmark.p',fact_smult__minus__left) ).

fof(fact_minus__pCons,axiom,
    ! [V_p,V_a,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)) ),
    file('theBenchmark.p',fact_minus__pCons) ).

fof(fact_minus__poly__code_I2_J,axiom,
    ! [V_p,V_a,T_b] :
      ( class_Groups_Oab__group__add(T_b)
     => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b,V_a,V_p)) = c_Polynomial_OpCons(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),V_p)) ),
    file('theBenchmark.p',fact_minus__poly__code_I2_J) ).

fof(fact_minus__minus,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = V_a ),
    file('theBenchmark.p',fact_minus__minus) ).

fof(fact_equation__minus__iff,axiom,
    ! [V_b_2,V_ab_2,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => ( V_ab_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
      <=> V_b_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2) ) ),
    file('theBenchmark.p',fact_equation__minus__iff) ).

fof(fact_minus__equation__iff,axiom,
    ! [V_b_2,V_ab_2,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => ( c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2) = V_b_2
      <=> c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) = V_ab_2 ) ),
    file('theBenchmark.p',fact_minus__equation__iff) ).

fof(fact_neg__equal__iff__equal,axiom,
    ! [V_b_2,V_ab_2,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => ( c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
      <=> V_ab_2 = V_b_2 ) ),
    file('theBenchmark.p',fact_neg__equal__iff__equal) ).

fof(fact_norm__power,axiom,
    ! [V_n,V_x,T_a] :
      ( class_RealVector_Oreal__normed__div__algebra(T_a)
     => c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n) ),
    file('theBenchmark.p',fact_norm__power) ).

fof(fact_realpow__two__disj,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Rings_Oidom(T_a)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
      <=> ( V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
          | V_x_2 = V_y_2 ) ) ),
    file('theBenchmark.p',fact_realpow__two__disj) ).

fof(fact_pos__poly__total,axiom,
    ! [V_p,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( c_Polynomial_Opos__poly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p))
        | c_Polynomial_Opos__poly(T_a,V_p)
        | V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
    file('theBenchmark.p',fact_pos__poly__total) ).

fof(fact_minus__monom,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_n) ),
    file('theBenchmark.p',fact_minus__monom) ).

fof(fact_poly__power,axiom,
    ! [V_x,V_n,V_p,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),V_p),V_n)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),V_n) ),
    file('theBenchmark.p',fact_poly__power) ).

fof(fact_poly__minus,axiom,
    ! [V_x,V_p,T_a] :
      ( class_Rings_Ocomm__ring(T_a)
     => hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_x) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)) ),
    file('theBenchmark.p',fact_poly__minus) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
    ! [V_q,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
    ! [V_q,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
    ! [V_q,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).

fof(fact_norm__power__ineq,axiom,
    ! [V_n,V_x,T_a] :
      ( class_RealVector_Oreal__normed__algebra__1(T_a)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n)) ),
    file('theBenchmark.p',fact_norm__power__ineq) ).

fof(fact_real__0__less__add__iff,axiom,
    ! [V_y_2,V_x_2] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) ),
    file('theBenchmark.p',fact_real__0__less__add__iff) ).

fof(fact_real__add__less__0__iff,axiom,
    ! [V_y_2,V_x_2] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) ),
    file('theBenchmark.p',fact_real__add__less__0__iff) ).

fof(fact_neg__equal__zero,axiom,
    ! [V_ab_2,T_a] :
      ( class_Groups_Olinordered__ab__group__add(T_a)
     => ( c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2) = V_ab_2
      <=> V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_neg__equal__zero) ).

fof(fact_neg__equal__0__iff__equal,axiom,
    ! [V_ab_2,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => ( c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a)
      <=> V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_neg__equal__0__iff__equal) ).

fof(fact_equal__neg__zero,axiom,
    ! [V_ab_2,T_a] :
      ( class_Groups_Olinordered__ab__group__add(T_a)
     => ( V_ab_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2)
      <=> V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_equal__neg__zero) ).

fof(fact_neg__0__equal__iff__equal,axiom,
    ! [V_ab_2,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2)
      <=> c_Groups_Ozero__class_Ozero(T_a) = V_ab_2 ) ),
    file('theBenchmark.p',fact_neg__0__equal__iff__equal) ).

fof(fact_minus__zero,axiom,
    ! [T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_minus__zero) ).

fof(fact_le__minus__iff,axiom,
    ! [V_b_2,V_ab_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
      <=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2)) ) ),
    file('theBenchmark.p',fact_le__minus__iff) ).

fof(fact_minus__le__iff,axiom,
    ! [V_b_2,V_ab_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2),V_b_2)
      <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_ab_2) ) ),
    file('theBenchmark.p',fact_minus__le__iff) ).

fof(fact_neg__le__iff__le,axiom,
    ! [V_ab_2,V_b_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2))
      <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2) ) ),
    file('theBenchmark.p',fact_neg__le__iff__le) ).

fof(fact_le__imp__neg__le,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
       => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)) ) ),
    file('theBenchmark.p',fact_le__imp__neg__le) ).

fof(fact_less__minus__iff,axiom,
    ! [V_b_2,V_ab_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
      <=> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2)) ) ),
    file('theBenchmark.p',fact_less__minus__iff) ).

fof(fact_minus__less__iff,axiom,
    ! [V_b_2,V_ab_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2),V_b_2)
      <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_ab_2) ) ),
    file('theBenchmark.p',fact_minus__less__iff) ).

fof(fact_neg__less__iff__less,axiom,
    ! [V_ab_2,V_b_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2))
      <=> c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2) ) ),
    file('theBenchmark.p',fact_neg__less__iff__less) ).

fof(fact_minus__mult__right,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oring(T_a)
     => c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ),
    file('theBenchmark.p',fact_minus__mult__right) ).

fof(fact_minus__mult__left,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oring(T_a)
     => c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) ),
    file('theBenchmark.p',fact_minus__mult__left) ).

fof(fact_minus__mult__commute,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ),
    file('theBenchmark.p',fact_minus__mult__commute) ).

fof(fact_minus__mult__minus,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Oring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ),
    file('theBenchmark.p',fact_minus__mult__minus) ).

fof(fact_square__eq__iff,axiom,
    ! [V_b_2,V_ab_2,T_a] :
      ( class_Rings_Oidom(T_a)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ab_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)
      <=> ( V_ab_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
          | V_ab_2 = V_b_2 ) ) ),
    file('theBenchmark.p',fact_square__eq__iff) ).

fof(fact_mult_Ominus__right,axiom,
    ! [V_b,V_a,T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ),
    file('theBenchmark.p',fact_mult_Ominus__right) ).

fof(fact_mult__right_Ominus,axiom,
    ! [V_x,V_xa,T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)) ),
    file('theBenchmark.p',fact_mult__right_Ominus) ).

fof(fact_mult_Ominus__left,axiom,
    ! [V_b,V_a,T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ),
    file('theBenchmark.p',fact_mult_Ominus__left) ).

fof(fact_mult__left_Ominus,axiom,
    ! [V_y,V_x,T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_x)),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) ),
    file('theBenchmark.p',fact_mult__left_Ominus) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
    ! [V_q,V_y,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).

fof(fact_minus__add__distrib,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ),
    file('theBenchmark.p',fact_minus__add__distrib) ).

fof(fact_minus__add,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)) ),
    file('theBenchmark.p',fact_minus__add) ).

fof(fact_add__minus__cancel,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)) = V_b ),
    file('theBenchmark.p',fact_add__minus__cancel) ).

fof(fact_minus__add__cancel,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = V_b ),
    file('theBenchmark.p',fact_minus__add__cancel) ).

fof(fact_minus__diff__eq,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Ominus__class_Ominus(T_a,V_b,V_a) ),
    file('theBenchmark.p',fact_minus__diff__eq) ).

fof(fact_less__fun__def,axiom,
    ! [V_g_2,V_f_2,T_a,T_b] :
      ( class_Orderings_Oord(T_b)
     => ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)
      <=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2)
          & c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) ) ) ),
    file('theBenchmark.p',fact_less__fun__def) ).

fof(fact_zpower__zadd__distrib,axiom,
    ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)),
    file('theBenchmark.p',fact_zpower__zadd__distrib) ).

fof(fact_norm__minus__cancel,axiom,
    ! [V_x,T_a] :
      ( class_RealVector_Oreal__normed__vector(T_a)
     => c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_RealVector_Onorm__class_Onorm(T_a,V_x) ),
    file('theBenchmark.p',fact_norm__minus__cancel) ).

fof(fact_Zero__not__Suc,axiom,
    ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m),
    file('theBenchmark.p',fact_Zero__not__Suc) ).

fof(fact_nat_Osimps_I2_J,axiom,
    ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_nat_H),
    file('theBenchmark.p',fact_nat_Osimps_I2_J) ).

fof(fact_Suc__not__Zero,axiom,
    ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_Suc__not__Zero) ).

fof(fact_nat_Osimps_I3_J,axiom,
    ! [V_nat_H_1] : c_Nat_OSuc(V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_nat_Osimps_I3_J) ).

fof(fact_Zero__neq__Suc,axiom,
    ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m),
    file('theBenchmark.p',fact_Zero__neq__Suc) ).

fof(fact_Suc__neq__Zero,axiom,
    ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_Suc__neq__Zero) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
    ! [V_q,V_p,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).

fof(fact_zpower__zpower,axiom,
    ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)),
    file('theBenchmark.p',fact_zpower__zpower) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
    ! [V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).

fof(fact_not__less__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)) ),
    file('theBenchmark.p',fact_not__less__eq) ).

fof(fact_less__Suc__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
    <=> ( V_m_2 = V_n_2
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ),
    file('theBenchmark.p',fact_less__Suc__eq) ).

fof(fact_Suc__less__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_n_2))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ),
    file('theBenchmark.p',fact_Suc__less__eq) ).

fof(fact_not__less__less__Suc__eq,axiom,
    ! [V_m_2,V_n_2] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))
      <=> V_n_2 = V_m_2 ) ),
    file('theBenchmark.p',fact_not__less__less__Suc__eq) ).

fof(fact_less__antisym,axiom,
    ! [V_m,V_n] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))
       => V_m = V_n ) ),
    file('theBenchmark.p',fact_less__antisym) ).

fof(fact_less__SucI,axiom,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ),
    file('theBenchmark.p',fact_less__SucI) ).

fof(fact_Suc__lessI,axiom,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
     => ( c_Nat_OSuc(V_m) != V_n
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ) ),
    file('theBenchmark.p',fact_Suc__lessI) ).

fof(fact_less__trans__Suc,axiom,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k) ) ),
    file('theBenchmark.p',fact_less__trans__Suc) ).

fof(fact_less__SucE,axiom,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
     => ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
       => V_m = V_n ) ),
    file('theBenchmark.p',fact_less__SucE) ).

fof(fact_Suc__lessD,axiom,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
    file('theBenchmark.p',fact_Suc__lessD) ).

fof(fact_Suc__less__SucD,axiom,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
    file('theBenchmark.p',fact_Suc__less__SucD) ).

fof(fact_add__Suc__right,axiom,
    ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
    file('theBenchmark.p',fact_add__Suc__right) ).

fof(fact_add__Suc,axiom,
    ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
    file('theBenchmark.p',fact_add__Suc) ).

fof(fact_add__Suc__shift,axiom,
    ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)),
    file('theBenchmark.p',fact_add__Suc__shift) ).

fof(fact_Suc__leD,axiom,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
    file('theBenchmark.p',fact_Suc__leD) ).

fof(fact_le__SucE,axiom,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
     => ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
       => V_m = c_Nat_OSuc(V_n) ) ),
    file('theBenchmark.p',fact_le__SucE) ).

fof(fact_le__SucI,axiom,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ),
    file('theBenchmark.p',fact_le__SucI) ).

fof(fact_Suc__le__mono,axiom,
    ! [V_m_2,V_n_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ),
    file('theBenchmark.p',fact_Suc__le__mono) ).

fof(fact_le__Suc__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
    <=> ( V_m_2 = c_Nat_OSuc(V_n_2)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ),
    file('theBenchmark.p',fact_le__Suc__eq) ).

fof(fact_not__less__eq__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2) ),
    file('theBenchmark.p',fact_not__less__eq__eq) ).

fof(fact_Suc__n__not__le__n,axiom,
    ! [V_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n),
    file('theBenchmark.p',fact_Suc__n__not__le__n) ).

fof(fact_Suc__mult__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)
    <=> V_m_2 = V_n_2 ),
    file('theBenchmark.p',fact_Suc__mult__cancel1) ).

fof(fact_minus__poly__code_I1_J,axiom,
    ! [T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
    file('theBenchmark.p',fact_minus__poly__code_I1_J) ).

fof(fact_real__less__def,axiom,
    ! [V_y_2,V_x_2] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
    <=> ( V_x_2 != V_y_2
        & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
    file('theBenchmark.p',fact_real__less__def) ).

fof(fact_less__eq__real__def,axiom,
    ! [V_y_2,V_x_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
    <=> ( V_x_2 = V_y_2
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
    file('theBenchmark.p',fact_less__eq__real__def) ).

fof(fact_diff__Suc__Suc,axiom,
    ! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),
    file('theBenchmark.p',fact_diff__Suc__Suc) ).

fof(fact_Suc__diff__diff,axiom,
    ! [V_k,V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n),c_Nat_OSuc(V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k),
    file('theBenchmark.p',fact_Suc__diff__diff) ).

fof(fact_real__zero__not__eq__one,axiom,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    file('theBenchmark.p',fact_real__zero__not__eq__one) ).

fof(fact_real__mult__1,axiom,
    ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z) = V_z,
    file('theBenchmark.p',fact_real__mult__1) ).

fof(fact_smult__minus__right,axiom,
    ! [V_p,V_a,T_a] :
      ( class_Rings_Ocomm__ring(T_a)
     => c_Polynomial_Osmult(T_a,V_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p)) ),
    file('theBenchmark.p',fact_smult__minus__right) ).

fof(fact_le__natfloor__eq__one,axiom,
    ! [V_x_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_x_2))
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2) ),
    file('theBenchmark.p',fact_le__natfloor__eq__one) ).

fof(fact_realpow__Suc__le__self,axiom,
    ! [V_n,V_r,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,V_r,c_Groups_Oone__class_Oone(T_a))
         => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_r),c_Nat_OSuc(V_n)),V_r) ) ) ),
    file('theBenchmark.p',fact_realpow__Suc__le__self) ).

fof(fact_complex__diff__def,axiom,
    ! [V_y,V_x] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_x,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,V_y)),
    file('theBenchmark.p',fact_complex__diff__def) ).

fof(fact_natfloor__zero,axiom,
    c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_natfloor__zero) ).

fof(fact_zero__le__natfloor,axiom,
    ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),
    file('theBenchmark.p',fact_zero__le__natfloor) ).

fof(fact_natfloor__mono,axiom,
    ! [V_y,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y)) ),
    file('theBenchmark.p',fact_natfloor__mono) ).

fof(fact_realpow__two__diff,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Ocomm__ring__1(T_a)
     => c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) ),
    file('theBenchmark.p',fact_realpow__two__diff) ).

fof(fact_minus__le__self__iff,axiom,
    ! [V_ab_2,T_a] :
      ( class_Groups_Olinordered__ab__group__add(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2),V_ab_2)
      <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) ) ),
    file('theBenchmark.p',fact_minus__le__self__iff) ).

fof(fact_neg__le__0__iff__le,axiom,
    ! [V_ab_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2),c_Groups_Ozero__class_Ozero(T_a))
      <=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) ) ),
    file('theBenchmark.p',fact_neg__le__0__iff__le) ).

fof(fact_le__minus__self__iff,axiom,
    ! [V_ab_2,T_a] :
      ( class_Groups_Olinordered__ab__group__add(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2))
      <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
    file('theBenchmark.p',fact_le__minus__self__iff) ).

fof(fact_neg__0__le__iff__le,axiom,
    ! [V_ab_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2))
      <=> c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
    file('theBenchmark.p',fact_neg__0__le__iff__le) ).

fof(fact_neg__0__less__iff__less,axiom,
    ! [V_ab_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2))
      <=> c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
    file('theBenchmark.p',fact_neg__0__less__iff__less) ).

fof(fact_neg__less__0__iff__less,axiom,
    ! [V_ab_2,T_a] :
      ( class_Groups_Oordered__ab__group__add(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2),c_Groups_Ozero__class_Ozero(T_a))
      <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) ) ),
    file('theBenchmark.p',fact_neg__less__0__iff__less) ).

fof(fact_neg__less__nonneg,axiom,
    ! [V_ab_2,T_a] :
      ( class_Groups_Olinordered__ab__group__add(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2),V_ab_2)
      <=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) ) ),
    file('theBenchmark.p',fact_neg__less__nonneg) ).

fof(fact_less__minus__self__iff,axiom,
    ! [V_ab_2,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2))
      <=> c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
    file('theBenchmark.p',fact_less__minus__self__iff) ).

fof(fact_minus__unique,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Ozero__class_Ozero(T_a)
       => c_Groups_Ouminus__class_Ouminus(T_a,V_a) = V_b ) ),
    file('theBenchmark.p',fact_minus__unique) ).

fof(fact_add__eq__0__iff,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
      <=> V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) ) ),
    file('theBenchmark.p',fact_add__eq__0__iff) ).

fof(fact_ab__left__minus,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_ab__left__minus) ).

fof(fact_left__minus,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_left__minus) ).

fof(fact_eq__neg__iff__add__eq__0,axiom,
    ! [V_b_2,V_ab_2,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => ( V_ab_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
      <=> c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).

fof(fact_right__minus,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_right__minus) ).

fof(fact_diff__0,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ),
    file('theBenchmark.p',fact_diff__0) ).

fof(fact_square__eq__1__iff,axiom,
    ! [V_x_2,T_a] :
      ( class_Rings_Oring__1__no__zero__divisors(T_a)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a)
      <=> ( V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
          | V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ),
    file('theBenchmark.p',fact_square__eq__1__iff) ).

fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
    ! [V_x,T_a] :
      ( class_Rings_Ocomm__ring__1(T_a)
     => c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ),
    file('theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).

fof(fact_diff__def,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ),
    file('theBenchmark.p',fact_diff__def) ).

fof(fact_ab__diff__minus,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ),
    file('theBenchmark.p',fact_ab__diff__minus) ).

fof(fact_diff__minus__eq__add,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) ),
    file('theBenchmark.p',fact_diff__minus__eq__add) ).

fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Ocomm__ring__1(T_a)
     => c_Groups_Ominus__class_Ominus(T_a,V_x,V_y) = c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y)) ),
    file('theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
    ! [V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
    ! [V_q,V_p,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).

fof(fact_real__minus__mult__self__le,axiom,
    ! [V_x,V_u] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_u),V_u)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)),
    file('theBenchmark.p',fact_real__minus__mult__self__le) ).

fof(fact_not__pos__poly__0,axiom,
    ! [T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ~ c_Polynomial_Opos__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ),
    file('theBenchmark.p',fact_not__pos__poly__0) ).

fof(fact_gr0__conv__Suc,axiom,
    ! [V_n_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
    <=> ? [B_m] : V_n_2 = c_Nat_OSuc(B_m) ),
    file('theBenchmark.p',fact_gr0__conv__Suc) ).

fof(fact_less__Suc0,axiom,
    ! [V_n_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_less__Suc0) ).

fof(fact_less__Suc__eq__0__disj,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
    <=> ( ? [B_j] :
            ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2)
            & V_m_2 = c_Nat_OSuc(B_j) )
        | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_less__Suc__eq__0__disj) ).

fof(fact_one__is__add,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)
    <=> ( ( V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
    file('theBenchmark.p',fact_one__is__add) ).

fof(fact_add__is__1,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( ( V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
    file('theBenchmark.p',fact_add__is__1) ).

fof(fact_real__add__minus__iff,axiom,
    ! [V_ab_2,V_x_2] :
      ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_ab_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    <=> V_x_2 = V_ab_2 ),
    file('theBenchmark.p',fact_real__add__minus__iff) ).

fof(fact_real__add__eq__0__iff,axiom,
    ! [V_y_2,V_x_2] :
      ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    <=> V_y_2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2) ),
    file('theBenchmark.p',fact_real__add__eq__0__iff) ).

fof(fact_mult__eq__1__iff,axiom,
    ! [V_n_2,V_m_2] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        & V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    file('theBenchmark.p',fact_mult__eq__1__iff) ).

fof(fact_less__iff__Suc__add,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
    <=> ? [B_k] : V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)) ),
    file('theBenchmark.p',fact_less__iff__Suc__add) ).

fof(fact_less__add__Suc2,axiom,
    ! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i))),
    file('theBenchmark.p',fact_less__add__Suc2) ).

fof(fact_less__add__Suc1,axiom,
    ! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m))),
    file('theBenchmark.p',fact_less__add__Suc1) ).

fof(fact_less__eq__Suc__le,axiom,
    ! [V_m_2,V_n_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2) ),
    file('theBenchmark.p',fact_less__eq__Suc__le) ).

fof(fact_less__Suc__eq__le,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ),
    file('theBenchmark.p',fact_less__Suc__eq__le) ).

fof(fact_Suc__le__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_n_2)
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ),
    file('theBenchmark.p',fact_Suc__le__eq) ).

fof(fact_le__imp__less__Suc,axiom,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ),
    file('theBenchmark.p',fact_le__imp__less__Suc) ).

fof(fact_Suc__leI,axiom,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ),
    file('theBenchmark.p',fact_Suc__leI) ).

fof(fact_le__less__Suc__eq,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))
      <=> V_n_2 = V_m_2 ) ),
    file('theBenchmark.p',fact_le__less__Suc__eq) ).

fof(fact_Suc__le__lessD,axiom,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
    file('theBenchmark.p',fact_Suc__le__lessD) ).

fof(fact_One__nat__def,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_One__nat__def) ).

fof(fact_Suc__mult__less__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ),
    file('theBenchmark.p',fact_Suc__mult__less__cancel1) ).

fof(fact_diff__less__Suc,axiom,
    ! [V_n,V_m] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m)),
    file('theBenchmark.p',fact_diff__less__Suc) ).

fof(fact_mult__Suc__right,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
    file('theBenchmark.p',fact_mult__Suc__right) ).

fof(fact_mult__Suc,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
    file('theBenchmark.p',fact_mult__Suc) ).

fof(fact_Suc__mult__le__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ),
    file('theBenchmark.p',fact_Suc__mult__le__cancel1) ).

fof(fact_Suc__diff__le,axiom,
    ! [V_m,V_n] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) ),
    file('theBenchmark.p',fact_Suc__diff__le) ).

fof(fact_Suc__eq__plus1__left,axiom,
    ! [V_n] : c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n),
    file('theBenchmark.p',fact_Suc__eq__plus1__left) ).

fof(fact_Suc__eq__plus1,axiom,
    ! [V_n] : c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('theBenchmark.p',fact_Suc__eq__plus1) ).

fof(fact_natfloor__add__one,axiom,
    ! [V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
     => c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    file('theBenchmark.p',fact_natfloor__add__one) ).

fof(fact_diff__Suc__1,axiom,
    ! [V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n,
    file('theBenchmark.p',fact_diff__Suc__1) ).

fof(fact_diff__Suc__eq__diff__pred,axiom,
    ! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n),
    file('theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).

fof(fact_real__diff__def,axiom,
    ! [V_s,V_r] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_r,V_s) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_s)),
    file('theBenchmark.p',fact_real__diff__def) ).

fof(fact_minus__real__def,axiom,
    ! [V_y,V_x] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y)),
    file('theBenchmark.p',fact_minus__real__def) ).

fof(fact_real__mult__less__mono2,axiom,
    ! [V_y,V_x,V_z] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
       => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_y)) ) ),
    file('theBenchmark.p',fact_real__mult__less__mono2) ).

fof(fact_real__mult__order,axiom,
    ! [V_y,V_x] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
       => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_real__mult__order) ).

fof(fact_real__mult__less__iff1,axiom,
    ! [V_y_2,V_x_2,V_z_2] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))
      <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
    file('theBenchmark.p',fact_real__mult__less__iff1) ).

fof(fact_norm__not__less__zero,axiom,
    ! [V_x,T_a] :
      ( class_RealVector_Oreal__normed__vector(T_a)
     => ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    file('theBenchmark.p',fact_norm__not__less__zero) ).

fof(fact_complex__mod__minus__le__complex__mod,axiom,
    ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)),
    file('theBenchmark.p',fact_complex__mod__minus__le__complex__mod) ).

fof(fact_pos__poly__add,axiom,
    ! [V_q,V_p,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( c_Polynomial_Opos__poly(T_a,V_p)
       => ( c_Polynomial_Opos__poly(T_a,V_q)
         => c_Polynomial_Opos__poly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) ) ) ),
    file('theBenchmark.p',fact_pos__poly__add) ).

fof(fact_pos__poly__mult,axiom,
    ! [V_q,V_p,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( c_Polynomial_Opos__poly(T_a,V_p)
       => ( c_Polynomial_Opos__poly(T_a,V_q)
         => c_Polynomial_Opos__poly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) ) ) ),
    file('theBenchmark.p',fact_pos__poly__mult) ).

fof(fact_diff__poly__code_I1_J,axiom,
    ! [V_q,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_q) ),
    file('theBenchmark.p',fact_diff__poly__code_I1_J) ).

fof(fact_natfloor__neg,axiom,
    ! [V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
     => c_RComplete_Onatfloor(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_natfloor__neg) ).

fof(fact_less__eq__poly__def,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)
      <=> ( c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2))
          | V_x_2 = V_y_2 ) ) ),
    file('theBenchmark.p',fact_less__eq__poly__def) ).

fof(fact_real__0__le__add__iff,axiom,
    ! [V_y_2,V_x_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) ),
    file('theBenchmark.p',fact_real__0__le__add__iff) ).

fof(fact_real__add__le__0__iff,axiom,
    ! [V_y_2,V_x_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) ),
    file('theBenchmark.p',fact_real__add__le__0__iff) ).

fof(fact_n__less__m__mult__n,axiom,
    ! [V_m,V_n] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ) ),
    file('theBenchmark.p',fact_n__less__m__mult__n) ).

fof(fact_n__less__n__mult__m,axiom,
    ! [V_m,V_n] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)) ) ),
    file('theBenchmark.p',fact_n__less__n__mult__m) ).

fof(fact_one__less__mult,axiom,
    ! [V_m,V_n] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ) ),
    file('theBenchmark.p',fact_one__less__mult) ).

fof(fact_Suc__pred,axiom,
    ! [V_n] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
     => c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n ),
    file('theBenchmark.p',fact_Suc__pred) ).

fof(fact_diff__Suc__less,axiom,
    ! [V_i,V_n] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
     => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i)),V_n) ),
    file('theBenchmark.p',fact_diff__Suc__less) ).

fof(fact_one__le__mult__iff,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))
    <=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)
        & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2) ) ),
    file('theBenchmark.p',fact_one__le__mult__iff) ).

fof(fact_zero__less__norm__iff,axiom,
    ! [V_x_2,T_a] :
      ( class_RealVector_Oreal__normed__vector(T_a)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))
      <=> V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_zero__less__norm__iff) ).

fof(fact_diff__Suc__diff__eq2,axiom,
    ! [V_m,V_j,V_k] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m)) ),
    file('theBenchmark.p',fact_diff__Suc__diff__eq2) ).

fof(fact_diff__Suc__diff__eq1,axiom,
    ! [V_m,V_j,V_k] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j)
     => c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Nat_OSuc(V_j)) ),
    file('theBenchmark.p',fact_diff__Suc__diff__eq1) ).

fof(fact_norm__mult__less,axiom,
    ! [V_s,V_y,V_r,V_x,T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
       => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
         => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_s)) ) ) ),
    file('theBenchmark.p',fact_norm__mult__less) ).

fof(fact_real__mult__le__cancel__iff1,axiom,
    ! [V_y_2,V_x_2,V_z_2] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))
      <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
    file('theBenchmark.p',fact_real__mult__le__cancel__iff1) ).

fof(fact_real__mult__le__cancel__iff2,axiom,
    ! [V_y_2,V_x_2,V_z_2] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2))
      <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
    file('theBenchmark.p',fact_real__mult__le__cancel__iff2) ).

fof(fact_norm__add__less,axiom,
    ! [V_s,V_y,V_r,V_x,T_a] :
      ( class_RealVector_Oreal__normed__vector(T_a)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
       => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
         => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,V_s)) ) ) ),
    file('theBenchmark.p',fact_norm__add__less) ).

fof(fact_poly__monom,axiom,
    ! [V_x,V_n,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ),
    file('theBenchmark.p',fact_poly__monom) ).

fof(fact_monom__Suc,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Groups_Ozero(T_a)
     => c_Polynomial_Omonom(T_a,V_a,c_Nat_OSuc(V_n)) = c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Polynomial_Omonom(T_a,V_a,V_n)) ),
    file('theBenchmark.p',fact_monom__Suc) ).

fof(fact_power__eq__if,axiom,
    ! [V_p,V_m] :
      ( ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
      & ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_power__eq__if) ).

fof(fact_Suc__diff__1,axiom,
    ! [V_n] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
     => c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n ),
    file('theBenchmark.p',fact_Suc__diff__1) ).

fof(fact_Suc__pred_H,axiom,
    ! [V_n] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
     => V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    file('theBenchmark.p',fact_Suc__pred_H) ).

fof(fact_realpow__num__eq__if,axiom,
    ! [V_m,V_n,T_a] :
      ( class_Power_Opower(T_a)
     => ( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
        & ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = c_Groups_Oone__class_Oone(T_a) ) ) ),
    file('theBenchmark.p',fact_realpow__num__eq__if) ).

fof(fact_power__strict__mono,axiom,
    ! [V_n,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
         => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
           => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ) ),
    file('theBenchmark.p',fact_power__strict__mono) ).

fof(fact_lemma__realpow__diff,axiom,
    ! [V_y,V_n,V_p,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_p,V_n)
       => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),V_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_p))),V_y) ) ),
    file('theBenchmark.p',fact_lemma__realpow__diff) ).

fof(fact_one__less__power,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
       => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
         => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ),
    file('theBenchmark.p',fact_one__less__power) ).

fof(fact_pos__zmult__eq__1__iff,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      <=> ( V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
    file('theBenchmark.p',fact_pos__zmult__eq__1__iff) ).

fof(fact_zmult__zless__mono2,axiom,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
       => c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j)) ) ),
    file('theBenchmark.p',fact_zmult__zless__mono2) ).

fof(fact_zmult__1__right,axiom,
    ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z,
    file('theBenchmark.p',fact_zmult__1__right) ).

fof(fact_zmult__1,axiom,
    ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z,
    file('theBenchmark.p',fact_zmult__1) ).

fof(fact_zmult__zminus,axiom,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)),V_w) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)),
    file('theBenchmark.p',fact_zmult__zminus) ).

fof(fact_zadd__zmult__distrib2,axiom,
    ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)),
    file('theBenchmark.p',fact_zadd__zmult__distrib2) ).

fof(fact_zadd__zmult__distrib,axiom,
    ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)),V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)),
    file('theBenchmark.p',fact_zadd__zmult__distrib) ).

fof(fact_zdiff__zmult__distrib,axiom,
    ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)),V_w) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)),
    file('theBenchmark.p',fact_zdiff__zmult__distrib) ).

fof(fact_zmult__assoc,axiom,
    ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)),
    file('theBenchmark.p',fact_zmult__assoc) ).

fof(fact_zdiff__zmult__distrib2,axiom,
    ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)),
    file('theBenchmark.p',fact_zdiff__zmult__distrib2) ).

fof(fact_zmult__commute,axiom,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z),
    file('theBenchmark.p',fact_zmult__commute) ).

fof(fact_field__power__not__zero,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Oring__1__no__zero__divisors(T_a)
     => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_field__power__not__zero) ).

fof(fact_power__commutes,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
    file('theBenchmark.p',fact_power__commutes) ).

fof(fact_power__mult__distrib,axiom,
    ! [V_n,V_b,V_a,T_a] :
      ( class_Groups_Ocomm__monoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ),
    file('theBenchmark.p',fact_power__mult__distrib) ).

fof(fact_power__one,axiom,
    ! [V_n,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_power__one) ).

fof(fact_power__Suc__0,axiom,
    ! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_power__Suc__0) ).

fof(fact_nat__power__eq__Suc__0__iff,axiom,
    ! [V_m_2,V_x_2] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( V_x_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).

fof(fact_nat__zero__less__power__iff,axiom,
    ! [V_n_2,V_x_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))
    <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) ),
    file('theBenchmark.p',fact_nat__zero__less__power__iff) ).

fof(fact_nat__power__less__imp__less,axiom,
    ! [V_n,V_m,V_i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ),
    file('theBenchmark.p',fact_nat__power__less__imp__less) ).

fof(fact_power__mult,axiom,
    ! [V_n,V_m,V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n) ),
    file('theBenchmark.p',fact_power__mult) ).

fof(fact_power__one__right,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ),
    file('theBenchmark.p',fact_power__one__right) ).

fof(fact_zero__le__power,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
       => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ),
    file('theBenchmark.p',fact_zero__le__power) ).

fof(fact_power__mono,axiom,
    ! [V_n,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
         => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ),
    file('theBenchmark.p',fact_power__mono) ).

fof(fact_zero__less__power,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
       => c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ),
    file('theBenchmark.p',fact_zero__less__power) ).

fof(fact_one__le__power,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
       => c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ),
    file('theBenchmark.p',fact_one__le__power) ).

fof(fact_power__eq__0__iff,axiom,
    ! [V_n_2,V_ab_2,T_a] :
      ( ( class_Rings_Ozero__neq__one(T_a)
        & class_Rings_Ono__zero__divisors(T_a)
        & class_Rings_Omult__zero(T_a)
        & class_Power_Opower(T_a) )
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ab_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
      <=> ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_power__eq__0__iff) ).

fof(fact_power__inject__exp,axiom,
    ! [V_n_2,V_m_2,V_ab_2,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_ab_2)
       => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ab_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ab_2),V_n_2)
        <=> V_m_2 = V_n_2 ) ) ),
    file('theBenchmark.p',fact_power__inject__exp) ).

fof(fact_power__0__Suc,axiom,
    ! [V_n,T_a] :
      ( ( class_Rings_Osemiring__0(T_a)
        & class_Power_Opower(T_a) )
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_OSuc(V_n)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_power__0__Suc) ).

fof(fact_power__Suc,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Power_Opower(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
    file('theBenchmark.p',fact_power__Suc) ).

fof(fact_power__Suc2,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) ),
    file('theBenchmark.p',fact_power__Suc2) ).

fof(fact_power__0,axiom,
    ! [V_a,T_a] :
      ( class_Power_Opower(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_power__0) ).

fof(fact_power__add,axiom,
    ! [V_n,V_m,V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
    file('theBenchmark.p',fact_power__add) ).

fof(fact_nat__one__le__power,axiom,
    ! [V_n,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)) ),
    file('theBenchmark.p',fact_nat__one__le__power) ).

fof(fact_power__less__imp__less__base,axiom,
    ! [V_b,V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))
       => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
         => c_Orderings_Oord__class_Oless(T_a,V_a,V_b) ) ) ),
    file('theBenchmark.p',fact_power__less__imp__less__base) ).

fof(fact_power__inject__base,axiom,
    ! [V_b,V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n))
       => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
         => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
           => V_a = V_b ) ) ) ),
    file('theBenchmark.p',fact_power__inject__base) ).

fof(fact_power__le__imp__le__base,axiom,
    ! [V_b,V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n)))
       => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
         => c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b) ) ) ),
    file('theBenchmark.p',fact_power__le__imp__le__base) ).

fof(fact_power__gt1__lemma,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
       => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
    file('theBenchmark.p',fact_power__gt1__lemma) ).

fof(fact_power__less__power__Suc,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
       => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
    file('theBenchmark.p',fact_power__less__power__Suc) ).

fof(fact_power__0__left,axiom,
    ! [V_n,T_a] :
      ( ( class_Rings_Osemiring__0(T_a)
        & class_Power_Opower(T_a) )
     => ( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ) ),
    file('theBenchmark.p',fact_power__0__left) ).

fof(fact_power__gt1,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
       => c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n))) ) ),
    file('theBenchmark.p',fact_power__gt1) ).

fof(fact_power__minus,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
    file('theBenchmark.p',fact_power__minus) ).

fof(fact_power__strict__increasing__iff,axiom,
    ! [V_y_2,V_x_2,V_b_2,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
       => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))
        <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) ) ) ),
    file('theBenchmark.p',fact_power__strict__increasing__iff) ).

fof(fact_power__less__imp__less__exp,axiom,
    ! [V_n,V_m,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
       => ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
         => c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ) ),
    file('theBenchmark.p',fact_power__less__imp__less__exp) ).

fof(fact_power__strict__increasing,axiom,
    ! [V_a,V_N,V_n,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
       => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
         => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)) ) ) ),
    file('theBenchmark.p',fact_power__strict__increasing) ).

fof(fact_power__increasing,axiom,
    ! [V_a,V_N,V_n,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
         => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)) ) ) ),
    file('theBenchmark.p',fact_power__increasing) ).

fof(fact_power__Suc__less,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
       => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
         => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ),
    file('theBenchmark.p',fact_power__Suc__less) ).

fof(fact_power__Suc__less__one,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
       => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
         => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),c_Groups_Oone__class_Oone(T_a)) ) ) ),
    file('theBenchmark.p',fact_power__Suc__less__one) ).

fof(fact_power__strict__decreasing,axiom,
    ! [V_a,V_N,V_n,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
       => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
         => ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
           => c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ),
    file('theBenchmark.p',fact_power__strict__decreasing) ).

fof(fact_power__eq__imp__eq__base,axiom,
    ! [V_b,V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
         => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
           => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
             => V_a = V_b ) ) ) ) ),
    file('theBenchmark.p',fact_power__eq__imp__eq__base) ).

fof(fact_power__decreasing,axiom,
    ! [V_a,V_N,V_n,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
         => ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
           => c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ),
    file('theBenchmark.p',fact_power__decreasing) ).

fof(fact_power__le__imp__le__exp,axiom,
    ! [V_n,V_m,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
         => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ) ),
    file('theBenchmark.p',fact_power__le__imp__le__exp) ).

fof(fact_power__increasing__iff,axiom,
    ! [V_y_2,V_x_2,V_b_2,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
       => ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))
        <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2) ) ) ),
    file('theBenchmark.p',fact_power__increasing__iff) ).

fof(fact_zero__less__power__nat__eq,axiom,
    ! [V_n_2,V_x_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))
    <=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
        | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_zero__less__power__nat__eq) ).

fof(fact_not__real__square__gt__zero,axiom,
    ! [V_x_2] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2))
    <=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    file('theBenchmark.p',fact_not__real__square__gt__zero) ).

fof(fact_nat__lt__two__imp__zero__or__one,axiom,
    ! [V_x] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
     => ( V_x = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__lt__two__imp__zero__or__one) ).

fof(fact_less__bin__lemma,axiom,
    ! [V_l_2,V_k_2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    file('theBenchmark.p',fact_less__bin__lemma) ).

fof(fact_zle__add1__eq__le,axiom,
    ! [V_z_2,V_w_2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,V_z_2) ),
    file('theBenchmark.p',fact_zle__add1__eq__le) ).

fof(fact_zle__diff1__eq,axiom,
    ! [V_z_2,V_w_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ),
    file('theBenchmark.p',fact_zle__diff1__eq) ).

fof(fact_add1__zle__eq,axiom,
    ! [V_z_2,V_w_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ),
    file('theBenchmark.p',fact_add1__zle__eq) ).

fof(fact_le__imp__0__less,axiom,
    ! [V_z] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z)) ),
    file('theBenchmark.p',fact_le__imp__0__less) ).

fof(fact_zless__imp__add1__zle,axiom,
    ! [V_z,V_w] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) ),
    file('theBenchmark.p',fact_zless__imp__add1__zle) ).

fof(fact_zadd__zless__mono,axiom,
    ! [V_z,V_z_H,V_w,V_w_H] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H,V_z)
       => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)) ) ),
    file('theBenchmark.p',fact_zadd__zless__mono) ).

fof(fact_zadd__strict__right__mono,axiom,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j)
     => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k)) ),
    file('theBenchmark.p',fact_zadd__strict__right__mono) ).

fof(fact_odd__less__0,axiom,
    ! [V_z_2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    file('theBenchmark.p',fact_odd__less__0) ).

fof(fact_zless__add1__eq,axiom,
    ! [V_z_2,V_w_2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> ( V_w_2 = V_z_2
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ) ),
    file('theBenchmark.p',fact_zless__add1__eq) ).

fof(fact_int__0__less__1,axiom,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('theBenchmark.p',fact_int__0__less__1) ).

fof(fact_zless__linear,axiom,
    ! [V_y,V_x] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x)
      | V_x = V_y
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y) ),
    file('theBenchmark.p',fact_zless__linear) ).

fof(fact_zless__le,axiom,
    ! [V_w_2,V_z_2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)
    <=> ( V_z_2 != V_w_2
        & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2,V_w_2) ) ),
    file('theBenchmark.p',fact_zless__le) ).

fof(fact_int__one__le__iff__zero__less,axiom,
    ! [V_z_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)
    <=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2) ),
    file('theBenchmark.p',fact_int__one__le__iff__zero__less) ).

fof(fact_zminus__zminus,axiom,
    ! [V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)) = V_z,
    file('theBenchmark.p',fact_zminus__zminus) ).

fof(fact_zminus__0,axiom,
    c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_zminus__0) ).

fof(fact_zminus__zadd__distrib,axiom,
    ! [V_w,V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)),
    file('theBenchmark.p',fact_zminus__zadd__distrib) ).

fof(fact_zadd__zminus__inverse2,axiom,
    ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_zadd__zminus__inverse2) ).

fof(fact_diff__int__def__symmetric,axiom,
    ! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w),
    file('theBenchmark.p',fact_diff__int__def__symmetric) ).

fof(fact_diff__int__def,axiom,
    ! [V_w,V_z] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)),
    file('theBenchmark.p',fact_diff__int__def) ).

fof(fact_zadd__left__mono,axiom,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j)) ),
    file('theBenchmark.p',fact_zadd__left__mono) ).

fof(fact_zadd__0,axiom,
    ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z,
    file('theBenchmark.p',fact_zadd__0) ).

fof(fact_zadd__0__right,axiom,
    ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z,
    file('theBenchmark.p',fact_zadd__0__right) ).

fof(fact_zadd__commute,axiom,
    ! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z),
    file('theBenchmark.p',fact_zadd__commute) ).

fof(fact_zadd__left__commute,axiom,
    ! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z)),
    file('theBenchmark.p',fact_zadd__left__commute) ).

fof(fact_zadd__assoc,axiom,
    ! [V_z3,V_z2,V_z1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3)),
    file('theBenchmark.p',fact_zadd__assoc) ).

fof(fact_int__0__neq__1,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    file('theBenchmark.p',fact_int__0__neq__1) ).

fof(fact_odd__nonzero,axiom,
    ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_odd__nonzero) ).

fof(fact_self__quotient__aux1,axiom,
    ! [V_q,V_r,V_a] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
     => ( V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q) ) ) ),
    file('theBenchmark.p',fact_self__quotient__aux1) ).

fof(fact_self__quotient__aux2,axiom,
    ! [V_q,V_r,V_a] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
     => ( V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
       => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
    file('theBenchmark.p',fact_self__quotient__aux2) ).

fof(fact_zle__refl,axiom,
    ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_w),
    file('theBenchmark.p',fact_zle__refl) ).

fof(fact_zle__linear,axiom,
    ! [V_w,V_z] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w) ),
    file('theBenchmark.p',fact_zle__linear) ).

fof(fact_zle__trans,axiom,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j,V_k)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_k) ) ),
    file('theBenchmark.p',fact_zle__trans) ).

fof(fact_zle__antisym,axiom,
    ! [V_w,V_z] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
       => V_z = V_w ) ),
    file('theBenchmark.p',fact_zle__antisym) ).

fof(fact_q__pos__lemma,axiom,
    ! [V_r_H,V_q_H,V_b_H] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H))
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H) ) ) ),
    file('theBenchmark.p',fact_q__pos__lemma) ).

fof(fact_q__neg__lemma,axiom,
    ! [V_r_H,V_q_H,V_b_H] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
    file('theBenchmark.p',fact_q__neg__lemma) ).

fof(fact_unique__quotient__lemma,axiom,
    ! [V_r,V_q,V_r_H,V_q_H,V_b] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r))
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)
         => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
           => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ),
    file('theBenchmark.p',fact_unique__quotient__lemma) ).

fof(fact_zdiv__mono2__lemma,axiom,
    ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
      ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H))
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
         => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
           => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
             => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
               => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ) ) ),
    file('theBenchmark.p',fact_zdiv__mono2__lemma) ).

fof(fact_unique__quotient__lemma__neg,axiom,
    ! [V_r,V_q,V_r_H,V_q_H,V_b] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r))
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
         => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)
           => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ),
    file('theBenchmark.p',fact_unique__quotient__lemma__neg) ).

fof(fact_zdiv__mono2__neg__lemma,axiom,
    ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
      ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
         => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
           => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
             => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
               => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ) ) ),
    file('theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
    ! [V_n,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
     => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
    ! [V_y,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
    ! [V_y,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y)) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).

fof(fact_natceiling__add__one,axiom,
    ! [V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
     => c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    file('theBenchmark.p',fact_natceiling__add__one) ).

fof(fact_power__power__power,axiom,
    ! [T_a] :
      ( class_Power_Opower(T_a)
     => c_Power_Opower__class_Opower(T_a) = c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a)) ),
    file('theBenchmark.p',fact_power__power__power) ).

fof(fact_natceiling__zero,axiom,
    c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_natceiling__zero) ).

fof(fact_zero__le__natceiling,axiom,
    ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),
    file('theBenchmark.p',fact_zero__le__natceiling) ).

fof(fact_natceiling__mono,axiom,
    ! [V_y,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y)) ),
    file('theBenchmark.p',fact_natceiling__mono) ).

fof(fact_natceiling__one,axiom,
    c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    file('theBenchmark.p',fact_natceiling__one) ).

fof(fact_power_Opower_Opower__0,axiom,
    ! [V_ab_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_ab_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2,
    file('theBenchmark.p',fact_power_Opower_Opower__0) ).

fof(fact_power_Opower_Opower__Suc,axiom,
    ! [V_n_2,V_ab_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_ab_2),c_Nat_OSuc(V_n_2)) = hAPP(hAPP(V_times_2,V_ab_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_ab_2),V_n_2)),
    file('theBenchmark.p',fact_power_Opower_Opower__Suc) ).

fof(fact_natceiling__neg,axiom,
    ! [V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
     => c_RComplete_Onatceiling(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_natceiling__neg) ).

fof(fact_natceiling__le__eq__one,axiom,
    ! [V_x_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    file('theBenchmark.p',fact_natceiling__le__eq__one) ).

fof(fact_unimodular__reduce__norm,axiom,
    ! [V_z] :
      ( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_z,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
    file('theBenchmark.p',fact_unimodular__reduce__norm) ).

fof(fact_order__2,axiom,
    ! [V_a,V_p,T_a] :
      ( class_Rings_Oidom(T_a)
     => ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
       => ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Nat_OSuc(c_Polynomial_Oorder(T_a,V_a,V_p))),V_p) ) ),
    file('theBenchmark.p',fact_order__2) ).

fof(fact_dvd__0__right,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) ),
    file('theBenchmark.p',fact_dvd__0__right) ).

fof(fact_power__le__dvd,axiom,
    ! [V_m,V_b,V_n,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),V_b)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
         => c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),V_b) ) ) ),
    file('theBenchmark.p',fact_power__le__dvd) ).

fof(fact_dvd__power__le,axiom,
    ! [V_m,V_n,V_y,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
         => c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_m)) ) ) ),
    file('theBenchmark.p',fact_dvd__power__le) ).

fof(fact_le__imp__power__dvd,axiom,
    ! [V_a,V_n,V_m,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
       => c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ),
    file('theBenchmark.p',fact_le__imp__power__dvd) ).

fof(fact_dvd__power__same,axiom,
    ! [V_n,V_y,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)
       => c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)) ) ),
    file('theBenchmark.p',fact_dvd__power__same) ).

fof(fact_dvd__triv__left,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ),
    file('theBenchmark.p',fact_dvd__triv__left) ).

fof(fact_dvd__triv__right,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)) ),
    file('theBenchmark.p',fact_dvd__triv__right) ).

fof(fact_dvd__mult2,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
       => c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ),
    file('theBenchmark.p',fact_dvd__mult2) ).

fof(fact_dvd__mult,axiom,
    ! [V_b,V_c,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)
       => c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ),
    file('theBenchmark.p',fact_dvd__mult) ).

fof(fact_mult__dvd__mono,axiom,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
       => ( c_Rings_Odvd__class_Odvd(T_a,V_c,V_d)
         => c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ),
    file('theBenchmark.p',fact_mult__dvd__mono) ).

fof(fact_dvdI,axiom,
    ! [V_k,V_b,V_a,T_a] :
      ( class_Rings_Odvd(T_a)
     => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
       => c_Rings_Odvd__class_Odvd(T_a,V_b,V_a) ) ),
    file('theBenchmark.p',fact_dvdI) ).

fof(fact_dvd__mult__left,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)
       => c_Rings_Odvd__class_Odvd(T_a,V_a,V_c) ) ),
    file('theBenchmark.p',fact_dvd__mult__left) ).

fof(fact_dvd__mult__right,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)
       => c_Rings_Odvd__class_Odvd(T_a,V_b,V_c) ) ),
    file('theBenchmark.p',fact_dvd__mult__right) ).

fof(fact_dvd__refl,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => c_Rings_Odvd__class_Odvd(T_a,V_a,V_a) ),
    file('theBenchmark.p',fact_dvd__refl) ).

fof(fact_dvd__trans,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
       => ( c_Rings_Odvd__class_Odvd(T_a,V_b,V_c)
         => c_Rings_Odvd__class_Odvd(T_a,V_a,V_c) ) ) ),
    file('theBenchmark.p',fact_dvd__trans) ).

fof(fact_smult__dvd__cancel,axiom,
    ! [V_q,V_p,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),V_q)
       => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q) ) ),
    file('theBenchmark.p',fact_smult__dvd__cancel) ).

fof(fact_dvd__smult,axiom,
    ! [V_a,V_q,V_p,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q)
       => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_a,V_q)) ) ),
    file('theBenchmark.p',fact_dvd__smult) ).

fof(fact_complex__i__not__one,axiom,
    c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
    file('theBenchmark.p',fact_complex__i__not__one) ).

fof(fact_dvd__0__left,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
       => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_dvd__0__left) ).

fof(fact_dvd__add,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
       => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)
         => c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ) ),
    file('theBenchmark.p',fact_dvd__add) ).

fof(fact_one__dvd,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => c_Rings_Odvd__class_Odvd(T_a,c_Groups_Oone__class_Oone(T_a),V_a) ),
    file('theBenchmark.p',fact_one__dvd) ).

fof(fact_complex__i__not__zero,axiom,
    c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    file('theBenchmark.p',fact_complex__i__not__zero) ).

fof(fact_dvd__smult__iff,axiom,
    ! [V_q_2,V_pa_2,V_ab_2,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_ab_2 != c_Groups_Ozero__class_Ozero(T_a)
       => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,c_Polynomial_Osmult(T_a,V_ab_2,V_q_2))
        <=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,V_q_2) ) ) ),
    file('theBenchmark.p',fact_dvd__smult__iff) ).

fof(fact_smult__dvd,axiom,
    ! [V_a,V_q,V_p,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q)
       => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
         => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),V_q) ) ) ),
    file('theBenchmark.p',fact_smult__dvd) ).

fof(fact_dvd__smult__cancel,axiom,
    ! [V_q,V_a,V_p,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_a,V_q))
       => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
         => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q) ) ) ),
    file('theBenchmark.p',fact_dvd__smult__cancel) ).

fof(fact_dvd__mult__cancel__left,axiom,
    ! [V_b_2,V_ab_2,V_ca_2,T_a] :
      ( class_Rings_Oidom(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
      <=> ( c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_b_2)
          | V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_dvd__mult__cancel__left) ).

fof(fact_dvd__mult__cancel__right,axiom,
    ! [V_b_2,V_ca_2,V_ab_2,T_a] :
      ( class_Rings_Oidom(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))
      <=> ( c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_b_2)
          | V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_dvd__mult__cancel__right) ).

fof(fact_dvd__diff,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Rings_Ocomm__ring__1(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)
       => ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_z)
         => c_Rings_Odvd__class_Odvd(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_z)) ) ) ),
    file('theBenchmark.p',fact_dvd__diff) ).

fof(fact_complex__i__mult__minus,axiom,
    ! [V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),V_x)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,V_x),
    file('theBenchmark.p',fact_complex__i__mult__minus) ).

fof(fact_minus__dvd__iff,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Rings_Ocomm__ring__1(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),V_y_2)
      <=> c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2) ) ),
    file('theBenchmark.p',fact_minus__dvd__iff) ).

fof(fact_dvd__minus__iff,axiom,
    ! [V_y_2,V_x_2,T_a] :
      ( class_Rings_Ocomm__ring__1(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,V_x_2,c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))
      <=> c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2) ) ),
    file('theBenchmark.p',fact_dvd__minus__iff) ).

fof(fact_i__mult__eq2,axiom,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
    file('theBenchmark.p',fact_i__mult__eq2) ).

fof(fact_smult__dvd__iff,axiom,
    ! [V_q_2,V_pa_2,V_ab_2,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_ab_2,V_pa_2),V_q_2)
      <=> ( ( V_ab_2 != c_Groups_Ozero__class_Ozero(T_a)
           => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,V_q_2) )
          & ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a)
           => V_q_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ) ),
    file('theBenchmark.p',fact_smult__dvd__iff) ).

fof(fact_dvd__power,axiom,
    ! [V_x,V_n,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( ( V_x = c_Groups_Oone__class_Oone(T_a)
          | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) )
       => c_Rings_Odvd__class_Odvd(T_a,V_x,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ),
    file('theBenchmark.p',fact_dvd__power) ).

fof(fact_dvd__iff__poly__eq__0,axiom,
    ! [V_pa_2,V_ca_2,T_a] :
      ( class_Rings_Oidom(T_a)
     => ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_ca_2,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2)
      <=> hAPP(c_Polynomial_Opoly(T_a,V_pa_2),c_Groups_Ouminus__class_Ouminus(T_a,V_ca_2)) = c_Groups_Ozero__class_Ozero(T_a) ) ),
    file('theBenchmark.p',fact_dvd__iff__poly__eq__0) ).

fof(fact_poly__eq__0__iff__dvd,axiom,
    ! [V_ca_2,V_pa_2,T_a] :
      ( class_Rings_Oidom(T_a)
     => ( hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_ca_2) = c_Groups_Ozero__class_Ozero(T_a)
      <=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ca_2),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2) ) ),
    file('theBenchmark.p',fact_poly__eq__0__iff__dvd) ).

fof(fact_order__1,axiom,
    ! [V_p,V_a,T_a] :
      ( class_Rings_Oidom(T_a)
     => c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p)),V_p) ),
    file('theBenchmark.p',fact_order__1) ).

fof(fact_order,axiom,
    ! [V_a,V_p,T_a] :
      ( class_Rings_Oidom(T_a)
     => ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
       => ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Nat_OSuc(c_Polynomial_Oorder(T_a,V_a,V_p))),V_p)
          & c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p)),V_p) ) ) ),
    file('theBenchmark.p',fact_order) ).

fof(fact_inf__period_I3_J,axiom,
    ! [V_t_2,V_D_2,V_db_2,T_a] :
      ( ( class_Rings_Odvd(T_a)
        & class_Rings_Ocomm__ring(T_a) )
     => ( c_Rings_Odvd__class_Odvd(T_a,V_db_2,V_D_2)
       => ! [B_x,B_k] :
            ( c_Rings_Odvd__class_Odvd(T_a,V_db_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))
          <=> c_Rings_Odvd__class_Odvd(T_a,V_db_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2)) ) ) ),
    file('theBenchmark.p',fact_inf__period_I3_J) ).

fof(fact_inf__period_I4_J,axiom,
    ! [V_t_2,V_D_2,V_db_2,T_a] :
      ( ( class_Rings_Odvd(T_a)
        & class_Rings_Ocomm__ring(T_a) )
     => ( c_Rings_Odvd__class_Odvd(T_a,V_db_2,V_D_2)
       => ! [B_x,B_k] :
            ( c_Rings_Odvd__class_Odvd(T_a,V_db_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))
          <=> c_Rings_Odvd__class_Odvd(T_a,V_db_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2)) ) ) ),
    file('theBenchmark.p',fact_inf__period_I4_J) ).

fof(fact_dvd__1__left,axiom,
    ! [V_k] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k),
    file('theBenchmark.p',fact_dvd__1__left) ).

fof(fact_zdvd__antisym__nonneg,axiom,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n)
       => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m,V_n)
         => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m)
           => V_m = V_n ) ) ) ),
    file('theBenchmark.p',fact_zdvd__antisym__nonneg) ).

fof(fact_dvd__diffD1,axiom,
    ! [V_n,V_m,V_k] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
         => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n) ) ) ),
    file('theBenchmark.p',fact_dvd__diffD1) ).

fof(fact_dvd__diffD,axiom,
    ! [V_n,V_m,V_k] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
         => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m) ) ) ),
    file('theBenchmark.p',fact_dvd__diffD) ).

fof(fact_dvd__reduce,axiom,
    ! [V_n_2,V_k_2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2))
    <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,V_n_2) ),
    file('theBenchmark.p',fact_dvd__reduce) ).

fof(fact_nat__dvd__1__iff__1,axiom,
    ! [V_m_2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,c_Groups_Oone__class_Oone(tc_Nat_Onat))
    <=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_nat__dvd__1__iff__1) ).

fof(fact_nat__mult__dvd__cancel__disj,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
    <=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,V_n_2)
        | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).

fof(fact_nat__dvd__not__less,axiom,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
       => ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_n,V_m) ) ),
    file('theBenchmark.p',fact_nat__dvd__not__less) ).

fof(fact_dvd__1__iff__1,axiom,
    ! [V_m_2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    <=> V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    file('theBenchmark.p',fact_dvd__1__iff__1) ).

fof(fact_zdvd__zdiffD,axiom,
    ! [V_n,V_m,V_k] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,V_n))
     => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_n)
       => c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_m) ) ),
    file('theBenchmark.p',fact_zdvd__zdiffD) ).

fof(fact_zdvd__mult__cancel,axiom,
    ! [V_n,V_m,V_k] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_n))
     => ( V_k != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m,V_n) ) ),
    file('theBenchmark.p',fact_zdvd__mult__cancel) ).

fof(fact_zdvd__period,axiom,
    ! [V_ca_2,V_t_2,V_x_2,V_db_2,V_ab_2] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ab_2,V_db_2)
     => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ab_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,V_t_2))
      <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ab_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ca_2),V_db_2)),V_t_2)) ) ),
    file('theBenchmark.p',fact_zdvd__period) ).

fof(fact_zdvd__mono,axiom,
    ! [V_t_2,V_m_2,V_k_2] :
      ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m_2,V_t_2)
      <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2)) ) ),
    file('theBenchmark.p',fact_zdvd__mono) ).

fof(fact_zdvd__reduce,axiom,
    ! [V_m_2,V_n_2,V_k_2] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_n_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)))
    <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,V_n_2) ),
    file('theBenchmark.p',fact_zdvd__reduce) ).

fof(fact_dvd__diff__nat,axiom,
    ! [V_n,V_m,V_k] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)
       => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) ) ),
    file('theBenchmark.p',fact_dvd__diff__nat) ).

fof(fact_uminus__dvd__conv_I2_J,axiom,
    ! [V_t_2,V_db_2] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_db_2,V_t_2)
    <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_db_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_t_2)) ),
    file('theBenchmark.p',fact_uminus__dvd__conv_I2_J) ).

fof(fact_uminus__dvd__conv_I1_J,axiom,
    ! [V_t_2,V_db_2] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_db_2,V_t_2)
    <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_db_2),V_t_2) ),
    file('theBenchmark.p',fact_uminus__dvd__conv_I1_J) ).

fof(fact_zdvd__not__zless,axiom,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_m,V_n)
       => ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m) ) ),
    file('theBenchmark.p',fact_zdvd__not__zless) ).

fof(fact_zdvd__imp__le,axiom,
    ! [V_n,V_z] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_z,V_n)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_n) ) ),
    file('theBenchmark.p',fact_zdvd__imp__le) ).

fof(fact_dvd__imp__le,axiom,
    ! [V_n,V_k] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ) ),
    file('theBenchmark.p',fact_dvd__imp__le) ).

fof(fact_nat__mult__dvd__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
      <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,V_n_2) ) ),
    file('theBenchmark.p',fact_nat__mult__dvd__cancel1) ).

fof(fact_dvd__mult__cancel,axiom,
    ! [V_n,V_m,V_k] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n))
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
       => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n) ) ),
    file('theBenchmark.p',fact_dvd__mult__cancel) ).

fof(fact_dvd__mult__cancel1,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2),V_m_2)
      <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_dvd__mult__cancel1) ).

fof(fact_dvd__mult__cancel2,axiom,
    ! [V_n_2,V_m_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_m_2),V_m_2)
      <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_dvd__mult__cancel2) ).

fof(fact_power__dvd__imp__le,axiom,
    ! [V_n,V_m,V_i] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))
     => ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_i)
       => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ),
    file('theBenchmark.p',fact_power__dvd__imp__le) ).

fof(fact_unity__coeff__ex,axiom,
    ! [V_l_2,V_P_2,T_a] :
      ( ( class_Rings_Osemiring__0(T_a)
        & class_Rings_Odvd(T_a) )
     => ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_l_2),B_x)))
      <=> ? [B_x] :
            ( hBOOL(hAPP(V_P_2,B_x))
            & c_Rings_Odvd__class_Odvd(T_a,V_l_2,c_Groups_Oplus__class_Oplus(T_a,B_x,c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
    file('theBenchmark.p',fact_unity__coeff__ex) ).

fof(fact_reduce__poly__simple,axiom,
    ! [V_n,V_b] :
      ( V_b != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
     => ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => ? [B_z] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_z),V_n)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
    file('theBenchmark.p',fact_reduce__poly__simple) ).

fof(fact_pow__divides__eq__nat,axiom,
    ! [V_b_2,V_ab_2,V_n_2] :
      ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_ab_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b_2),V_n_2))
      <=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ab_2,V_b_2) ) ),
    file('theBenchmark.p',fact_pow__divides__eq__nat) ).

fof(fact_dvd_Oorder__refl,axiom,
    ! [V_x] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_x),
    file('theBenchmark.p',fact_dvd_Oorder__refl) ).

fof(fact_dvd_Oeq__iff,axiom,
    ! [V_y_2,V_x_2] :
      ( V_x_2 = V_y_2
    <=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) ) ),
    file('theBenchmark.p',fact_dvd_Oeq__iff) ).

fof(fact_dvd_Ole__less,axiom,
    ! [V_y_2,V_x_2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
    <=> ( V_x_2 = V_y_2
        | ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) ) ) ),
    file('theBenchmark.p',fact_dvd_Ole__less) ).

fof(fact_dvd_Oless__le,axiom,
    ! [V_y_2,V_x_2] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) )
    <=> ( V_x_2 != V_y_2
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) ) ),
    file('theBenchmark.p',fact_dvd_Oless__le) ).

fof(fact_dvd_Oneq__le__trans,axiom,
    ! [V_b,V_a] :
      ( V_a != V_b
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
       => ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) ) ) ),
    file('theBenchmark.p',fact_dvd_Oneq__le__trans) ).

fof(fact_dvd_Oeq__refl,axiom,
    ! [V_y,V_x] :
      ( V_x = V_y
     => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
    file('theBenchmark.p',fact_dvd_Oeq__refl) ).

fof(fact_dvd_Oantisym__conv,axiom,
    ! [V_x_2,V_y_2] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_dvd_Oantisym__conv) ).

fof(fact_dvd_Ole__imp__less__or__eq,axiom,
    ! [V_y,V_x] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
     => ( V_x = V_y
        | ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ) ) ),
    file('theBenchmark.p',fact_dvd_Ole__imp__less__or__eq) ).

fof(fact_dvd_Ole__neq__trans,axiom,
    ! [V_b,V_a] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
     => ( V_a != V_b
       => ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) ) ) ),
    file('theBenchmark.p',fact_dvd_Ole__neq__trans) ).

fof(fact_dvd_Oord__eq__le__trans,axiom,
    ! [V_c,V_b,V_a] :
      ( V_a = V_b
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c)
       => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c) ) ),
    file('theBenchmark.p',fact_dvd_Oord__eq__le__trans) ).

fof(fact_dvd_Oord__le__eq__trans,axiom,
    ! [V_c,V_b,V_a] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
     => ( V_b = V_c
       => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c) ) ),
    file('theBenchmark.p',fact_dvd_Oord__le__eq__trans) ).

fof(fact_dvd__antisym,axiom,
    ! [V_n,V_m] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_n,V_m)
       => V_m = V_n ) ),
    file('theBenchmark.p',fact_dvd__antisym) ).

fof(fact_dvd_Oantisym,axiom,
    ! [V_y,V_x] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
       => V_x = V_y ) ),
    file('theBenchmark.p',fact_dvd_Oantisym) ).

fof(fact_dvd_Oorder__trans,axiom,
    ! [V_z,V_y,V_x] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)
       => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z) ) ),
    file('theBenchmark.p',fact_dvd_Oorder__trans) ).

fof(fact_dvd_Oord__eq__less__trans,axiom,
    ! [V_c,V_b,V_a] :
      ( V_a = V_b
     => ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_b)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c) )
       => ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_a)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c) ) ) ),
    file('theBenchmark.p',fact_dvd_Oord__eq__less__trans) ).

fof(fact_dvd_Ole__less__trans,axiom,
    ! [V_z,V_y,V_x] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
     => ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z) )
       => ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z) ) ) ),
    file('theBenchmark.p',fact_dvd_Ole__less__trans) ).

fof(fact_dvd_Oless__imp__neq,axiom,
    ! [V_y,V_x] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) )
     => V_x != V_y ),
    file('theBenchmark.p',fact_dvd_Oless__imp__neq) ).

fof(fact_dvd_Oless__not__sym,axiom,
    ! [V_y,V_x] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) )
     => ~ ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) ) ),
    file('theBenchmark.p',fact_dvd_Oless__not__sym) ).

fof(fact_dvd_Oless__imp__le,axiom,
    ! [V_y,V_x] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) )
     => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
    file('theBenchmark.p',fact_dvd_Oless__imp__le) ).

fof(fact_dvd_Oless__imp__not__less,axiom,
    ! [V_y,V_x] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) )
     => ~ ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) ) ),
    file('theBenchmark.p',fact_dvd_Oless__imp__not__less) ).

fof(fact_dvd_Oless__imp__not__eq,axiom,
    ! [V_y,V_x] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) )
     => V_x != V_y ),
    file('theBenchmark.p',fact_dvd_Oless__imp__not__eq) ).

fof(fact_dvd_Oless__imp__not__eq2,axiom,
    ! [V_y,V_x] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) )
     => V_y != V_x ),
    file('theBenchmark.p',fact_dvd_Oless__imp__not__eq2) ).

fof(fact_dvd_Oord__less__eq__trans,axiom,
    ! [V_c,V_b,V_a] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) )
     => ( V_b = V_c
       => ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_a)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c) ) ) ),
    file('theBenchmark.p',fact_dvd_Oord__less__eq__trans) ).

fof(fact_dvd_Oless__le__trans,axiom,
    ! [V_z,V_y,V_x] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) )
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)
       => ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z) ) ) ),
    file('theBenchmark.p',fact_dvd_Oless__le__trans) ).

fof(fact_dvd_Oless__asym_H,axiom,
    ! [V_b,V_a] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) )
     => ~ ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a) ) ),
    file('theBenchmark.p',fact_dvd_Oless__asym_H) ).

fof(fact_dvd_Oless__trans,axiom,
    ! [V_z,V_y,V_x] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) )
     => ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z) )
       => ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z) ) ) ),
    file('theBenchmark.p',fact_dvd_Oless__trans) ).

fof(fact_dvd_Oless__asym,axiom,
    ! [V_y,V_x] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) )
     => ~ ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) ) ),
    file('theBenchmark.p',fact_dvd_Oless__asym) ).

fof(fact_gcd__lcm__complete__lattice__nat_Otop__greatest,axiom,
    ! [V_x] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Otop__greatest) ).

fof(fact_gcd__lcm__complete__lattice__nat_Obot__least,axiom,
    ! [V_x] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_x),
    file('theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Obot__least) ).

fof(fact_dvd__pos__nat,axiom,
    ! [V_m,V_n] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
     => ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n)
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) ) ),
    file('theBenchmark.p',fact_dvd__pos__nat) ).

fof(fact_pow__divides__pow__int,axiom,
    ! [V_b,V_n,V_a] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b),V_n))
     => ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a,V_b) ) ),
    file('theBenchmark.p',fact_pow__divides__pow__int) ).

fof(fact_pow__divides__eq__int,axiom,
    ! [V_b_2,V_ab_2,V_n_2] :
      ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_ab_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b_2),V_n_2))
      <=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ab_2,V_b_2) ) ),
    file('theBenchmark.p',fact_pow__divides__eq__int) ).

fof(fact_pow__divides__pow__nat,axiom,
    ! [V_b,V_n,V_a] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b),V_n))
     => ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) ) ),
    file('theBenchmark.p',fact_pow__divides__pow__nat) ).

fof(fact_mult_Opos__bounded,axiom,
    ! [T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => ? [B_K] :
          ( ! [B_a,B_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ),
    file('theBenchmark.p',fact_mult_Opos__bounded) ).

fof(fact_mult__right_Opos__bounded,axiom,
    ! [V_x,T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => ? [B_K] :
          ( ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ),
    file('theBenchmark.p',fact_mult__right_Opos__bounded) ).

fof(fact_mult__left_Opos__bounded,axiom,
    ! [V_y,T_a] :
      ( class_RealVector_Oreal__normed__algebra(T_a)
     => ? [B_K] :
          ( ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ),
    file('theBenchmark.p',fact_mult__left_Opos__bounded) ).

fof(fact_poly__cont,axiom,
    ! [V_p,V_z,V_e] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_e)
     => ? [B_d] :
          ( ! [B_w] :
              ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B_w,V_z)),B_d)
                & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B_w,V_z))) )
             => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),B_w),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),V_z))),V_e) )
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d) ) ),
    file('theBenchmark.p',fact_poly__cont) ).

fof(fact_tsub__def,axiom,
    ! [V_x,V_y] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
       => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
       => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) ) ),
    file('theBenchmark.p',fact_tsub__def) ).

fof(fact_natceiling__eq,axiom,
    ! [V_x,V_n] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
       => c_RComplete_Onatceiling(V_x) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    file('theBenchmark.p',fact_natceiling__eq) ).

fof(fact_real__of__nat__ge__zero,axiom,
    ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),
    file('theBenchmark.p',fact_real__of__nat__ge__zero) ).

fof(fact_real__of__nat__power,axiom,
    ! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n),
    file('theBenchmark.p',fact_real__of__nat__power) ).

fof(fact_power__real__of__nat,axiom,
    ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)),
    file('theBenchmark.p',fact_power__real__of__nat) ).

fof(fact_real__of__nat__le__zero__cancel__iff,axiom,
    ! [V_n_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_real__of__nat__le__zero__cancel__iff) ).

fof(fact_real__of__nat__Suc__gt__zero,axiom,
    ! [V_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))),
    file('theBenchmark.p',fact_real__of__nat__Suc__gt__zero) ).

fof(fact_real__of__nat__one,axiom,
    c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    file('theBenchmark.p',fact_real__of__nat__one) ).

fof(fact_real__of__nat__1,axiom,
    c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    file('theBenchmark.p',fact_real__of__nat__1) ).

fof(fact_real__of__nat__less__iff,axiom,
    ! [V_m_2,V_n_2] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) ),
    file('theBenchmark.p',fact_real__of__nat__less__iff) ).

fof(fact_real__of__nat__add,axiom,
    ! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)),
    file('theBenchmark.p',fact_real__of__nat__add) ).

fof(fact_natfloor__real__of__nat,axiom,
    ! [V_n] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n,
    file('theBenchmark.p',fact_natfloor__real__of__nat) ).

fof(fact_real__of__nat__inject,axiom,
    ! [V_m_2,V_n_2] :
      ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_RealDef_Oreal(tc_Nat_Onat,V_m_2)
    <=> V_n_2 = V_m_2 ),
    file('theBenchmark.p',fact_real__of__nat__inject) ).

fof(fact_real__of__nat__le__iff,axiom,
    ! [V_m_2,V_n_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))
    <=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ),
    file('theBenchmark.p',fact_real__of__nat__le__iff) ).

fof(fact_real__natceiling__ge,axiom,
    ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x))),
    file('theBenchmark.p',fact_real__natceiling__ge) ).

fof(fact_natceiling__real__of__nat,axiom,
    ! [V_n] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n,
    file('theBenchmark.p',fact_natceiling__real__of__nat) ).

fof(fact_real__of__nat__mult,axiom,
    ! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n)),
    file('theBenchmark.p',fact_real__of__nat__mult) ).

fof(fact_real__of__nat__zero,axiom,
    c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    file('theBenchmark.p',fact_real__of__nat__zero) ).

fof(fact_real__of__nat__zero__iff,axiom,
    ! [V_n_2] :
      ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_real__of__nat__zero__iff) ).

fof(fact_not__real__of__nat__less__zero,axiom,
    ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    file('theBenchmark.p',fact_not__real__of__nat__less__zero) ).

fof(fact_natceiling__le,axiom,
    ! [V_a,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ),
    file('theBenchmark.p',fact_natceiling__le) ).

fof(fact_le__natfloor,axiom,
    ! [V_a,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a)
     => c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a)) ),
    file('theBenchmark.p',fact_le__natfloor) ).

fof(fact_real__natfloor__le,axiom,
    ! [V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_x) ),
    file('theBenchmark.p',fact_real__natfloor__le) ).

fof(fact_real__of__nat__diff,axiom,
    ! [V_m,V_n] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
     => c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)) ),
    file('theBenchmark.p',fact_real__of__nat__diff) ).

fof(fact_real__of__nat__Suc,axiom,
    ! [V_n] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    file('theBenchmark.p',fact_real__of__nat__Suc) ).

fof(fact_natfloor__power,axiom,
    ! [V_n,V_x] :
      ( V_x = c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))
     => c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_n) ),
    file('theBenchmark.p',fact_natfloor__power) ).

fof(fact_real__of__nat__gt__zero__cancel__iff,axiom,
    ! [V_n_2] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2))
    <=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ),
    file('theBenchmark.p',fact_real__of__nat__gt__zero__cancel__iff) ).

fof(fact_nat__less__real__le,axiom,
    ! [V_m_2,V_n_2] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
    <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)) ),
    file('theBenchmark.p',fact_nat__less__real__le) ).

fof(fact_nat__le__real__less,axiom,
    ! [V_m_2,V_n_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2)
    <=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
    file('theBenchmark.p',fact_nat__le__real__less) ).

fof(fact_le__natfloor__eq,axiom,
    ! [V_ab_2,V_x_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ab_2,c_RComplete_Onatfloor(V_x_2))
      <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_ab_2),V_x_2) ) ),
    file('theBenchmark.p',fact_le__natfloor__eq) ).

fof(fact_natceiling__le__eq,axiom,
    ! [V_ab_2,V_x_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_ab_2)
      <=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_ab_2)) ) ),
    file('theBenchmark.p',fact_natceiling__le__eq) ).

fof(fact_real__natfloor__add__one__gt,axiom,
    ! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
    file('theBenchmark.p',fact_real__natfloor__add__one__gt) ).

fof(fact_natfloor__subtract,axiom,
    ! [V_x,V_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)
     => c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a) ),
    file('theBenchmark.p',fact_natfloor__subtract) ).

fof(fact_real__natfloor__gt__diff__one,axiom,
    ! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))),
    file('theBenchmark.p',fact_real__natfloor__gt__diff__one) ).

fof(fact_natceiling__subtract,axiom,
    ! [V_x,V_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)
     => c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ),
    file('theBenchmark.p',fact_natceiling__subtract) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
    ! [V_y,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(V_x,V_y)) ) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).

fof(fact_less__natfloor,axiom,
    ! [V_n,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n))
       => c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n) ) ),
    file('theBenchmark.p',fact_less__natfloor) ).

fof(fact_tsub__eq,axiom,
    ! [V_x,V_y] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
     => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) ),
    file('theBenchmark.p',fact_tsub__eq) ).

fof(fact_natfloor__add,axiom,
    ! [V_a,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
     => c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a) ),
    file('theBenchmark.p',fact_natfloor__add) ).

fof(fact_ge__natfloor__plus__one__imp__gt,axiom,
    ! [V_n,V_z] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_z),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)
     => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,c_RealDef_Oreal(tc_Nat_Onat,V_n)) ),
    file('theBenchmark.p',fact_ge__natfloor__plus__one__imp__gt) ).

fof(fact_natfloor__eq,axiom,
    ! [V_x,V_n] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)
     => ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
       => c_RComplete_Onatfloor(V_x) = V_n ) ),
    file('theBenchmark.p',fact_natfloor__eq) ).

fof(fact_natceiling__add,axiom,
    ! [V_a,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
     => c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ),
    file('theBenchmark.p',fact_natceiling__add) ).

fof(fact_LIMSEQ__inverse__realpow__zero__lemma,axiom,
    ! [V_n,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
     => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n)) ),
    file('theBenchmark.p',fact_LIMSEQ__inverse__realpow__zero__lemma) ).

fof(fact_lemma__NBseq__def,axiom,
    ! [V_X_2,T_b] :
      ( class_RealVector_Oreal__normed__vector(T_b)
     => ( ? [B_K] :
            ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K)
            & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
      <=> ? [B_N] :
          ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) ) ),
    file('theBenchmark.p',fact_lemma__NBseq__def) ).

fof(fact_lemma__NBseq__def2,axiom,
    ! [V_X_2,T_b] :
      ( class_RealVector_Oreal__normed__vector(T_b)
     => ( ? [B_K] :
            ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K)
            & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
      <=> ? [B_N] :
          ! [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) ) ),
    file('theBenchmark.p',fact_lemma__NBseq__def2) ).

fof(fact_reals__Archimedean6,axiom,
    ! [V_r] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)
     => ? [B_n] :
          ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,B_n))
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_r) ) ),
    file('theBenchmark.p',fact_reals__Archimedean6) ).

fof(fact_reals__Archimedean4,axiom,
    ! [V_x,V_y] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
     => ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
       => ? [B_n] :
            ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n))),V_y))
            & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_y),V_x) ) ) ),
    file('theBenchmark.p',fact_reals__Archimedean4) ).

fof(fact_lemmaCauchy,axiom,
    ! [V_X_2,V_M_2,T_a,T_b] :
      ( ( class_Orderings_Oord(T_a)
        & class_RealVector_Oreal__normed__vector(T_b) )
     => ( ! [B_n] :
            ( c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n)
           => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,c_Groups_Ominus__class_Ominus(T_b,hAPP(V_X_2,V_M_2),hAPP(V_X_2,B_n))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
       => ! [B_n] :
            ( c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n)
           => c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2)))) ) ) ),
    file('theBenchmark.p',fact_lemmaCauchy) ).

fof(fact_poly__bound__exists,axiom,
    ! [V_p,V_r] :
    ? [B_m] :
      ( ! [B_z] :
          ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),V_r)
         => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),B_z)),B_m) )
      & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_m) ),
    file('theBenchmark.p',fact_poly__bound__exists) ).

fof(fact_Limits_Ominus__diff__minus,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oab__group__add(T_a)
     => c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) ),
    file('theBenchmark.p',fact_Limits_Ominus__diff__minus) ).

fof(fact_int__power__div__base,axiom,
    ! [V_k,V_m] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
       => c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    file('theBenchmark.p',fact_int__power__div__base) ).

fof(fact_div__mult__self1,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)) ) ),
    file('theBenchmark.p',fact_div__mult__self1) ).

fof(fact_div__mult__self2,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b)) ) ),
    file('theBenchmark.p',fact_div__mult__self2) ).

fof(fact_div__add__self2,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b),c_Groups_Oone__class_Oone(T_a)) ) ),
    file('theBenchmark.p',fact_div__add__self2) ).

fof(fact_div__add__self1,axiom,
    ! [V_a,V_b,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
       => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_a),V_b) = c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b),c_Groups_Oone__class_Oone(T_a)) ) ),
    file('theBenchmark.p',fact_div__add__self1) ).

fof(fact_dvd__div__eq__mult,axiom,
    ! [V_ca_2,V_b_2,V_ab_2,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_ab_2 != c_Groups_Ozero__class_Ozero(T_a)
       => ( c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_b_2)
         => ( c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_ab_2) = V_ca_2
          <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2) ) ) ) ),
    file('theBenchmark.p',fact_dvd__div__eq__mult) ).

fof(fact_dvd__div__div__eq__mult,axiom,
    ! [V_db_2,V_b_2,V_ca_2,V_ab_2,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( V_ab_2 != c_Groups_Ozero__class_Ozero(T_a)
       => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a)
         => ( c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_b_2)
           => ( c_Rings_Odvd__class_Odvd(T_a,V_ca_2,V_db_2)
             => ( c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_ab_2) = c_Divides_Odiv__class_Odiv(T_a,V_db_2,V_ca_2)
              <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_db_2) ) ) ) ) ) ),
    file('theBenchmark.p',fact_dvd__div__div__eq__mult) ).

fof(fact_dvd__neg__div,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Divides_Oring__div(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,V_y,V_x)
       => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)) ) ),
    file('theBenchmark.p',fact_dvd__neg__div) ).

fof(fact_dvd__div__neg,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Divides_Oring__div(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,V_y,V_x)
       => c_Divides_Odiv__class_Odiv(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)) ) ),
    file('theBenchmark.p',fact_dvd__div__neg) ).

fof(fact_div__add,axiom,
    ! [V_y,V_x,V_z,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,V_z,V_x)
       => ( c_Rings_Odvd__class_Odvd(T_a,V_z,V_y)
         => c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_z) = c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_z),c_Divides_Odiv__class_Odiv(T_a,V_y,V_z)) ) ) ),
    file('theBenchmark.p',fact_div__add) ).

fof(fact_div__dvd__div,axiom,
    ! [V_ca_2,V_b_2,V_ab_2,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_b_2)
       => ( c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_ca_2)
         => ( c_Rings_Odvd__class_Odvd(T_a,c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_ab_2),c_Divides_Odiv__class_Odiv(T_a,V_ca_2,V_ab_2))
          <=> c_Rings_Odvd__class_Odvd(T_a,V_b_2,V_ca_2) ) ) ) ),
    file('theBenchmark.p',fact_div__dvd__div) ).

fof(fact_div__mult__div__if__dvd,axiom,
    ! [V_w,V_z,V_x,V_y,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,V_y,V_x)
       => ( c_Rings_Odvd__class_Odvd(T_a,V_z,V_w)
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)),c_Divides_Odiv__class_Odiv(T_a,V_w,V_z)) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ),
    file('theBenchmark.p',fact_div__mult__div__if__dvd) ).

fof(fact_dvd__div__mult,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)),V_c) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c),V_a) ) ),
    file('theBenchmark.p',fact_dvd__div__mult) ).

fof(fact_dvd__div__mult__self,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)),V_a) = V_b ) ),
    file('theBenchmark.p',fact_dvd__div__mult__self) ).

fof(fact_div__mult__swap,axiom,
    ! [V_a,V_b,V_c,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,V_c,V_b)
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_c)) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) ) ),
    file('theBenchmark.p',fact_div__mult__swap) ).

fof(fact_zdvd__mult__div__cancel,axiom,
    ! [V_m,V_n] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m,V_n)) = V_m ),
    file('theBenchmark.p',fact_zdvd__mult__div__cancel) ).

fof(fact_dvd__mult__div__cancel,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b ) ),
    file('theBenchmark.p',fact_dvd__mult__div__cancel) ).

fof(fact_div__power,axiom,
    ! [V_n,V_x,V_y,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( c_Rings_Odvd__class_Odvd(T_a,V_y,V_x)
       => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)),V_n) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)) ) ),
    file('theBenchmark.p',fact_div__power) ).

fof(fact_zdiv__eq__0__iff,axiom,
    ! [V_k_2,V_i_2] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2)
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        | ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,V_k_2)
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i_2) )
        | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_zdiv__eq__0__iff) ).

fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
    ! [V_ab_2,V_b_2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_ab_2,V_b_2))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ab_2) ) ),
    file('theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).

fof(fact_pos__imp__zdiv__pos__iff,axiom,
    ! [V_i_2,V_k_2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_i_2) ) ),
    file('theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).

fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
    ! [V_b_2,V_ab_2] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ab_2)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_ab_2,V_b_2))
      <=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_2,V_ab_2) ) ) ),
    file('theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).

fof(fact_zdiv__mono2,axiom,
    ! [V_b,V_b_H,V_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H)) ) ) ),
    file('theBenchmark.p',fact_zdiv__mono2) ).

fof(fact_div__nonneg__neg__le0,axiom,
    ! [V_b,V_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    file('theBenchmark.p',fact_div__nonneg__neg__le0) ).

fof(fact_div__pos__pos__trivial,axiom,
    ! [V_b,V_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,V_b)
       => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_div__pos__pos__trivial) ).

fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
    ! [V_ab_2,V_b_2] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_ab_2,V_b_2))
      <=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_ab_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    file('theBenchmark.p',fact_neg__imp__zdiv__nonneg__iff) ).

fof(fact_div__nonpos__pos__le0,axiom,
    ! [V_b,V_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    file('theBenchmark.p',fact_div__nonpos__pos__le0) ).

fof(fact_zdiv__mono2__neg,axiom,
    ! [V_b,V_b_H,V_a] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
       => ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
         => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)) ) ) ),
    file('theBenchmark.p',fact_zdiv__mono2__neg) ).

fof(fact_div__neg__neg__trivial,axiom,
    ! [V_b,V_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_a)
       => c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_div__neg__neg__trivial) ).

fof(fact_zdiv__mono1,axiom,
    ! [V_b,V_a_H,V_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b)) ) ),
    file('theBenchmark.p',fact_zdiv__mono1) ).

fof(fact_zdiv__mono1__neg,axiom,
    ! [V_b,V_a_H,V_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
       => c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b)) ) ),
    file('theBenchmark.p',fact_zdiv__mono1__neg) ).

fof(fact_int__div__less__self,axiom,
    ! [V_k,V_x] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x)
     => ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k)
       => c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k),V_x) ) ),
    file('theBenchmark.p',fact_int__div__less__self) ).

fof(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom,
    ! [T_1] :
      ( class_Groups_Ocancel__comm__monoid__add(T_1)
     => class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).

fof(arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,axiom,
    class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add) ).

fof(arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add,axiom,
    class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add) ).

fof(arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,axiom,
    class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).

fof(arity_Int__Oint__Groups_Ocancel__comm__monoid__add,axiom,
    class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).

fof(arity_fun__Orderings_Opreorder,axiom,
    ! [T_2,T_1] :
      ( class_Orderings_Opreorder(T_1)
     => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Orderings_Opreorder) ).

fof(arity_fun__Orderings_Oorder,axiom,
    ! [T_2,T_1] :
      ( class_Orderings_Oorder(T_1)
     => class_Orderings_Oorder(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Orderings_Oorder) ).

fof(arity_fun__Orderings_Oord,axiom,
    ! [T_2,T_1] :
      ( class_Orderings_Oord(T_1)
     => class_Orderings_Oord(tc_fun(T_2,T_1)) ),
    file('theBenchmark.p',arity_fun__Orderings_Oord) ).

fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).

fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).

fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).

fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).

fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).

fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).

fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).

fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).

fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).

fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).

fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).

fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).

fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).

fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).

fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).

fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).

fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).

fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).

fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).

fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).

fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).

fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).

fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).

fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).

fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).

fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).

fof(arity_Int__Oint__Rings_Ocomm__semiring__0,axiom,
    class_Rings_Ocomm__semiring__0(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).

fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
    class_Divides_Osemiring__div(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).

fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).

fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
    class_Groups_Oab__group__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).

fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).

fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
    class_Rings_Oordered__ring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).

fof(arity_Int__Oint__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).

fof(arity_Int__Oint__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).

fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).

fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).

fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
    class_Groups_Omonoid__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).

fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
    class_Rings_Osemiring__0(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).

fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
    class_Groups_Ogroup__add(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).

fof(arity_Int__Oint__Divides_Oring__div,axiom,
    class_Divides_Oring__div(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Divides_Oring__div) ).

fof(arity_Int__Oint__Rings_Omult__zero,axiom,
    class_Rings_Omult__zero(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).

fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).

fof(arity_Int__Oint__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).

fof(arity_Int__Oint__Int_Oring__char__0,axiom,
    class_Int_Oring__char__0(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).

fof(arity_Int__Oint__Rings_Osemiring,axiom,
    class_Rings_Osemiring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).

fof(arity_Int__Oint__Orderings_Oord,axiom,
    class_Orderings_Oord(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).

fof(arity_Int__Oint__Rings_Oring__1,axiom,
    class_Rings_Oring__1(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).

fof(arity_Int__Oint__Power_Opower,axiom,
    class_Power_Opower(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Power_Opower) ).

fof(arity_Int__Oint__Groups_Ozero,axiom,
    class_Groups_Ozero(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).

fof(arity_Int__Oint__Rings_Oring,axiom,
    class_Rings_Oring(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oring) ).

fof(arity_Int__Oint__Rings_Oidom,axiom,
    class_Rings_Oidom(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).

fof(arity_Int__Oint__Groups_Oone,axiom,
    class_Groups_Oone(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Groups_Oone) ).

fof(arity_Int__Oint__Rings_Odvd,axiom,
    class_Rings_Odvd(tc_Int_Oint),
    file('theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).

fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).

fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).

fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).

fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).

fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).

fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).

fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).

fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).

fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).

fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).

fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).

fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).

fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).

fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).

fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).

fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).

fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).

fof(arity_Nat__Onat__Rings_Ocomm__semiring__0,axiom,
    class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).

fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).

fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).

fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).

fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).

fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).

fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).

fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).

fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).

fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
    class_Rings_Omult__zero(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).

fof(arity_Nat__Onat__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).

fof(arity_Nat__Onat__Rings_Osemiring,axiom,
    class_Rings_Osemiring(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).

fof(arity_Nat__Onat__Orderings_Oord,axiom,
    class_Orderings_Oord(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).

fof(arity_Nat__Onat__Power_Opower,axiom,
    class_Power_Opower(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Power_Opower) ).

fof(arity_Nat__Onat__Groups_Ozero,axiom,
    class_Groups_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).

fof(arity_Nat__Onat__Groups_Oone,axiom,
    class_Groups_Oone(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).

fof(arity_Nat__Onat__Rings_Odvd,axiom,
    class_Rings_Odvd(tc_Nat_Onat),
    file('theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).

fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).

fof(arity_HOL__Obool__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).

fof(arity_HOL__Obool__Orderings_Oord,axiom,
    class_Orderings_Oord(tc_HOL_Obool),
    file('theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).

fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
    class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).

fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,axiom,
    class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).

fof(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
    class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).

fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
    class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).

fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
    class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).

fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
    class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).

fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
    class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).

fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
    class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).

fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
    class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).

fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).

fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).

fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom,
    class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).

fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
    class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).

fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
    class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).

fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,axiom,
    class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).

fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
    class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).

fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1,axiom,
    class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).

fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
    class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).

fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
    class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).

fof(arity_RealDef__Oreal__Rings_Olinordered__semiring,axiom,
    class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).

fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).

fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult,axiom,
    class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).

fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom,
    class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).

fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
    class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).

fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom,
    class_Rings_Oordered__semiring(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).

fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom,
    class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).

fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
    class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).

fof(arity_RealDef__Oreal__Rings_Olinordered__ring,axiom,
    class_Rings_Olinordered__ring(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).

fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).

fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).

fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__0,axiom,
    class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__0) ).

fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom,
    class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).

fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom,
    class_Groups_Oab__group__add(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).

fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom,
    class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).

fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
    class_Rings_Oordered__ring(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).

fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).

fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).

fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
    class_Groups_Omonoid__mult(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).

fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1,axiom,
    class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).

fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
    class_Groups_Omonoid__add(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).

fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom,
    class_Rings_Osemiring__0(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__0) ).

fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).

fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
    class_Rings_Omult__zero(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).

fof(arity_RealDef__Oreal__Rings_Ocomm__ring,axiom,
    class_Rings_Ocomm__ring(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring) ).

fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).

fof(arity_RealDef__Oreal__Int_Oring__char__0,axiom,
    class_Int_Oring__char__0(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).

fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
    class_Rings_Osemiring(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).

fof(arity_RealDef__Oreal__Orderings_Oord,axiom,
    class_Orderings_Oord(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Orderings_Oord) ).

fof(arity_RealDef__Oreal__Rings_Oring__1,axiom,
    class_Rings_Oring__1(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).

fof(arity_RealDef__Oreal__Fields_Ofield,axiom,
    class_Fields_Ofield(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield) ).

fof(arity_RealDef__Oreal__Power_Opower,axiom,
    class_Power_Opower(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Power_Opower) ).

fof(arity_RealDef__Oreal__Groups_Ozero,axiom,
    class_Groups_Ozero(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).

fof(arity_RealDef__Oreal__Rings_Oring,axiom,
    class_Rings_Oring(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).

fof(arity_RealDef__Oreal__Rings_Oidom,axiom,
    class_Rings_Oidom(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).

fof(arity_RealDef__Oreal__Groups_Oone,axiom,
    class_Groups_Oone(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).

fof(arity_RealDef__Oreal__Rings_Odvd,axiom,
    class_Rings_Odvd(tc_RealDef_Oreal),
    file('theBenchmark.p',arity_RealDef__Oreal__Rings_Odvd) ).

fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
    class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).

fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
    class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).

fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).

fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
    class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).

fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
    class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).

fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
    class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).

fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
    class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).

fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom,
    class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).

fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
    class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).

fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
    class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).

fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
    class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).

fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
    class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).

fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).

fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
    class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).

fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
    class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).

fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
    class_Groups_Oab__group__add(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).

fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
    class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).

fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
    class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).

fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
    class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).

fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
    class_Groups_Omonoid__add(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).

fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
    class_Rings_Osemiring__0(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).

fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
    class_Groups_Ogroup__add(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).

fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
    class_Rings_Omult__zero(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).

fof(arity_Complex__Ocomplex__Rings_Ocomm__ring,axiom,
    class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).

fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
    class_Int_Oring__char__0(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).

fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
    class_Rings_Osemiring(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).

fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
    class_Rings_Oring__1(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).

fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
    class_Fields_Ofield(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).

fof(arity_Complex__Ocomplex__Power_Opower,axiom,
    class_Power_Opower(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).

fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
    class_Groups_Ozero(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).

fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
    class_Rings_Oring(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).

fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).

fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
    class_Groups_Oone(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).

fof(arity_Complex__Ocomplex__Rings_Odvd,axiom,
    class_Rings_Odvd(tc_Complex_Ocomplex),
    file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Odvd) ).

fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
    ! [T_1] :
      ( class_Rings_Oidom(T_1)
     => class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).

fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).

fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).

fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).

fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).

fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).

fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).

fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).

fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,axiom,
    ! [T_1] :
      ( class_Groups_Ocancel__comm__monoid__add(T_1)
     => class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).

fof(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,axiom,
    ! [T_1] :
      ( class_Rings_Oidom(T_1)
     => class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).

fof(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).

fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).

fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,axiom,
    ! [T_1] :
      ( class_Rings_Oidom(T_1)
     => class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).

fof(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).

fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).

fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).

fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,axiom,
    ! [T_1] :
      ( class_Groups_Ocancel__comm__monoid__add(T_1)
     => class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).

fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring) ).

fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).

fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,axiom,
    ! [T_1] :
      ( class_Rings_Ocomm__semiring__0(T_1)
     => class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).

fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,axiom,
    ! [T_1] :
      ( class_Rings_Ocomm__semiring__1(T_1)
     => class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).

fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add,axiom,
    ! [T_1] :
      ( class_Groups_Ocomm__monoid__add(T_1)
     => class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).

fof(arity_Polynomial__Opoly__Rings_Oordered__semiring,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).

fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom,
    ! [T_1] :
      ( class_Rings_Oidom(T_1)
     => class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).

fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom,
    ! [T_1] :
      ( class_Groups_Ocomm__monoid__add(T_1)
     => class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).

fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).

fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).

fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
    ! [T_1] :
      ( class_Rings_Ocomm__semiring__1(T_1)
     => class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).

fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
    ! [T_1] :
      ( class_Rings_Ocomm__semiring__0(T_1)
     => class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).

fof(arity_Polynomial__Opoly__Divides_Osemiring__div,axiom,
    ! [T_1] :
      ( class_Fields_Ofield(T_1)
     => class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Divides_Osemiring__div) ).

fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom,
    ! [T_1] :
      ( class_Rings_Ocomm__semiring__0(T_1)
     => class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).

fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom,
    ! [T_1] :
      ( class_Groups_Oab__group__add(T_1)
     => class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).

fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
    ! [T_1] :
      ( class_Rings_Ocomm__semiring__1(T_1)
     => class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).

fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).

fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Orderings_Opreorder) ).

fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).

fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom,
    ! [T_1] :
      ( class_Rings_Ocomm__semiring__1(T_1)
     => class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).

fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1,axiom,
    ! [T_1] :
      ( class_Rings_Ocomm__ring__1(T_1)
     => class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).

fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom,
    ! [T_1] :
      ( class_Groups_Ocomm__monoid__add(T_1)
     => class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).

fof(arity_Polynomial__Opoly__Rings_Osemiring__0,axiom,
    ! [T_1] :
      ( class_Rings_Ocomm__semiring__0(T_1)
     => class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__0) ).

fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
    ! [T_1] :
      ( class_Groups_Oab__group__add(T_1)
     => class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).

fof(arity_Polynomial__Opoly__Divides_Oring__div,axiom,
    ! [T_1] :
      ( class_Fields_Ofield(T_1)
     => class_Divides_Oring__div(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Divides_Oring__div) ).

fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
    ! [T_1] :
      ( class_Rings_Ocomm__semiring__0(T_1)
     => class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).

fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom,
    ! [T_1] :
      ( class_Rings_Ocomm__ring(T_1)
     => class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).

fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oorder) ).

fof(arity_Polynomial__Opoly__Int_Oring__char__0,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).

fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom,
    ! [T_1] :
      ( class_Rings_Ocomm__semiring__0(T_1)
     => class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).

fof(arity_Polynomial__Opoly__Orderings_Oord,axiom,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(T_1)
     => class_Orderings_Oord(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oord) ).

fof(arity_Polynomial__Opoly__Rings_Oring__1,axiom,
    ! [T_1] :
      ( class_Rings_Ocomm__ring__1(T_1)
     => class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).

fof(arity_Polynomial__Opoly__Power_Opower,axiom,
    ! [T_1] :
      ( class_Rings_Ocomm__semiring__1(T_1)
     => class_Power_Opower(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).

fof(arity_Polynomial__Opoly__Groups_Ozero,axiom,
    ! [T_1] :
      ( class_Groups_Ozero(T_1)
     => class_Groups_Ozero(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).

fof(arity_Polynomial__Opoly__Rings_Oring,axiom,
    ! [T_1] :
      ( class_Rings_Ocomm__ring(T_1)
     => class_Rings_Oring(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).

fof(arity_Polynomial__Opoly__Rings_Oidom,axiom,
    ! [T_1] :
      ( class_Rings_Oidom(T_1)
     => class_Rings_Oidom(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).

fof(arity_Polynomial__Opoly__Groups_Oone,axiom,
    ! [T_1] :
      ( class_Rings_Ocomm__semiring__1(T_1)
     => class_Groups_Oone(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).

fof(arity_Polynomial__Opoly__Rings_Odvd,axiom,
    ! [T_1] :
      ( class_Rings_Ocomm__semiring__1(T_1)
     => class_Rings_Odvd(tc_Polynomial_Opoly(T_1)) ),
    file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Odvd) ).

fof(help_c__fequal__1,axiom,
    ! [V_y_2,V_x_2] :
      ( V_x_2 = V_y_2
      | ~ hBOOL(c_fequal(V_x_2,V_y_2)) ),
    file('theBenchmark.p',help_c__fequal__1) ).

fof(help_c__fequal__2,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(c_fequal(V_x_2,V_y_2))
      | V_x_2 != V_y_2 ),
    file('theBenchmark.p',help_c__fequal__2) ).

fof(conj_0,hypothesis,
    ( ? [B_r] :
      ! [B_z] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_r,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z))
       => c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_da____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),B_z))) )
   => v_thesis____ ),
    file('theBenchmark.p',conj_0) ).

fof(conj_1,conjecture,
    v_thesis____,
    file('theBenchmark.p',conj_1) ).

fof(f_1_1,plain,
    ! [V_g_2,V_f_2] :
      ( V_f_2 = V_g_2
      | ? [B_x] : hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x) ),
    inference(fof_nnf,[status(thm)],[fact_ext]) ).

fof(f_1_2,plain,
    ! [U_2,U_1] :
      ( U_1 = U_2
      | ? [U_0] : hAPP(U_1,U_0) != hAPP(U_2,U_0) ),
    inference(variable_rename,[status(thm)],[f_1_1]) ).

fof(f_1_3,plain,
    ! [U_2,U_1] :
      ( U_1 = U_2
      | hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1(U_2,U_1))],[f_1_2]) ).

fof(f_1_4,plain,
    ! [U_1,U_2] :
      ( U_1 = U_2
      | hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
    inference(definitional_conversion,[status(esa)],[f_1_3]) ).

cnf(f_1_5,plain,
    ( U_1 = U_2
    | hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
    inference(clausify,[status(thm)],[f_1_4]) ).

fof(f_2_1,plain,
    v_cs____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(fof_nnf,[status(thm)],[fact_H]) ).

fof(f_2_2,plain,
    v_cs____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(definitional_conversion,[status(esa)],[f_2_1]) ).

cnf(f_2_3,plain,
    v_cs____ != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(clausify,[status(thm)],[f_2_2]) ).

fof(f_3_1,plain,
    c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(fof_nnf,[status(thm)],[fact_pCons_Oprems]) ).

fof(f_3_2,plain,
    c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(definitional_conversion,[status(esa)],[f_3_1]) ).

cnf(f_3_3,plain,
    c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(clausify,[status(thm)],[f_3_2]) ).

fof(f_4_1,plain,
    ! [V_a,V_d] :
      ( ? [B_r] :
        ! [B_z] :
          ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_d,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,V_a,v_cs____)),B_z)))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_r,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z)) )
      | v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    inference(fof_nnf,[status(thm)],[fact_pCons_Ohyps]) ).

fof(f_4_2,plain,
    ! [U_6,U_5] :
      ( ? [U_4] :
        ! [U_3] :
          ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_5,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,U_6,v_cs____)),U_3)))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_4,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_3)) )
      | v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    inference(variable_rename,[status(thm)],[f_4_1]) ).

fof(f_4_3,plain,
    ( ! [U_6,U_5] :
      ? [U_4] :
      ! [U_3] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_5,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,U_6,v_cs____)),U_3)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_4,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_3)) )
    | v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    inference(miniscope,[status(thm)],[f_4_2]) ).

fof(f_4_4,plain,
    ( ! [U_6,U_5,U_3] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_5,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,U_6,v_cs____)),U_3)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sK2(U_6,U_5),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_3)) )
    | v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_4,sK2(U_6,U_5))],[f_4_3]) ).

fof(f_4_5,plain,
    ! [U_3,U_5,U_6] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_5,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,U_6,v_cs____)),U_3)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sK2(U_6,U_5),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_3))
      | v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    inference(definitional_conversion,[status(esa)],[f_4_4]) ).

cnf(f_4_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_5,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,U_6,v_cs____)),U_3)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,sK2(U_6,U_5),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_3))
    | v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    inference(clausify,[status(thm)],[f_4_5]) ).

fof(f_5_1,plain,
    v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(fof_nnf,[status(thm)],[fact_assms]) ).

fof(f_5_2,plain,
    v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(definitional_conversion,[status(esa)],[f_5_1]) ).

cnf(f_5_3,plain,
    v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
    inference(clausify,[status(thm)],[f_5_2]) ).

fof(f_6_1,plain,
    ! [V_y,V_x,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_RealVector_Onorm__class_Onorm(T_a,V_y)))
      | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq]) ).

fof(f_6_2,plain,
    ! [U_9,U_8,U_7] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_7,c_Groups_Oplus__class_Oplus(U_7,U_8,U_9)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_7,U_8),c_RealVector_Onorm__class_Onorm(U_7,U_9)))
      | ~ class_RealVector_Oreal__normed__vector(U_7) ),
    inference(variable_rename,[status(thm)],[f_6_1]) ).

fof(f_6_3,plain,
    ! [U_7,U_8,U_9] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_7,c_Groups_Oplus__class_Oplus(U_7,U_8,U_9)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_7,U_8),c_RealVector_Onorm__class_Onorm(U_7,U_9)))
      | ~ class_RealVector_Oreal__normed__vector(U_7) ),
    inference(definitional_conversion,[status(esa)],[f_6_2]) ).

cnf(f_6_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_7,c_Groups_Oplus__class_Oplus(U_7,U_8,U_9)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_7,U_8),c_RealVector_Onorm__class_Onorm(U_7,U_9)))
    | ~ class_RealVector_Oreal__normed__vector(U_7) ),
    inference(clausify,[status(thm)],[f_6_3]) ).

fof(f_7_1,plain,
    ! [V_x,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_x)
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__refl]) ).

fof(f_7_2,plain,
    ! [U_11,U_10] :
      ( c_Orderings_Oord__class_Oless__eq(U_10,U_11,U_11)
      | ~ class_Orderings_Opreorder(U_10) ),
    inference(variable_rename,[status(thm)],[f_7_1]) ).

fof(f_7_3,plain,
    ! [U_11,U_10] :
      ( c_Orderings_Oord__class_Oless__eq(U_10,U_11,U_11)
      | ~ class_Orderings_Opreorder(U_10) ),
    inference(definitional_conversion,[status(esa)],[f_7_2]) ).

cnf(f_7_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_10,U_11,U_11)
    | ~ class_Orderings_Opreorder(U_10) ),
    inference(clausify,[status(thm)],[f_7_3]) ).

fof(f_8_1,plain,
    ! [V_x,V_q,V_p,T_a] :
      ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_poly__add]) ).

fof(f_8_2,plain,
    ! [U_15,U_14,U_13,U_12] :
      ( hAPP(c_Polynomial_Opoly(U_12,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_12),U_13,U_14)),U_15) = c_Groups_Oplus__class_Oplus(U_12,hAPP(c_Polynomial_Opoly(U_12,U_13),U_15),hAPP(c_Polynomial_Opoly(U_12,U_14),U_15))
      | ~ class_Rings_Ocomm__semiring__0(U_12) ),
    inference(variable_rename,[status(thm)],[f_8_1]) ).

fof(f_8_3,plain,
    ! [U_12,U_13,U_14,U_15] :
      ( hAPP(c_Polynomial_Opoly(U_12,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_12),U_13,U_14)),U_15) = c_Groups_Oplus__class_Oplus(U_12,hAPP(c_Polynomial_Opoly(U_12,U_13),U_15),hAPP(c_Polynomial_Opoly(U_12,U_14),U_15))
      | ~ class_Rings_Ocomm__semiring__0(U_12) ),
    inference(definitional_conversion,[status(esa)],[f_8_2]) ).

cnf(f_8_4,plain,
    ( hAPP(c_Polynomial_Opoly(U_12,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_12),U_13,U_14)),U_15) = c_Groups_Oplus__class_Oplus(U_12,hAPP(c_Polynomial_Opoly(U_12,U_13),U_15),hAPP(c_Polynomial_Opoly(U_12,U_14),U_15))
    | ~ class_Rings_Ocomm__semiring__0(U_12) ),
    inference(clausify,[status(thm)],[f_8_3]) ).

fof(f_9_1,plain,
    ! [V_q,V_b,V_p,V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q)) = c_Polynomial_OpCons(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q))
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__pCons]) ).

fof(f_9_2,plain,
    ! [U_20,U_19,U_18,U_17,U_16] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_16),c_Polynomial_OpCons(U_16,U_17,U_18),c_Polynomial_OpCons(U_16,U_19,U_20)) = c_Polynomial_OpCons(U_16,c_Groups_Oplus__class_Oplus(U_16,U_17,U_19),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_16),U_18,U_20))
      | ~ class_Groups_Ocomm__monoid__add(U_16) ),
    inference(variable_rename,[status(thm)],[f_9_1]) ).

fof(f_9_3,plain,
    ! [U_16,U_17,U_18,U_19,U_20] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_16),c_Polynomial_OpCons(U_16,U_17,U_18),c_Polynomial_OpCons(U_16,U_19,U_20)) = c_Polynomial_OpCons(U_16,c_Groups_Oplus__class_Oplus(U_16,U_17,U_19),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_16),U_18,U_20))
      | ~ class_Groups_Ocomm__monoid__add(U_16) ),
    inference(definitional_conversion,[status(esa)],[f_9_2]) ).

cnf(f_9_4,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_16),c_Polynomial_OpCons(U_16,U_17,U_18),c_Polynomial_OpCons(U_16,U_19,U_20)) = c_Polynomial_OpCons(U_16,c_Groups_Oplus__class_Oplus(U_16,U_17,U_19),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_16),U_18,U_20))
    | ~ class_Groups_Ocomm__monoid__add(U_16) ),
    inference(clausify,[status(thm)],[f_9_3]) ).

fof(f_10_1,plain,
    ! [V_z,V_y,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_x),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z,V_y))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y) ),
    inference(fof_nnf,[status(thm)],[fact_real__add__left__mono]) ).

fof(f_10_2,plain,
    ! [U_23,U_22,U_21] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_23,U_21),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_23,U_22))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_21,U_22) ),
    inference(variable_rename,[status(thm)],[f_10_1]) ).

fof(f_10_3,plain,
    ! [U_21,U_23,U_22] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_23,U_21),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_23,U_22))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_21,U_22) ),
    inference(definitional_conversion,[status(esa)],[f_10_2]) ).

cnf(f_10_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_23,U_21),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_23,U_22))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_21,U_22) ),
    inference(clausify,[status(thm)],[f_10_3]) ).

fof(f_11_1,plain,
    ! [V_b_2,V_ca_2,V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2)) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right]) ).

fof(f_11_2,plain,
    ! [U_27,U_26,U_25,U_24] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_24,c_Groups_Oplus__class_Oplus(U_24,U_25,U_26),c_Groups_Oplus__class_Oplus(U_24,U_27,U_26))
          | ~ c_Orderings_Oord__class_Oless__eq(U_24,U_25,U_27) )
        & ( c_Orderings_Oord__class_Oless__eq(U_24,U_25,U_27)
          | ~ c_Orderings_Oord__class_Oless__eq(U_24,c_Groups_Oplus__class_Oplus(U_24,U_25,U_26),c_Groups_Oplus__class_Oplus(U_24,U_27,U_26)) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_24) ),
    inference(variable_rename,[status(thm)],[f_11_1]) ).

fof(f_11_3,plain,
    ( ! [U_24,U_25,U_26,U_27] :
        ( c_Orderings_Oord__class_Oless__eq(U_24,c_Groups_Oplus__class_Oplus(U_24,U_25,U_26),c_Groups_Oplus__class_Oplus(U_24,U_27,U_26))
        | ~ c_Orderings_Oord__class_Oless__eq(U_24,U_25,U_27)
        | ~ sP0(U_24,U_25,U_26,U_27) )
    & ! [U_24,U_25,U_26,U_27] :
        ( c_Orderings_Oord__class_Oless__eq(U_24,U_25,U_27)
        | ~ c_Orderings_Oord__class_Oless__eq(U_24,c_Groups_Oplus__class_Oplus(U_24,U_25,U_26),c_Groups_Oplus__class_Oplus(U_24,U_27,U_26))
        | ~ sP0(U_24,U_25,U_26,U_27) )
    & ! [U_24,U_25,U_26,U_27] :
        ( sP0(U_24,U_25,U_26,U_27)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_24) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_11_2]) ).

cnf(f_11_4,plain,
    ( sP0(U_24,U_25,U_26,U_27)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_24) ),
    inference(clausify,[status(thm)],[f_11_3]) ).

cnf(f_11_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_24,U_25,U_27)
    | ~ c_Orderings_Oord__class_Oless__eq(U_24,c_Groups_Oplus__class_Oplus(U_24,U_25,U_26),c_Groups_Oplus__class_Oplus(U_24,U_27,U_26))
    | ~ sP0(U_24,U_25,U_26,U_27) ),
    inference(clausify,[status(thm)],[f_11_3]) ).

cnf(f_11_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_24,c_Groups_Oplus__class_Oplus(U_24,U_25,U_26),c_Groups_Oplus__class_Oplus(U_24,U_27,U_26))
    | ~ c_Orderings_Oord__class_Oless__eq(U_24,U_25,U_27)
    | ~ sP0(U_24,U_25,U_26,U_27) ),
    inference(clausify,[status(thm)],[f_11_3]) ).

fof(f_12_1,plain,
    ! [V_b_2,V_ab_2,V_ca_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2)) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left]) ).

fof(f_12_2,plain,
    ! [U_31,U_30,U_29,U_28] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_28,c_Groups_Oplus__class_Oplus(U_28,U_29,U_30),c_Groups_Oplus__class_Oplus(U_28,U_29,U_31))
          | ~ c_Orderings_Oord__class_Oless__eq(U_28,U_30,U_31) )
        & ( c_Orderings_Oord__class_Oless__eq(U_28,U_30,U_31)
          | ~ c_Orderings_Oord__class_Oless__eq(U_28,c_Groups_Oplus__class_Oplus(U_28,U_29,U_30),c_Groups_Oplus__class_Oplus(U_28,U_29,U_31)) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_28) ),
    inference(variable_rename,[status(thm)],[f_12_1]) ).

fof(f_12_3,plain,
    ( ! [U_31,U_28,U_30,U_29] :
        ( c_Orderings_Oord__class_Oless__eq(U_28,c_Groups_Oplus__class_Oplus(U_28,U_29,U_30),c_Groups_Oplus__class_Oplus(U_28,U_29,U_31))
        | ~ c_Orderings_Oord__class_Oless__eq(U_28,U_30,U_31)
        | ~ sP1(U_31,U_28,U_30,U_29) )
    & ! [U_31,U_28,U_30,U_29] :
        ( c_Orderings_Oord__class_Oless__eq(U_28,U_30,U_31)
        | ~ c_Orderings_Oord__class_Oless__eq(U_28,c_Groups_Oplus__class_Oplus(U_28,U_29,U_30),c_Groups_Oplus__class_Oplus(U_28,U_29,U_31))
        | ~ sP1(U_31,U_28,U_30,U_29) )
    & ! [U_31,U_28,U_30,U_29] :
        ( sP1(U_31,U_28,U_30,U_29)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_28) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_12_2]) ).

cnf(f_12_4,plain,
    ( sP1(U_31,U_28,U_30,U_29)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_28) ),
    inference(clausify,[status(thm)],[f_12_3]) ).

cnf(f_12_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_28,U_30,U_31)
    | ~ c_Orderings_Oord__class_Oless__eq(U_28,c_Groups_Oplus__class_Oplus(U_28,U_29,U_30),c_Groups_Oplus__class_Oplus(U_28,U_29,U_31))
    | ~ sP1(U_31,U_28,U_30,U_29) ),
    inference(clausify,[status(thm)],[f_12_3]) ).

cnf(f_12_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_28,c_Groups_Oplus__class_Oplus(U_28,U_29,U_30),c_Groups_Oplus__class_Oplus(U_28,U_29,U_31))
    | ~ c_Orderings_Oord__class_Oless__eq(U_28,U_30,U_31)
    | ~ sP1(U_31,U_28,U_30,U_29) ),
    inference(clausify,[status(thm)],[f_12_3]) ).

fof(f_13_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
      | ~ class_Groups_Oordered__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__right__mono]) ).

fof(f_13_2,plain,
    ! [U_35,U_34,U_33,U_32] :
      ( c_Orderings_Oord__class_Oless__eq(U_32,c_Groups_Oplus__class_Oplus(U_32,U_33,U_35),c_Groups_Oplus__class_Oplus(U_32,U_34,U_35))
      | ~ c_Orderings_Oord__class_Oless__eq(U_32,U_33,U_34)
      | ~ class_Groups_Oordered__ab__semigroup__add(U_32) ),
    inference(variable_rename,[status(thm)],[f_13_1]) ).

fof(f_13_3,plain,
    ! [U_33,U_34,U_32,U_35] :
      ( c_Orderings_Oord__class_Oless__eq(U_32,c_Groups_Oplus__class_Oplus(U_32,U_33,U_35),c_Groups_Oplus__class_Oplus(U_32,U_34,U_35))
      | ~ c_Orderings_Oord__class_Oless__eq(U_32,U_33,U_34)
      | ~ class_Groups_Oordered__ab__semigroup__add(U_32) ),
    inference(definitional_conversion,[status(esa)],[f_13_2]) ).

cnf(f_13_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_32,c_Groups_Oplus__class_Oplus(U_32,U_33,U_35),c_Groups_Oplus__class_Oplus(U_32,U_34,U_35))
    | ~ c_Orderings_Oord__class_Oless__eq(U_32,U_33,U_34)
    | ~ class_Groups_Oordered__ab__semigroup__add(U_32) ),
    inference(clausify,[status(thm)],[f_13_3]) ).

fof(f_14_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
      | ~ class_Groups_Oordered__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__left__mono]) ).

fof(f_14_2,plain,
    ! [U_39,U_38,U_37,U_36] :
      ( c_Orderings_Oord__class_Oless__eq(U_36,c_Groups_Oplus__class_Oplus(U_36,U_39,U_37),c_Groups_Oplus__class_Oplus(U_36,U_39,U_38))
      | ~ c_Orderings_Oord__class_Oless__eq(U_36,U_37,U_38)
      | ~ class_Groups_Oordered__ab__semigroup__add(U_36) ),
    inference(variable_rename,[status(thm)],[f_14_1]) ).

fof(f_14_3,plain,
    ! [U_39,U_36,U_37,U_38] :
      ( c_Orderings_Oord__class_Oless__eq(U_36,c_Groups_Oplus__class_Oplus(U_36,U_39,U_37),c_Groups_Oplus__class_Oplus(U_36,U_39,U_38))
      | ~ c_Orderings_Oord__class_Oless__eq(U_36,U_37,U_38)
      | ~ class_Groups_Oordered__ab__semigroup__add(U_36) ),
    inference(definitional_conversion,[status(esa)],[f_14_2]) ).

cnf(f_14_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_36,c_Groups_Oplus__class_Oplus(U_36,U_39,U_37),c_Groups_Oplus__class_Oplus(U_36,U_39,U_38))
    | ~ c_Orderings_Oord__class_Oless__eq(U_36,U_37,U_38)
    | ~ class_Groups_Oordered__ab__semigroup__add(U_36) ),
    inference(clausify,[status(thm)],[f_14_3]) ).

fof(f_15_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
      | ~ class_Groups_Oordered__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__mono]) ).

fof(f_15_2,plain,
    ! [U_44,U_43,U_42,U_41,U_40] :
      ( c_Orderings_Oord__class_Oless__eq(U_40,c_Groups_Oplus__class_Oplus(U_40,U_41,U_43),c_Groups_Oplus__class_Oplus(U_40,U_42,U_44))
      | ~ c_Orderings_Oord__class_Oless__eq(U_40,U_43,U_44)
      | ~ c_Orderings_Oord__class_Oless__eq(U_40,U_41,U_42)
      | ~ class_Groups_Oordered__ab__semigroup__add(U_40) ),
    inference(variable_rename,[status(thm)],[f_15_1]) ).

fof(f_15_3,plain,
    ! [U_42,U_41,U_40,U_43,U_44] :
      ( c_Orderings_Oord__class_Oless__eq(U_40,c_Groups_Oplus__class_Oplus(U_40,U_41,U_43),c_Groups_Oplus__class_Oplus(U_40,U_42,U_44))
      | ~ c_Orderings_Oord__class_Oless__eq(U_40,U_43,U_44)
      | ~ c_Orderings_Oord__class_Oless__eq(U_40,U_41,U_42)
      | ~ class_Groups_Oordered__ab__semigroup__add(U_40) ),
    inference(definitional_conversion,[status(esa)],[f_15_2]) ).

cnf(f_15_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_40,c_Groups_Oplus__class_Oplus(U_40,U_41,U_43),c_Groups_Oplus__class_Oplus(U_40,U_42,U_44))
    | ~ c_Orderings_Oord__class_Oless__eq(U_40,U_43,U_44)
    | ~ c_Orderings_Oord__class_Oless__eq(U_40,U_41,U_42)
    | ~ class_Groups_Oordered__ab__semigroup__add(U_40) ),
    inference(clausify,[status(thm)],[f_15_3]) ).

fof(f_16_1,plain,
    ! [T_a] :
      ( c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
      | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_norm__zero]) ).

fof(f_16_2,plain,
    ! [U_45] :
      ( c_RealVector_Onorm__class_Onorm(U_45,c_Groups_Ozero__class_Ozero(U_45)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
      | ~ class_RealVector_Oreal__normed__vector(U_45) ),
    inference(variable_rename,[status(thm)],[f_16_1]) ).

fof(f_16_3,plain,
    ! [U_45] :
      ( c_RealVector_Onorm__class_Onorm(U_45,c_Groups_Ozero__class_Ozero(U_45)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
      | ~ class_RealVector_Oreal__normed__vector(U_45) ),
    inference(definitional_conversion,[status(esa)],[f_16_2]) ).

cnf(f_16_4,plain,
    ( c_RealVector_Onorm__class_Onorm(U_45,c_Groups_Ozero__class_Ozero(U_45)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__vector(U_45) ),
    inference(clausify,[status(thm)],[f_16_3]) ).

fof(f_17_1,plain,
    ! [T_a] :
      ( c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
      | ~ class_Groups_Ozero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_pCons__0__0]) ).

fof(f_17_2,plain,
    ! [U_46] :
      ( c_Polynomial_OpCons(U_46,c_Groups_Ozero__class_Ozero(U_46),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_46))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_46))
      | ~ class_Groups_Ozero(U_46) ),
    inference(variable_rename,[status(thm)],[f_17_1]) ).

fof(f_17_3,plain,
    ! [U_46] :
      ( c_Polynomial_OpCons(U_46,c_Groups_Ozero__class_Ozero(U_46),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_46))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_46))
      | ~ class_Groups_Ozero(U_46) ),
    inference(definitional_conversion,[status(esa)],[f_17_2]) ).

cnf(f_17_4,plain,
    ( c_Polynomial_OpCons(U_46,c_Groups_Ozero__class_Ozero(U_46),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_46))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_46))
    | ~ class_Groups_Ozero(U_46) ),
    inference(clausify,[status(thm)],[f_17_3]) ).

fof(f_18_1,plain,
    ! [V_x,T_a] :
      ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_poly__0]) ).

fof(f_18_2,plain,
    ! [U_48,U_47] :
      ( hAPP(c_Polynomial_Opoly(U_47,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_47))),U_48) = c_Groups_Ozero__class_Ozero(U_47)
      | ~ class_Rings_Ocomm__semiring__0(U_47) ),
    inference(variable_rename,[status(thm)],[f_18_1]) ).

fof(f_18_3,plain,
    ! [U_47,U_48] :
      ( hAPP(c_Polynomial_Opoly(U_47,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_47))),U_48) = c_Groups_Ozero__class_Ozero(U_47)
      | ~ class_Rings_Ocomm__semiring__0(U_47) ),
    inference(definitional_conversion,[status(esa)],[f_18_2]) ).

cnf(f_18_4,plain,
    ( hAPP(c_Polynomial_Opoly(U_47,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_47))),U_48) = c_Groups_Ozero__class_Ozero(U_47)
    | ~ class_Rings_Ocomm__semiring__0(U_47) ),
    inference(clausify,[status(thm)],[f_18_3]) ).

fof(f_19_1,plain,
    ! [V_q,T_a] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = V_q
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__poly__code_I1_J]) ).

fof(f_19_2,plain,
    ! [U_50,U_49] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_49),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_49)),U_50) = U_50
      | ~ class_Groups_Ocomm__monoid__add(U_49) ),
    inference(variable_rename,[status(thm)],[f_19_1]) ).

fof(f_19_3,plain,
    ! [U_49,U_50] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_49),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_49)),U_50) = U_50
      | ~ class_Groups_Ocomm__monoid__add(U_49) ),
    inference(definitional_conversion,[status(esa)],[f_19_2]) ).

cnf(f_19_4,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_49),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_49)),U_50) = U_50
    | ~ class_Groups_Ocomm__monoid__add(U_49) ),
    inference(clausify,[status(thm)],[f_19_3]) ).

fof(f_20_1,plain,
    ! [V_x_2,T_a] :
      ( ( ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
          | c_Groups_Ozero__class_Ozero(T_a) != V_x_2 ) )
      | ~ class_Groups_Ozero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__reorient]) ).

fof(f_20_2,plain,
    ! [U_52,U_51] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_51) = U_52
          | U_52 != c_Groups_Ozero__class_Ozero(U_51) )
        & ( U_52 = c_Groups_Ozero__class_Ozero(U_51)
          | c_Groups_Ozero__class_Ozero(U_51) != U_52 ) )
      | ~ class_Groups_Ozero(U_51) ),
    inference(variable_rename,[status(thm)],[f_20_1]) ).

fof(f_20_3,plain,
    ( ! [U_51,U_52] :
        ( c_Groups_Ozero__class_Ozero(U_51) = U_52
        | U_52 != c_Groups_Ozero__class_Ozero(U_51)
        | ~ sP2(U_51,U_52) )
    & ! [U_51,U_52] :
        ( U_52 = c_Groups_Ozero__class_Ozero(U_51)
        | c_Groups_Ozero__class_Ozero(U_51) != U_52
        | ~ sP2(U_51,U_52) )
    & ! [U_51,U_52] :
        ( sP2(U_51,U_52)
        | ~ class_Groups_Ozero(U_51) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_20_2]) ).

cnf(f_20_4,plain,
    ( sP2(U_51,U_52)
    | ~ class_Groups_Ozero(U_51) ),
    inference(clausify,[status(thm)],[f_20_3]) ).

cnf(f_20_5,plain,
    ( U_52 = c_Groups_Ozero__class_Ozero(U_51)
    | c_Groups_Ozero__class_Ozero(U_51) != U_52
    | ~ sP2(U_51,U_52) ),
    inference(clausify,[status(thm)],[f_20_3]) ).

cnf(f_20_6,plain,
    ( c_Groups_Ozero__class_Ozero(U_51) = U_52
    | U_52 != c_Groups_Ozero__class_Ozero(U_51)
    | ~ sP2(U_51,U_52) ),
    inference(clausify,[status(thm)],[f_20_3]) ).

fof(f_21_1,plain,
    ! [V_p,T_a] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__poly__code_I2_J]) ).

fof(f_21_2,plain,
    ! [U_54,U_53] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_53),U_54,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_53))) = U_54
      | ~ class_Groups_Ocomm__monoid__add(U_53) ),
    inference(variable_rename,[status(thm)],[f_21_1]) ).

fof(f_21_3,plain,
    ! [U_54,U_53] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_53),U_54,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_53))) = U_54
      | ~ class_Groups_Ocomm__monoid__add(U_53) ),
    inference(definitional_conversion,[status(esa)],[f_21_2]) ).

cnf(f_21_4,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_53),U_54,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_53))) = U_54
    | ~ class_Groups_Ocomm__monoid__add(U_53) ),
    inference(clausify,[status(thm)],[f_21_3]) ).

fof(f_22_1,plain,
    ! [V_x_2,T_a] :
      ( ( ( c_RealVector_Onorm__class_Onorm(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
          | c_RealVector_Onorm__class_Onorm(T_a,V_x_2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
      | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_norm__eq__zero]) ).

fof(f_22_2,plain,
    ! [U_56,U_55] :
      ( ( ( c_RealVector_Onorm__class_Onorm(U_55,U_56) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
          | U_56 != c_Groups_Ozero__class_Ozero(U_55) )
        & ( U_56 = c_Groups_Ozero__class_Ozero(U_55)
          | c_RealVector_Onorm__class_Onorm(U_55,U_56) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_55) ),
    inference(variable_rename,[status(thm)],[f_22_1]) ).

fof(f_22_3,plain,
    ( ! [U_55,U_56] :
        ( c_RealVector_Onorm__class_Onorm(U_55,U_56) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_56 != c_Groups_Ozero__class_Ozero(U_55)
        | ~ sP3(U_55,U_56) )
    & ! [U_55,U_56] :
        ( U_56 = c_Groups_Ozero__class_Ozero(U_55)
        | c_RealVector_Onorm__class_Onorm(U_55,U_56) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | ~ sP3(U_55,U_56) )
    & ! [U_55,U_56] :
        ( sP3(U_55,U_56)
        | ~ class_RealVector_Oreal__normed__vector(U_55) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_22_2]) ).

cnf(f_22_4,plain,
    ( sP3(U_55,U_56)
    | ~ class_RealVector_Oreal__normed__vector(U_55) ),
    inference(clausify,[status(thm)],[f_22_3]) ).

cnf(f_22_5,plain,
    ( U_56 = c_Groups_Ozero__class_Ozero(U_55)
    | c_RealVector_Onorm__class_Onorm(U_55,U_56) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ sP3(U_55,U_56) ),
    inference(clausify,[status(thm)],[f_22_3]) ).

cnf(f_22_6,plain,
    ( c_RealVector_Onorm__class_Onorm(U_55,U_56) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | U_56 != c_Groups_Ozero__class_Ozero(U_55)
    | ~ sP3(U_55,U_56) ),
    inference(clausify,[status(thm)],[f_22_3]) ).

fof(f_23_1,plain,
    ! [V_pa_2,V_ab_2,T_a] :
      ( ( ( c_Polynomial_OpCons(T_a,V_ab_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
          | V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
          | V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
            & V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) )
          | c_Polynomial_OpCons(T_a,V_ab_2,V_pa_2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
      | ~ class_Groups_Ozero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_pCons__eq__0__iff]) ).

fof(f_23_2,plain,
    ! [U_59,U_58,U_57] :
      ( ( ( c_Polynomial_OpCons(U_57,U_58,U_59) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_57))
          | U_59 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_57))
          | U_58 != c_Groups_Ozero__class_Ozero(U_57) )
        & ( ( U_59 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_57))
            & U_58 = c_Groups_Ozero__class_Ozero(U_57) )
          | c_Polynomial_OpCons(U_57,U_58,U_59) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_57)) ) )
      | ~ class_Groups_Ozero(U_57) ),
    inference(variable_rename,[status(thm)],[f_23_1]) ).

fof(f_23_3,plain,
    ( ! [U_58,U_59,U_57] :
        ( U_59 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_57))
        | ~ sP4(U_58,U_59,U_57) )
    & ! [U_58,U_59,U_57] :
        ( U_58 = c_Groups_Ozero__class_Ozero(U_57)
        | ~ sP4(U_58,U_59,U_57) )
    & ! [U_58,U_59,U_57] :
        ( c_Polynomial_OpCons(U_57,U_58,U_59) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_57))
        | U_59 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_57))
        | U_58 != c_Groups_Ozero__class_Ozero(U_57)
        | ~ sP5(U_58,U_59,U_57) )
    & ! [U_58,U_59,U_57] :
        ( sP4(U_58,U_59,U_57)
        | c_Polynomial_OpCons(U_57,U_58,U_59) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_57))
        | ~ sP5(U_58,U_59,U_57) )
    & ! [U_58,U_59,U_57] :
        ( sP5(U_58,U_59,U_57)
        | ~ class_Groups_Ozero(U_57) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4,sP5])],[f_23_2]) ).

cnf(f_23_4,plain,
    ( sP5(U_58,U_59,U_57)
    | ~ class_Groups_Ozero(U_57) ),
    inference(clausify,[status(thm)],[f_23_3]) ).

cnf(f_23_5,plain,
    ( sP4(U_58,U_59,U_57)
    | c_Polynomial_OpCons(U_57,U_58,U_59) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_57))
    | ~ sP5(U_58,U_59,U_57) ),
    inference(clausify,[status(thm)],[f_23_3]) ).

cnf(f_23_6,plain,
    ( c_Polynomial_OpCons(U_57,U_58,U_59) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_57))
    | U_59 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_57))
    | U_58 != c_Groups_Ozero__class_Ozero(U_57)
    | ~ sP5(U_58,U_59,U_57) ),
    inference(clausify,[status(thm)],[f_23_3]) ).

cnf(f_23_7,plain,
    ( U_58 = c_Groups_Ozero__class_Ozero(U_57)
    | ~ sP4(U_58,U_59,U_57) ),
    inference(clausify,[status(thm)],[f_23_3]) ).

cnf(f_23_8,plain,
    ( U_59 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_57))
    | ~ sP4(U_58,U_59,U_57) ),
    inference(clausify,[status(thm)],[f_23_3]) ).

fof(f_24_1,plain,
    ! [V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral]) ).

fof(f_24_2,plain,
    ! [U_61,U_60] :
      ( c_Groups_Oplus__class_Oplus(U_60,U_61,c_Groups_Ozero__class_Ozero(U_60)) = U_61
      | ~ class_Groups_Ocomm__monoid__add(U_60) ),
    inference(variable_rename,[status(thm)],[f_24_1]) ).

fof(f_24_3,plain,
    ! [U_61,U_60] :
      ( c_Groups_Oplus__class_Oplus(U_60,U_61,c_Groups_Ozero__class_Ozero(U_60)) = U_61
      | ~ class_Groups_Ocomm__monoid__add(U_60) ),
    inference(definitional_conversion,[status(esa)],[f_24_2]) ).

cnf(f_24_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_60,U_61,c_Groups_Ozero__class_Ozero(U_60)) = U_61
    | ~ class_Groups_Ocomm__monoid__add(U_60) ),
    inference(clausify,[status(thm)],[f_24_3]) ).

fof(f_25_1,plain,
    ! [V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a
      | ~ class_Groups_Omonoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__0__right]) ).

fof(f_25_2,plain,
    ! [U_63,U_62] :
      ( c_Groups_Oplus__class_Oplus(U_62,U_63,c_Groups_Ozero__class_Ozero(U_62)) = U_63
      | ~ class_Groups_Omonoid__add(U_62) ),
    inference(variable_rename,[status(thm)],[f_25_1]) ).

fof(f_25_3,plain,
    ! [U_63,U_62] :
      ( c_Groups_Oplus__class_Oplus(U_62,U_63,c_Groups_Ozero__class_Ozero(U_62)) = U_63
      | ~ class_Groups_Omonoid__add(U_62) ),
    inference(definitional_conversion,[status(esa)],[f_25_2]) ).

cnf(f_25_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_62,U_63,c_Groups_Ozero__class_Ozero(U_62)) = U_63
    | ~ class_Groups_Omonoid__add(U_62) ),
    inference(clausify,[status(thm)],[f_25_3]) ).

fof(f_26_1,plain,
    ! [V_ab_2,T_a] :
      ( ( ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2)
          | V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a)
          | c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_double__zero__sym]) ).

fof(f_26_2,plain,
    ! [U_65,U_64] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_64) = c_Groups_Oplus__class_Oplus(U_64,U_65,U_65)
          | U_65 != c_Groups_Ozero__class_Ozero(U_64) )
        & ( U_65 = c_Groups_Ozero__class_Ozero(U_64)
          | c_Groups_Ozero__class_Ozero(U_64) != c_Groups_Oplus__class_Oplus(U_64,U_65,U_65) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_64) ),
    inference(variable_rename,[status(thm)],[f_26_1]) ).

fof(f_26_3,plain,
    ( ! [U_65,U_64] :
        ( c_Groups_Ozero__class_Ozero(U_64) = c_Groups_Oplus__class_Oplus(U_64,U_65,U_65)
        | U_65 != c_Groups_Ozero__class_Ozero(U_64)
        | ~ sP6(U_65,U_64) )
    & ! [U_65,U_64] :
        ( U_65 = c_Groups_Ozero__class_Ozero(U_64)
        | c_Groups_Ozero__class_Ozero(U_64) != c_Groups_Oplus__class_Oplus(U_64,U_65,U_65)
        | ~ sP6(U_65,U_64) )
    & ! [U_65,U_64] :
        ( sP6(U_65,U_64)
        | ~ class_Groups_Olinordered__ab__group__add(U_64) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_26_2]) ).

cnf(f_26_4,plain,
    ( sP6(U_65,U_64)
    | ~ class_Groups_Olinordered__ab__group__add(U_64) ),
    inference(clausify,[status(thm)],[f_26_3]) ).

cnf(f_26_5,plain,
    ( U_65 = c_Groups_Ozero__class_Ozero(U_64)
    | c_Groups_Ozero__class_Ozero(U_64) != c_Groups_Oplus__class_Oplus(U_64,U_65,U_65)
    | ~ sP6(U_65,U_64) ),
    inference(clausify,[status(thm)],[f_26_3]) ).

cnf(f_26_6,plain,
    ( c_Groups_Ozero__class_Ozero(U_64) = c_Groups_Oplus__class_Oplus(U_64,U_65,U_65)
    | U_65 != c_Groups_Ozero__class_Ozero(U_64)
    | ~ sP6(U_65,U_64) ),
    inference(clausify,[status(thm)],[f_26_3]) ).

fof(f_27_1,plain,
    ! [V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__0]) ).

fof(f_27_2,plain,
    ! [U_67,U_66] :
      ( c_Groups_Oplus__class_Oplus(U_66,c_Groups_Ozero__class_Ozero(U_66),U_67) = U_67
      | ~ class_Groups_Ocomm__monoid__add(U_66) ),
    inference(variable_rename,[status(thm)],[f_27_1]) ).

fof(f_27_3,plain,
    ! [U_67,U_66] :
      ( c_Groups_Oplus__class_Oplus(U_66,c_Groups_Ozero__class_Ozero(U_66),U_67) = U_67
      | ~ class_Groups_Ocomm__monoid__add(U_66) ),
    inference(definitional_conversion,[status(esa)],[f_27_2]) ).

cnf(f_27_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_66,c_Groups_Ozero__class_Ozero(U_66),U_67) = U_67
    | ~ class_Groups_Ocomm__monoid__add(U_66) ),
    inference(clausify,[status(thm)],[f_27_3]) ).

fof(f_28_1,plain,
    ! [V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a
      | ~ class_Groups_Omonoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__0__left]) ).

fof(f_28_2,plain,
    ! [U_69,U_68] :
      ( c_Groups_Oplus__class_Oplus(U_68,c_Groups_Ozero__class_Ozero(U_68),U_69) = U_69
      | ~ class_Groups_Omonoid__add(U_68) ),
    inference(variable_rename,[status(thm)],[f_28_1]) ).

fof(f_28_3,plain,
    ! [U_68,U_69] :
      ( c_Groups_Oplus__class_Oplus(U_68,c_Groups_Ozero__class_Ozero(U_68),U_69) = U_69
      | ~ class_Groups_Omonoid__add(U_68) ),
    inference(definitional_conversion,[status(esa)],[f_28_2]) ).

cnf(f_28_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_68,c_Groups_Ozero__class_Ozero(U_68),U_69) = U_69
    | ~ class_Groups_Omonoid__add(U_68) ),
    inference(clausify,[status(thm)],[f_28_3]) ).

fof(f_29_1,plain,
    ! [V_x_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
      | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_norm__le__zero__iff]) ).

fof(f_29_2,plain,
    ! [U_71,U_70] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_70,U_71),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
          | U_71 != c_Groups_Ozero__class_Ozero(U_70) )
        & ( U_71 = c_Groups_Ozero__class_Ozero(U_70)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_70,U_71),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_70) ),
    inference(variable_rename,[status(thm)],[f_29_1]) ).

fof(f_29_3,plain,
    ( ! [U_70,U_71] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_70,U_71),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | U_71 != c_Groups_Ozero__class_Ozero(U_70)
        | ~ sP7(U_70,U_71) )
    & ! [U_70,U_71] :
        ( U_71 = c_Groups_Ozero__class_Ozero(U_70)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_70,U_71),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ sP7(U_70,U_71) )
    & ! [U_70,U_71] :
        ( sP7(U_70,U_71)
        | ~ class_RealVector_Oreal__normed__vector(U_70) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_29_2]) ).

cnf(f_29_4,plain,
    ( sP7(U_70,U_71)
    | ~ class_RealVector_Oreal__normed__vector(U_70) ),
    inference(clausify,[status(thm)],[f_29_3]) ).

cnf(f_29_5,plain,
    ( U_71 = c_Groups_Ozero__class_Ozero(U_70)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_70,U_71),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ sP7(U_70,U_71) ),
    inference(clausify,[status(thm)],[f_29_3]) ).

cnf(f_29_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_70,U_71),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | U_71 != c_Groups_Ozero__class_Ozero(U_70)
    | ~ sP7(U_70,U_71) ),
    inference(clausify,[status(thm)],[f_29_3]) ).

fof(f_30_1,plain,
    ! [V_pa_2,T_a] :
      ( ( ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
          | V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
        & ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
          | c_Polynomial_Opoly(T_a,V_pa_2) != c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) )
      | ~ class_Rings_Oidom(T_a)
      | ~ class_Int_Oring__char__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_poly__zero]) ).

fof(f_30_2,plain,
    ! [U_73,U_72] :
      ( ( ( c_Polynomial_Opoly(U_72,U_73) = c_Polynomial_Opoly(U_72,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_72)))
          | U_73 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_72)) )
        & ( U_73 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_72))
          | c_Polynomial_Opoly(U_72,U_73) != c_Polynomial_Opoly(U_72,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_72))) ) )
      | ~ class_Rings_Oidom(U_72)
      | ~ class_Int_Oring__char__0(U_72) ),
    inference(variable_rename,[status(thm)],[f_30_1]) ).

fof(f_30_3,plain,
    ( ! [U_73,U_72] :
        ( c_Polynomial_Opoly(U_72,U_73) = c_Polynomial_Opoly(U_72,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_72)))
        | U_73 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_72))
        | ~ sP8(U_73,U_72) )
    & ! [U_73,U_72] :
        ( U_73 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_72))
        | c_Polynomial_Opoly(U_72,U_73) != c_Polynomial_Opoly(U_72,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_72)))
        | ~ sP8(U_73,U_72) )
    & ! [U_73,U_72] :
        ( sP8(U_73,U_72)
        | ~ class_Rings_Oidom(U_72)
        | ~ class_Int_Oring__char__0(U_72) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_30_2]) ).

cnf(f_30_4,plain,
    ( sP8(U_73,U_72)
    | ~ class_Rings_Oidom(U_72)
    | ~ class_Int_Oring__char__0(U_72) ),
    inference(clausify,[status(thm)],[f_30_3]) ).

cnf(f_30_5,plain,
    ( U_73 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_72))
    | c_Polynomial_Opoly(U_72,U_73) != c_Polynomial_Opoly(U_72,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_72)))
    | ~ sP8(U_73,U_72) ),
    inference(clausify,[status(thm)],[f_30_3]) ).

cnf(f_30_6,plain,
    ( c_Polynomial_Opoly(U_72,U_73) = c_Polynomial_Opoly(U_72,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_72)))
    | U_73 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_72))
    | ~ sP8(U_73,U_72) ),
    inference(clausify,[status(thm)],[f_30_3]) ).

fof(f_31_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos]) ).

fof(f_31_2,plain,
    ! [U_76,U_75,U_74] :
      ( c_Orderings_Oord__class_Oless__eq(U_74,c_Groups_Oplus__class_Oplus(U_74,U_75,U_76),c_Groups_Ozero__class_Ozero(U_74))
      | ~ c_Orderings_Oord__class_Oless__eq(U_74,U_76,c_Groups_Ozero__class_Ozero(U_74))
      | ~ c_Orderings_Oord__class_Oless__eq(U_74,U_75,c_Groups_Ozero__class_Ozero(U_74))
      | ~ class_Groups_Oordered__comm__monoid__add(U_74) ),
    inference(variable_rename,[status(thm)],[f_31_1]) ).

fof(f_31_3,plain,
    ! [U_75,U_76,U_74] :
      ( c_Orderings_Oord__class_Oless__eq(U_74,c_Groups_Oplus__class_Oplus(U_74,U_75,U_76),c_Groups_Ozero__class_Ozero(U_74))
      | ~ c_Orderings_Oord__class_Oless__eq(U_74,U_76,c_Groups_Ozero__class_Ozero(U_74))
      | ~ c_Orderings_Oord__class_Oless__eq(U_74,U_75,c_Groups_Ozero__class_Ozero(U_74))
      | ~ class_Groups_Oordered__comm__monoid__add(U_74) ),
    inference(definitional_conversion,[status(esa)],[f_31_2]) ).

cnf(f_31_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_74,c_Groups_Oplus__class_Oplus(U_74,U_75,U_76),c_Groups_Ozero__class_Ozero(U_74))
    | ~ c_Orderings_Oord__class_Oless__eq(U_74,U_76,c_Groups_Ozero__class_Ozero(U_74))
    | ~ c_Orderings_Oord__class_Oless__eq(U_74,U_75,c_Groups_Ozero__class_Ozero(U_74))
    | ~ class_Groups_Oordered__comm__monoid__add(U_74) ),
    inference(clausify,[status(thm)],[f_31_3]) ).

fof(f_32_1,plain,
    ! [V_a,V_b,V_c,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__increasing2]) ).

fof(f_32_2,plain,
    ! [U_80,U_79,U_78,U_77] :
      ( c_Orderings_Oord__class_Oless__eq(U_77,U_79,c_Groups_Oplus__class_Oplus(U_77,U_80,U_78))
      | ~ c_Orderings_Oord__class_Oless__eq(U_77,U_79,U_80)
      | ~ c_Orderings_Oord__class_Oless__eq(U_77,c_Groups_Ozero__class_Ozero(U_77),U_78)
      | ~ class_Groups_Oordered__comm__monoid__add(U_77) ),
    inference(variable_rename,[status(thm)],[f_32_1]) ).

fof(f_32_3,plain,
    ! [U_77,U_78,U_79,U_80] :
      ( c_Orderings_Oord__class_Oless__eq(U_77,U_79,c_Groups_Oplus__class_Oplus(U_77,U_80,U_78))
      | ~ c_Orderings_Oord__class_Oless__eq(U_77,U_79,U_80)
      | ~ c_Orderings_Oord__class_Oless__eq(U_77,c_Groups_Ozero__class_Ozero(U_77),U_78)
      | ~ class_Groups_Oordered__comm__monoid__add(U_77) ),
    inference(definitional_conversion,[status(esa)],[f_32_2]) ).

cnf(f_32_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_77,U_79,c_Groups_Oplus__class_Oplus(U_77,U_80,U_78))
    | ~ c_Orderings_Oord__class_Oless__eq(U_77,U_79,U_80)
    | ~ c_Orderings_Oord__class_Oless__eq(U_77,c_Groups_Ozero__class_Ozero(U_77),U_78)
    | ~ class_Groups_Oordered__comm__monoid__add(U_77) ),
    inference(clausify,[status(thm)],[f_32_3]) ).

fof(f_33_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__increasing]) ).

fof(f_33_2,plain,
    ! [U_84,U_83,U_82,U_81] :
      ( c_Orderings_Oord__class_Oless__eq(U_81,U_83,c_Groups_Oplus__class_Oplus(U_81,U_82,U_84))
      | ~ c_Orderings_Oord__class_Oless__eq(U_81,U_83,U_84)
      | ~ c_Orderings_Oord__class_Oless__eq(U_81,c_Groups_Ozero__class_Ozero(U_81),U_82)
      | ~ class_Groups_Oordered__comm__monoid__add(U_81) ),
    inference(variable_rename,[status(thm)],[f_33_1]) ).

fof(f_33_3,plain,
    ! [U_81,U_83,U_82,U_84] :
      ( c_Orderings_Oord__class_Oless__eq(U_81,U_83,c_Groups_Oplus__class_Oplus(U_81,U_82,U_84))
      | ~ c_Orderings_Oord__class_Oless__eq(U_81,U_83,U_84)
      | ~ c_Orderings_Oord__class_Oless__eq(U_81,c_Groups_Ozero__class_Ozero(U_81),U_82)
      | ~ class_Groups_Oordered__comm__monoid__add(U_81) ),
    inference(definitional_conversion,[status(esa)],[f_33_2]) ).

cnf(f_33_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_81,U_83,c_Groups_Oplus__class_Oplus(U_81,U_82,U_84))
    | ~ c_Orderings_Oord__class_Oless__eq(U_81,U_83,U_84)
    | ~ c_Orderings_Oord__class_Oless__eq(U_81,c_Groups_Ozero__class_Ozero(U_81),U_82)
    | ~ class_Groups_Oordered__comm__monoid__add(U_81) ),
    inference(clausify,[status(thm)],[f_33_3]) ).

fof(f_34_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
          | V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
            & V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
          | c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff]) ).

fof(f_34_2,plain,
    ! [U_87,U_86,U_85] :
      ( ( ( c_Groups_Oplus__class_Oplus(U_85,U_86,U_87) = c_Groups_Ozero__class_Ozero(U_85)
          | U_87 != c_Groups_Ozero__class_Ozero(U_85)
          | U_86 != c_Groups_Ozero__class_Ozero(U_85) )
        & ( ( U_87 = c_Groups_Ozero__class_Ozero(U_85)
            & U_86 = c_Groups_Ozero__class_Ozero(U_85) )
          | c_Groups_Oplus__class_Oplus(U_85,U_86,U_87) != c_Groups_Ozero__class_Ozero(U_85) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(U_85,c_Groups_Ozero__class_Ozero(U_85),U_87)
      | ~ c_Orderings_Oord__class_Oless__eq(U_85,c_Groups_Ozero__class_Ozero(U_85),U_86)
      | ~ class_Groups_Oordered__comm__monoid__add(U_85) ),
    inference(variable_rename,[status(thm)],[f_34_1]) ).

fof(f_34_3,plain,
    ( ! [U_86,U_85,U_87] :
        ( U_87 = c_Groups_Ozero__class_Ozero(U_85)
        | ~ sP9(U_86,U_85,U_87) )
    & ! [U_86,U_85,U_87] :
        ( U_86 = c_Groups_Ozero__class_Ozero(U_85)
        | ~ sP9(U_86,U_85,U_87) )
    & ! [U_86,U_85,U_87] :
        ( c_Groups_Oplus__class_Oplus(U_85,U_86,U_87) = c_Groups_Ozero__class_Ozero(U_85)
        | U_87 != c_Groups_Ozero__class_Ozero(U_85)
        | U_86 != c_Groups_Ozero__class_Ozero(U_85)
        | ~ sP10(U_86,U_85,U_87) )
    & ! [U_86,U_85,U_87] :
        ( sP9(U_86,U_85,U_87)
        | c_Groups_Oplus__class_Oplus(U_85,U_86,U_87) != c_Groups_Ozero__class_Ozero(U_85)
        | ~ sP10(U_86,U_85,U_87) )
    & ! [U_86,U_85,U_87] :
        ( sP10(U_86,U_85,U_87)
        | ~ c_Orderings_Oord__class_Oless__eq(U_85,c_Groups_Ozero__class_Ozero(U_85),U_87)
        | ~ c_Orderings_Oord__class_Oless__eq(U_85,c_Groups_Ozero__class_Ozero(U_85),U_86)
        | ~ class_Groups_Oordered__comm__monoid__add(U_85) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9,sP10])],[f_34_2]) ).

cnf(f_34_4,plain,
    ( sP10(U_86,U_85,U_87)
    | ~ c_Orderings_Oord__class_Oless__eq(U_85,c_Groups_Ozero__class_Ozero(U_85),U_87)
    | ~ c_Orderings_Oord__class_Oless__eq(U_85,c_Groups_Ozero__class_Ozero(U_85),U_86)
    | ~ class_Groups_Oordered__comm__monoid__add(U_85) ),
    inference(clausify,[status(thm)],[f_34_3]) ).

cnf(f_34_5,plain,
    ( sP9(U_86,U_85,U_87)
    | c_Groups_Oplus__class_Oplus(U_85,U_86,U_87) != c_Groups_Ozero__class_Ozero(U_85)
    | ~ sP10(U_86,U_85,U_87) ),
    inference(clausify,[status(thm)],[f_34_3]) ).

cnf(f_34_6,plain,
    ( c_Groups_Oplus__class_Oplus(U_85,U_86,U_87) = c_Groups_Ozero__class_Ozero(U_85)
    | U_87 != c_Groups_Ozero__class_Ozero(U_85)
    | U_86 != c_Groups_Ozero__class_Ozero(U_85)
    | ~ sP10(U_86,U_85,U_87) ),
    inference(clausify,[status(thm)],[f_34_3]) ).

cnf(f_34_7,plain,
    ( U_86 = c_Groups_Ozero__class_Ozero(U_85)
    | ~ sP9(U_86,U_85,U_87) ),
    inference(clausify,[status(thm)],[f_34_3]) ).

cnf(f_34_8,plain,
    ( U_87 = c_Groups_Ozero__class_Ozero(U_85)
    | ~ sP9(U_86,U_85,U_87) ),
    inference(clausify,[status(thm)],[f_34_3]) ).

fof(f_35_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg]) ).

fof(f_35_2,plain,
    ! [U_90,U_89,U_88] :
      ( c_Orderings_Oord__class_Oless__eq(U_88,c_Groups_Ozero__class_Ozero(U_88),c_Groups_Oplus__class_Oplus(U_88,U_89,U_90))
      | ~ c_Orderings_Oord__class_Oless__eq(U_88,c_Groups_Ozero__class_Ozero(U_88),U_90)
      | ~ c_Orderings_Oord__class_Oless__eq(U_88,c_Groups_Ozero__class_Ozero(U_88),U_89)
      | ~ class_Groups_Oordered__comm__monoid__add(U_88) ),
    inference(variable_rename,[status(thm)],[f_35_1]) ).

fof(f_35_3,plain,
    ! [U_90,U_89,U_88] :
      ( c_Orderings_Oord__class_Oless__eq(U_88,c_Groups_Ozero__class_Ozero(U_88),c_Groups_Oplus__class_Oplus(U_88,U_89,U_90))
      | ~ c_Orderings_Oord__class_Oless__eq(U_88,c_Groups_Ozero__class_Ozero(U_88),U_90)
      | ~ c_Orderings_Oord__class_Oless__eq(U_88,c_Groups_Ozero__class_Ozero(U_88),U_89)
      | ~ class_Groups_Oordered__comm__monoid__add(U_88) ),
    inference(definitional_conversion,[status(esa)],[f_35_2]) ).

cnf(f_35_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_88,c_Groups_Ozero__class_Ozero(U_88),c_Groups_Oplus__class_Oplus(U_88,U_89,U_90))
    | ~ c_Orderings_Oord__class_Oless__eq(U_88,c_Groups_Ozero__class_Ozero(U_88),U_90)
    | ~ c_Orderings_Oord__class_Oless__eq(U_88,c_Groups_Ozero__class_Ozero(U_88),U_89)
    | ~ class_Groups_Oordered__comm__monoid__add(U_88) ),
    inference(clausify,[status(thm)],[f_35_3]) ).

fof(f_36_1,plain,
    ! [V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2),c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_double__add__le__zero__iff__single__add__le__zero]) ).

fof(f_36_2,plain,
    ! [U_92,U_91] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_91,c_Groups_Oplus__class_Oplus(U_91,U_92,U_92),c_Groups_Ozero__class_Ozero(U_91))
          | ~ c_Orderings_Oord__class_Oless__eq(U_91,U_92,c_Groups_Ozero__class_Ozero(U_91)) )
        & ( c_Orderings_Oord__class_Oless__eq(U_91,U_92,c_Groups_Ozero__class_Ozero(U_91))
          | ~ c_Orderings_Oord__class_Oless__eq(U_91,c_Groups_Oplus__class_Oplus(U_91,U_92,U_92),c_Groups_Ozero__class_Ozero(U_91)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_91) ),
    inference(variable_rename,[status(thm)],[f_36_1]) ).

fof(f_36_3,plain,
    ( ! [U_91,U_92] :
        ( c_Orderings_Oord__class_Oless__eq(U_91,c_Groups_Oplus__class_Oplus(U_91,U_92,U_92),c_Groups_Ozero__class_Ozero(U_91))
        | ~ c_Orderings_Oord__class_Oless__eq(U_91,U_92,c_Groups_Ozero__class_Ozero(U_91))
        | ~ sP11(U_91,U_92) )
    & ! [U_91,U_92] :
        ( c_Orderings_Oord__class_Oless__eq(U_91,U_92,c_Groups_Ozero__class_Ozero(U_91))
        | ~ c_Orderings_Oord__class_Oless__eq(U_91,c_Groups_Oplus__class_Oplus(U_91,U_92,U_92),c_Groups_Ozero__class_Ozero(U_91))
        | ~ sP11(U_91,U_92) )
    & ! [U_91,U_92] :
        ( sP11(U_91,U_92)
        | ~ class_Groups_Olinordered__ab__group__add(U_91) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11])],[f_36_2]) ).

cnf(f_36_4,plain,
    ( sP11(U_91,U_92)
    | ~ class_Groups_Olinordered__ab__group__add(U_91) ),
    inference(clausify,[status(thm)],[f_36_3]) ).

cnf(f_36_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_91,U_92,c_Groups_Ozero__class_Ozero(U_91))
    | ~ c_Orderings_Oord__class_Oless__eq(U_91,c_Groups_Oplus__class_Oplus(U_91,U_92,U_92),c_Groups_Ozero__class_Ozero(U_91))
    | ~ sP11(U_91,U_92) ),
    inference(clausify,[status(thm)],[f_36_3]) ).

cnf(f_36_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_91,c_Groups_Oplus__class_Oplus(U_91,U_92,U_92),c_Groups_Ozero__class_Ozero(U_91))
    | ~ c_Orderings_Oord__class_Oless__eq(U_91,U_92,c_Groups_Ozero__class_Ozero(U_91))
    | ~ sP11(U_91,U_92) ),
    inference(clausify,[status(thm)],[f_36_3]) ).

fof(f_37_1,plain,
    ! [V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__double__add__iff__zero__le__single__add]) ).

fof(f_37_2,plain,
    ! [U_94,U_93] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_93,c_Groups_Ozero__class_Ozero(U_93),c_Groups_Oplus__class_Oplus(U_93,U_94,U_94))
          | ~ c_Orderings_Oord__class_Oless__eq(U_93,c_Groups_Ozero__class_Ozero(U_93),U_94) )
        & ( c_Orderings_Oord__class_Oless__eq(U_93,c_Groups_Ozero__class_Ozero(U_93),U_94)
          | ~ c_Orderings_Oord__class_Oless__eq(U_93,c_Groups_Ozero__class_Ozero(U_93),c_Groups_Oplus__class_Oplus(U_93,U_94,U_94)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_93) ),
    inference(variable_rename,[status(thm)],[f_37_1]) ).

fof(f_37_3,plain,
    ( ! [U_94,U_93] :
        ( c_Orderings_Oord__class_Oless__eq(U_93,c_Groups_Ozero__class_Ozero(U_93),c_Groups_Oplus__class_Oplus(U_93,U_94,U_94))
        | ~ c_Orderings_Oord__class_Oless__eq(U_93,c_Groups_Ozero__class_Ozero(U_93),U_94)
        | ~ sP12(U_94,U_93) )
    & ! [U_94,U_93] :
        ( c_Orderings_Oord__class_Oless__eq(U_93,c_Groups_Ozero__class_Ozero(U_93),U_94)
        | ~ c_Orderings_Oord__class_Oless__eq(U_93,c_Groups_Ozero__class_Ozero(U_93),c_Groups_Oplus__class_Oplus(U_93,U_94,U_94))
        | ~ sP12(U_94,U_93) )
    & ! [U_94,U_93] :
        ( sP12(U_94,U_93)
        | ~ class_Groups_Olinordered__ab__group__add(U_93) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12])],[f_37_2]) ).

cnf(f_37_4,plain,
    ( sP12(U_94,U_93)
    | ~ class_Groups_Olinordered__ab__group__add(U_93) ),
    inference(clausify,[status(thm)],[f_37_3]) ).

cnf(f_37_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_93,c_Groups_Ozero__class_Ozero(U_93),U_94)
    | ~ c_Orderings_Oord__class_Oless__eq(U_93,c_Groups_Ozero__class_Ozero(U_93),c_Groups_Oplus__class_Oplus(U_93,U_94,U_94))
    | ~ sP12(U_94,U_93) ),
    inference(clausify,[status(thm)],[f_37_3]) ).

cnf(f_37_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_93,c_Groups_Ozero__class_Ozero(U_93),c_Groups_Oplus__class_Oplus(U_93,U_94,U_94))
    | ~ c_Orderings_Oord__class_Oless__eq(U_93,c_Groups_Ozero__class_Ozero(U_93),U_94)
    | ~ sP12(U_94,U_93) ),
    inference(clausify,[status(thm)],[f_37_3]) ).

fof(f_38_1,plain,
    ! [V_y,V_x,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
      | c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__le__cases]) ).

fof(f_38_2,plain,
    ! [U_97,U_96,U_95] :
      ( c_Orderings_Oord__class_Oless__eq(U_95,U_97,U_96)
      | c_Orderings_Oord__class_Oless__eq(U_95,U_96,U_97)
      | ~ class_Orderings_Olinorder(U_95) ),
    inference(variable_rename,[status(thm)],[f_38_1]) ).

fof(f_38_3,plain,
    ! [U_95,U_97,U_96] :
      ( c_Orderings_Oord__class_Oless__eq(U_95,U_97,U_96)
      | c_Orderings_Oord__class_Oless__eq(U_95,U_96,U_97)
      | ~ class_Orderings_Olinorder(U_95) ),
    inference(definitional_conversion,[status(esa)],[f_38_2]) ).

cnf(f_38_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_95,U_97,U_96)
    | c_Orderings_Oord__class_Oless__eq(U_95,U_96,U_97)
    | ~ class_Orderings_Olinorder(U_95) ),
    inference(clausify,[status(thm)],[f_38_3]) ).

fof(f_39_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
      ( c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__funE]) ).

fof(f_39_2,plain,
    ! [U_102,U_101,U_100,U_99,U_98] :
      ( c_Orderings_Oord__class_Oless__eq(U_98,hAPP(U_100,U_102),hAPP(U_101,U_102))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_99,U_98),U_100,U_101)
      | ~ class_Orderings_Oord(U_98) ),
    inference(variable_rename,[status(thm)],[f_39_1]) ).

fof(f_39_3,plain,
    ! [U_98,U_99,U_100,U_101,U_102] :
      ( c_Orderings_Oord__class_Oless__eq(U_98,hAPP(U_100,U_102),hAPP(U_101,U_102))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_99,U_98),U_100,U_101)
      | ~ class_Orderings_Oord(U_98) ),
    inference(definitional_conversion,[status(esa)],[f_39_2]) ).

cnf(f_39_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_98,hAPP(U_100,U_102),hAPP(U_101,U_102))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_99,U_98),U_100,U_101)
    | ~ class_Orderings_Oord(U_98) ),
    inference(clausify,[status(thm)],[f_39_3]) ).

fof(f_40_1,plain,
    ! [V_z,V_x,V_y,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I6_J]) ).

fof(f_40_2,plain,
    ! [U_106,U_105,U_104,U_103] :
      ( c_Orderings_Oord__class_Oless__eq(U_103,U_106,U_105)
      | ~ c_Orderings_Oord__class_Oless__eq(U_103,U_106,U_104)
      | ~ c_Orderings_Oord__class_Oless__eq(U_103,U_104,U_105)
      | ~ class_Orderings_Oorder(U_103) ),
    inference(variable_rename,[status(thm)],[f_40_1]) ).

fof(f_40_3,plain,
    ! [U_103,U_105,U_106,U_104] :
      ( c_Orderings_Oord__class_Oless__eq(U_103,U_106,U_105)
      | ~ c_Orderings_Oord__class_Oless__eq(U_103,U_106,U_104)
      | ~ c_Orderings_Oord__class_Oless__eq(U_103,U_104,U_105)
      | ~ class_Orderings_Oorder(U_103) ),
    inference(definitional_conversion,[status(esa)],[f_40_2]) ).

cnf(f_40_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_103,U_106,U_105)
    | ~ c_Orderings_Oord__class_Oless__eq(U_103,U_106,U_104)
    | ~ c_Orderings_Oord__class_Oless__eq(U_103,U_104,U_105)
    | ~ class_Orderings_Oorder(U_103) ),
    inference(clausify,[status(thm)],[f_40_3]) ).

fof(f_41_1,plain,
    ! [V_x,V_y,T_a] :
      ( V_x = V_y
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I5_J]) ).

fof(f_41_2,plain,
    ! [U_109,U_108,U_107] :
      ( U_109 = U_108
      | ~ c_Orderings_Oord__class_Oless__eq(U_107,U_109,U_108)
      | ~ c_Orderings_Oord__class_Oless__eq(U_107,U_108,U_109)
      | ~ class_Orderings_Oorder(U_107) ),
    inference(variable_rename,[status(thm)],[f_41_1]) ).

fof(f_41_3,plain,
    ! [U_109,U_107,U_108] :
      ( U_109 = U_108
      | ~ c_Orderings_Oord__class_Oless__eq(U_107,U_109,U_108)
      | ~ c_Orderings_Oord__class_Oless__eq(U_107,U_108,U_109)
      | ~ class_Orderings_Oorder(U_107) ),
    inference(definitional_conversion,[status(esa)],[f_41_2]) ).

cnf(f_41_4,plain,
    ( U_109 = U_108
    | ~ c_Orderings_Oord__class_Oless__eq(U_107,U_109,U_108)
    | ~ c_Orderings_Oord__class_Oless__eq(U_107,U_108,U_109)
    | ~ class_Orderings_Oorder(U_107) ),
    inference(clausify,[status(thm)],[f_41_3]) ).

fof(f_42_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__trans]) ).

fof(f_42_2,plain,
    ! [U_113,U_112,U_111,U_110] :
      ( c_Orderings_Oord__class_Oless__eq(U_110,U_111,U_113)
      | ~ c_Orderings_Oord__class_Oless__eq(U_110,U_112,U_113)
      | ~ c_Orderings_Oord__class_Oless__eq(U_110,U_111,U_112)
      | ~ class_Orderings_Opreorder(U_110) ),
    inference(variable_rename,[status(thm)],[f_42_1]) ).

fof(f_42_3,plain,
    ! [U_112,U_111,U_113,U_110] :
      ( c_Orderings_Oord__class_Oless__eq(U_110,U_111,U_113)
      | ~ c_Orderings_Oord__class_Oless__eq(U_110,U_112,U_113)
      | ~ c_Orderings_Oord__class_Oless__eq(U_110,U_111,U_112)
      | ~ class_Orderings_Opreorder(U_110) ),
    inference(definitional_conversion,[status(esa)],[f_42_2]) ).

cnf(f_42_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_110,U_111,U_113)
    | ~ c_Orderings_Oord__class_Oless__eq(U_110,U_112,U_113)
    | ~ c_Orderings_Oord__class_Oless__eq(U_110,U_111,U_112)
    | ~ class_Orderings_Opreorder(U_110) ),
    inference(clausify,[status(thm)],[f_42_3]) ).

fof(f_43_1,plain,
    ! [V_y,V_x,T_a] :
      ( V_x = V_y
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__antisym]) ).

fof(f_43_2,plain,
    ! [U_116,U_115,U_114] :
      ( U_115 = U_116
      | ~ c_Orderings_Oord__class_Oless__eq(U_114,U_116,U_115)
      | ~ c_Orderings_Oord__class_Oless__eq(U_114,U_115,U_116)
      | ~ class_Orderings_Oorder(U_114) ),
    inference(variable_rename,[status(thm)],[f_43_1]) ).

fof(f_43_3,plain,
    ! [U_116,U_114,U_115] :
      ( U_115 = U_116
      | ~ c_Orderings_Oord__class_Oless__eq(U_114,U_116,U_115)
      | ~ c_Orderings_Oord__class_Oless__eq(U_114,U_115,U_116)
      | ~ class_Orderings_Oorder(U_114) ),
    inference(definitional_conversion,[status(esa)],[f_43_2]) ).

cnf(f_43_4,plain,
    ( U_115 = U_116
    | ~ c_Orderings_Oord__class_Oless__eq(U_114,U_116,U_115)
    | ~ c_Orderings_Oord__class_Oless__eq(U_114,U_115,U_116)
    | ~ class_Orderings_Oorder(U_114) ),
    inference(clausify,[status(thm)],[f_43_3]) ).

fof(f_44_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
      | V_b != V_c
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I4_J]) ).

fof(f_44_2,plain,
    ! [U_120,U_119,U_118,U_117] :
      ( c_Orderings_Oord__class_Oless__eq(U_117,U_120,U_119)
      | U_118 != U_120
      | ~ c_Orderings_Oord__class_Oless__eq(U_117,U_118,U_119)
      | ~ class_Orderings_Oorder(U_117) ),
    inference(variable_rename,[status(thm)],[f_44_1]) ).

fof(f_44_3,plain,
    ! [U_117,U_119,U_120,U_118] :
      ( c_Orderings_Oord__class_Oless__eq(U_117,U_120,U_119)
      | U_118 != U_120
      | ~ c_Orderings_Oord__class_Oless__eq(U_117,U_118,U_119)
      | ~ class_Orderings_Oorder(U_117) ),
    inference(definitional_conversion,[status(esa)],[f_44_2]) ).

cnf(f_44_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_117,U_120,U_119)
    | U_118 != U_120
    | ~ c_Orderings_Oord__class_Oless__eq(U_117,U_118,U_119)
    | ~ class_Orderings_Oorder(U_117) ),
    inference(clausify,[status(thm)],[f_44_3]) ).

fof(f_45_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
      | V_b != V_c
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
      | ~ class_Orderings_Oord(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ord__le__eq__trans]) ).

fof(f_45_2,plain,
    ! [U_124,U_123,U_122,U_121] :
      ( c_Orderings_Oord__class_Oless__eq(U_121,U_122,U_124)
      | U_123 != U_124
      | ~ c_Orderings_Oord__class_Oless__eq(U_121,U_122,U_123)
      | ~ class_Orderings_Oord(U_121) ),
    inference(variable_rename,[status(thm)],[f_45_1]) ).

fof(f_45_3,plain,
    ! [U_122,U_123,U_124,U_121] :
      ( c_Orderings_Oord__class_Oless__eq(U_121,U_122,U_124)
      | U_123 != U_124
      | ~ c_Orderings_Oord__class_Oless__eq(U_121,U_122,U_123)
      | ~ class_Orderings_Oord(U_121) ),
    inference(definitional_conversion,[status(esa)],[f_45_2]) ).

cnf(f_45_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_121,U_122,U_124)
    | U_123 != U_124
    | ~ c_Orderings_Oord__class_Oless__eq(U_121,U_122,U_123)
    | ~ class_Orderings_Oord(U_121) ),
    inference(clausify,[status(thm)],[f_45_3]) ).

fof(f_46_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b)
      | V_a != V_b
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I3_J]) ).

fof(f_46_2,plain,
    ! [U_128,U_127,U_126,U_125] :
      ( c_Orderings_Oord__class_Oless__eq(U_125,U_128,U_126)
      | ~ c_Orderings_Oord__class_Oless__eq(U_125,U_128,U_127)
      | U_126 != U_127
      | ~ class_Orderings_Oorder(U_125) ),
    inference(variable_rename,[status(thm)],[f_46_1]) ).

fof(f_46_3,plain,
    ! [U_128,U_127,U_125,U_126] :
      ( c_Orderings_Oord__class_Oless__eq(U_125,U_128,U_126)
      | ~ c_Orderings_Oord__class_Oless__eq(U_125,U_128,U_127)
      | U_126 != U_127
      | ~ class_Orderings_Oorder(U_125) ),
    inference(definitional_conversion,[status(esa)],[f_46_2]) ).

cnf(f_46_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_125,U_128,U_126)
    | ~ c_Orderings_Oord__class_Oless__eq(U_125,U_128,U_127)
    | U_126 != U_127
    | ~ class_Orderings_Oorder(U_125) ),
    inference(clausify,[status(thm)],[f_46_3]) ).

fof(f_47_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
      | V_a != V_b
      | ~ class_Orderings_Oord(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ord__eq__le__trans]) ).

fof(f_47_2,plain,
    ! [U_132,U_131,U_130,U_129] :
      ( c_Orderings_Oord__class_Oless__eq(U_129,U_130,U_132)
      | ~ c_Orderings_Oord__class_Oless__eq(U_129,U_131,U_132)
      | U_130 != U_131
      | ~ class_Orderings_Oord(U_129) ),
    inference(variable_rename,[status(thm)],[f_47_1]) ).

fof(f_47_3,plain,
    ! [U_131,U_132,U_130,U_129] :
      ( c_Orderings_Oord__class_Oless__eq(U_129,U_130,U_132)
      | ~ c_Orderings_Oord__class_Oless__eq(U_129,U_131,U_132)
      | U_130 != U_131
      | ~ class_Orderings_Oord(U_129) ),
    inference(definitional_conversion,[status(esa)],[f_47_2]) ).

cnf(f_47_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_129,U_130,U_132)
    | ~ c_Orderings_Oord__class_Oless__eq(U_129,U_131,U_132)
    | U_130 != U_131
    | ~ class_Orderings_Oord(U_129) ),
    inference(clausify,[status(thm)],[f_47_3]) ).

fof(f_48_1,plain,
    ! [V_x_2,V_y_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__antisym__conv]) ).

fof(f_48_2,plain,
    ! [U_135,U_134,U_133] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_133,U_135,U_134)
          | U_135 != U_134 )
        & ( U_135 = U_134
          | ~ c_Orderings_Oord__class_Oless__eq(U_133,U_135,U_134) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(U_133,U_134,U_135)
      | ~ class_Orderings_Oorder(U_133) ),
    inference(variable_rename,[status(thm)],[f_48_1]) ).

fof(f_48_3,plain,
    ( ! [U_134,U_135,U_133] :
        ( c_Orderings_Oord__class_Oless__eq(U_133,U_135,U_134)
        | U_135 != U_134
        | ~ sP13(U_134,U_135,U_133) )
    & ! [U_134,U_135,U_133] :
        ( U_135 = U_134
        | ~ c_Orderings_Oord__class_Oless__eq(U_133,U_135,U_134)
        | ~ sP13(U_134,U_135,U_133) )
    & ! [U_134,U_135,U_133] :
        ( sP13(U_134,U_135,U_133)
        | ~ c_Orderings_Oord__class_Oless__eq(U_133,U_134,U_135)
        | ~ class_Orderings_Oorder(U_133) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP13])],[f_48_2]) ).

cnf(f_48_4,plain,
    ( sP13(U_134,U_135,U_133)
    | ~ c_Orderings_Oord__class_Oless__eq(U_133,U_134,U_135)
    | ~ class_Orderings_Oorder(U_133) ),
    inference(clausify,[status(thm)],[f_48_3]) ).

cnf(f_48_5,plain,
    ( U_135 = U_134
    | ~ c_Orderings_Oord__class_Oless__eq(U_133,U_135,U_134)
    | ~ sP13(U_134,U_135,U_133) ),
    inference(clausify,[status(thm)],[f_48_3]) ).

cnf(f_48_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_133,U_135,U_134)
    | U_135 != U_134
    | ~ sP13(U_134,U_135,U_133) ),
    inference(clausify,[status(thm)],[f_48_3]) ).

fof(f_49_1,plain,
    ! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
      ( c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__funD]) ).

fof(f_49_2,plain,
    ! [U_140,U_139,U_138,U_137,U_136] :
      ( c_Orderings_Oord__class_Oless__eq(U_136,hAPP(U_138,U_140),hAPP(U_139,U_140))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_137,U_136),U_138,U_139)
      | ~ class_Orderings_Oord(U_136) ),
    inference(variable_rename,[status(thm)],[f_49_1]) ).

fof(f_49_3,plain,
    ! [U_137,U_139,U_138,U_136,U_140] :
      ( c_Orderings_Oord__class_Oless__eq(U_136,hAPP(U_138,U_140),hAPP(U_139,U_140))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_137,U_136),U_138,U_139)
      | ~ class_Orderings_Oord(U_136) ),
    inference(definitional_conversion,[status(esa)],[f_49_2]) ).

cnf(f_49_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_136,hAPP(U_138,U_140),hAPP(U_139,U_140))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_137,U_136),U_138,U_139)
    | ~ class_Orderings_Oord(U_136) ),
    inference(clausify,[status(thm)],[f_49_3]) ).

fof(f_50_1,plain,
    ! [V_y,V_x,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
      | V_x != V_y
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__eq__refl]) ).

fof(f_50_2,plain,
    ! [U_143,U_142,U_141] :
      ( c_Orderings_Oord__class_Oless__eq(U_141,U_142,U_143)
      | U_142 != U_143
      | ~ class_Orderings_Opreorder(U_141) ),
    inference(variable_rename,[status(thm)],[f_50_1]) ).

fof(f_50_3,plain,
    ! [U_142,U_143,U_141] :
      ( c_Orderings_Oord__class_Oless__eq(U_141,U_142,U_143)
      | U_142 != U_143
      | ~ class_Orderings_Opreorder(U_141) ),
    inference(definitional_conversion,[status(esa)],[f_50_2]) ).

cnf(f_50_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_141,U_142,U_143)
    | U_142 != U_143
    | ~ class_Orderings_Opreorder(U_141) ),
    inference(clausify,[status(thm)],[f_50_3]) ).

fof(f_51_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( V_x_2 = V_y_2
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
        & ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
            & c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
          | V_x_2 != V_y_2 ) )
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__eq__iff]) ).

fof(f_51_2,plain,
    ! [U_146,U_145,U_144] :
      ( ( ( U_145 = U_146
          | ~ c_Orderings_Oord__class_Oless__eq(U_144,U_146,U_145)
          | ~ c_Orderings_Oord__class_Oless__eq(U_144,U_145,U_146) )
        & ( ( c_Orderings_Oord__class_Oless__eq(U_144,U_146,U_145)
            & c_Orderings_Oord__class_Oless__eq(U_144,U_145,U_146) )
          | U_145 != U_146 ) )
      | ~ class_Orderings_Oorder(U_144) ),
    inference(variable_rename,[status(thm)],[f_51_1]) ).

fof(f_51_3,plain,
    ( ! [U_145,U_144,U_146] :
        ( c_Orderings_Oord__class_Oless__eq(U_144,U_146,U_145)
        | ~ sP14(U_145,U_144,U_146) )
    & ! [U_145,U_144,U_146] :
        ( c_Orderings_Oord__class_Oless__eq(U_144,U_145,U_146)
        | ~ sP14(U_145,U_144,U_146) )
    & ! [U_145,U_144,U_146] :
        ( U_145 = U_146
        | ~ c_Orderings_Oord__class_Oless__eq(U_144,U_146,U_145)
        | ~ c_Orderings_Oord__class_Oless__eq(U_144,U_145,U_146)
        | ~ sP15(U_145,U_144,U_146) )
    & ! [U_145,U_144,U_146] :
        ( sP14(U_145,U_144,U_146)
        | U_145 != U_146
        | ~ sP15(U_145,U_144,U_146) )
    & ! [U_145,U_144,U_146] :
        ( sP15(U_145,U_144,U_146)
        | ~ class_Orderings_Oorder(U_144) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14,sP15])],[f_51_2]) ).

cnf(f_51_4,plain,
    ( sP15(U_145,U_144,U_146)
    | ~ class_Orderings_Oorder(U_144) ),
    inference(clausify,[status(thm)],[f_51_3]) ).

cnf(f_51_5,plain,
    ( sP14(U_145,U_144,U_146)
    | U_145 != U_146
    | ~ sP15(U_145,U_144,U_146) ),
    inference(clausify,[status(thm)],[f_51_3]) ).

cnf(f_51_6,plain,
    ( U_145 = U_146
    | ~ c_Orderings_Oord__class_Oless__eq(U_144,U_146,U_145)
    | ~ c_Orderings_Oord__class_Oless__eq(U_144,U_145,U_146)
    | ~ sP15(U_145,U_144,U_146) ),
    inference(clausify,[status(thm)],[f_51_3]) ).

cnf(f_51_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_144,U_145,U_146)
    | ~ sP14(U_145,U_144,U_146) ),
    inference(clausify,[status(thm)],[f_51_3]) ).

cnf(f_51_8,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_144,U_146,U_145)
    | ~ sP14(U_145,U_144,U_146) ),
    inference(clausify,[status(thm)],[f_51_3]) ).

fof(f_52_1,plain,
    ! [V_y,V_x,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
      | c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__linear]) ).

fof(f_52_2,plain,
    ! [U_149,U_148,U_147] :
      ( c_Orderings_Oord__class_Oless__eq(U_147,U_149,U_148)
      | c_Orderings_Oord__class_Oless__eq(U_147,U_148,U_149)
      | ~ class_Orderings_Olinorder(U_147) ),
    inference(variable_rename,[status(thm)],[f_52_1]) ).

fof(f_52_3,plain,
    ! [U_147,U_148,U_149] :
      ( c_Orderings_Oord__class_Oless__eq(U_147,U_149,U_148)
      | c_Orderings_Oord__class_Oless__eq(U_147,U_148,U_149)
      | ~ class_Orderings_Olinorder(U_147) ),
    inference(definitional_conversion,[status(esa)],[f_52_2]) ).

cnf(f_52_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_147,U_149,U_148)
    | c_Orderings_Oord__class_Oless__eq(U_147,U_148,U_149)
    | ~ class_Orderings_Olinorder(U_147) ),
    inference(clausify,[status(thm)],[f_52_3]) ).

fof(f_53_1,plain,
    ! [V_g_2,V_f_2,T_a,T_b] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
          | ? [B_x] : ~ c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)) )
        & ( ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) ) )
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_le__fun__def]) ).

fof(f_53_2,plain,
    ! [U_155,U_154,U_153,U_152] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_153,U_152),U_154,U_155)
          | ? [U_151] : ~ c_Orderings_Oord__class_Oless__eq(U_152,hAPP(U_154,U_151),hAPP(U_155,U_151)) )
        & ( ! [U_150] : c_Orderings_Oord__class_Oless__eq(U_152,hAPP(U_154,U_150),hAPP(U_155,U_150))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_153,U_152),U_154,U_155) ) )
      | ~ class_Orderings_Oord(U_152) ),
    inference(variable_rename,[status(thm)],[f_53_1]) ).

fof(f_53_3,plain,
    ! [U_155,U_154,U_153,U_152] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_153,U_152),U_154,U_155)
          | ~ c_Orderings_Oord__class_Oless__eq(U_152,hAPP(U_154,sK3(U_155,U_154,U_153,U_152)),hAPP(U_155,sK3(U_155,U_154,U_153,U_152))) )
        & ( ! [U_150] : c_Orderings_Oord__class_Oless__eq(U_152,hAPP(U_154,U_150),hAPP(U_155,U_150))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_153,U_152),U_154,U_155) ) )
      | ~ class_Orderings_Oord(U_152) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_151,sK3(U_155,U_154,U_153,U_152))],[f_53_2]) ).

fof(f_53_4,plain,
    ( ! [U_154,U_155,U_150,U_152,U_153] :
        ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_153,U_152),U_154,U_155)
        | ~ c_Orderings_Oord__class_Oless__eq(U_152,hAPP(U_154,sK3(U_155,U_154,U_153,U_152)),hAPP(U_155,sK3(U_155,U_154,U_153,U_152)))
        | ~ sP16(U_154,U_155,U_150,U_152,U_153) )
    & ! [U_154,U_155,U_150,U_152,U_153] :
        ( c_Orderings_Oord__class_Oless__eq(U_152,hAPP(U_154,U_150),hAPP(U_155,U_150))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_153,U_152),U_154,U_155)
        | ~ sP16(U_154,U_155,U_150,U_152,U_153) )
    & ! [U_154,U_155,U_150,U_152,U_153] :
        ( sP16(U_154,U_155,U_150,U_152,U_153)
        | ~ class_Orderings_Oord(U_152) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16])],[f_53_3]) ).

cnf(f_53_5,plain,
    ( sP16(U_154,U_155,U_150,U_152,U_153)
    | ~ class_Orderings_Oord(U_152) ),
    inference(clausify,[status(thm)],[f_53_4]) ).

cnf(f_53_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_152,hAPP(U_154,U_150),hAPP(U_155,U_150))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_153,U_152),U_154,U_155)
    | ~ sP16(U_154,U_155,U_150,U_152,U_153) ),
    inference(clausify,[status(thm)],[f_53_4]) ).

cnf(f_53_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_153,U_152),U_154,U_155)
    | ~ c_Orderings_Oord__class_Oless__eq(U_152,hAPP(U_154,sK3(U_155,U_154,U_153,U_152)),hAPP(U_155,sK3(U_155,U_154,U_153,U_152)))
    | ~ sP16(U_154,U_155,U_150,U_152,U_153) ),
    inference(clausify,[status(thm)],[f_53_4]) ).

fof(f_54_1,plain,
    ! [V_z,V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_w),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_w,V_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z))),
    inference(fof_nnf,[status(thm)],[fact_complex__mod__triangle__sub]) ).

fof(f_54_2,plain,
    ! [U_157,U_156] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_156),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_156,U_157)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_157))),
    inference(variable_rename,[status(thm)],[f_54_1]) ).

fof(f_54_3,plain,
    ! [U_157,U_156] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_156),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_156,U_157)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_157))),
    inference(definitional_conversion,[status(esa)],[f_54_2]) ).

cnf(f_54_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_156),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_156,U_157)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_157))),
    inference(clausify,[status(thm)],[f_54_3]) ).

fof(f_55_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( V_b = V_c
      | c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) != c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
      | ~ class_Groups_Ocancel__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq]) ).

fof(f_55_2,plain,
    ! [U_161,U_160,U_159,U_158] :
      ( U_159 = U_161
      | c_Groups_Oplus__class_Oplus(U_158,U_159,U_160) != c_Groups_Oplus__class_Oplus(U_158,U_161,U_160)
      | ~ class_Groups_Ocancel__semigroup__add(U_158) ),
    inference(variable_rename,[status(thm)],[f_55_1]) ).

fof(f_55_3,plain,
    ! [U_159,U_158,U_160,U_161] :
      ( U_159 = U_161
      | c_Groups_Oplus__class_Oplus(U_158,U_159,U_160) != c_Groups_Oplus__class_Oplus(U_158,U_161,U_160)
      | ~ class_Groups_Ocancel__semigroup__add(U_158) ),
    inference(definitional_conversion,[status(esa)],[f_55_2]) ).

cnf(f_55_4,plain,
    ( U_159 = U_161
    | c_Groups_Oplus__class_Oplus(U_158,U_159,U_160) != c_Groups_Oplus__class_Oplus(U_158,U_161,U_160)
    | ~ class_Groups_Ocancel__semigroup__add(U_158) ),
    inference(clausify,[status(thm)],[f_55_3]) ).

fof(f_56_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( V_b = V_c
      | c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) != c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
      | ~ class_Groups_Ocancel__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__imp__eq]) ).

fof(f_56_2,plain,
    ! [U_165,U_164,U_163,U_162] :
      ( U_164 = U_165
      | c_Groups_Oplus__class_Oplus(U_162,U_163,U_164) != c_Groups_Oplus__class_Oplus(U_162,U_163,U_165)
      | ~ class_Groups_Ocancel__ab__semigroup__add(U_162) ),
    inference(variable_rename,[status(thm)],[f_56_1]) ).

fof(f_56_3,plain,
    ! [U_164,U_163,U_162,U_165] :
      ( U_164 = U_165
      | c_Groups_Oplus__class_Oplus(U_162,U_163,U_164) != c_Groups_Oplus__class_Oplus(U_162,U_163,U_165)
      | ~ class_Groups_Ocancel__ab__semigroup__add(U_162) ),
    inference(definitional_conversion,[status(esa)],[f_56_2]) ).

cnf(f_56_4,plain,
    ( U_164 = U_165
    | c_Groups_Oplus__class_Oplus(U_162,U_163,U_164) != c_Groups_Oplus__class_Oplus(U_162,U_163,U_165)
    | ~ class_Groups_Ocancel__ab__semigroup__add(U_162) ),
    inference(clausify,[status(thm)],[f_56_3]) ).

fof(f_57_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( V_b = V_c
      | c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) != c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)
      | ~ class_Groups_Ocancel__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq]) ).

fof(f_57_2,plain,
    ! [U_169,U_168,U_167,U_166] :
      ( U_168 = U_169
      | c_Groups_Oplus__class_Oplus(U_166,U_167,U_168) != c_Groups_Oplus__class_Oplus(U_166,U_167,U_169)
      | ~ class_Groups_Ocancel__semigroup__add(U_166) ),
    inference(variable_rename,[status(thm)],[f_57_1]) ).

fof(f_57_3,plain,
    ! [U_168,U_169,U_166,U_167] :
      ( U_168 = U_169
      | c_Groups_Oplus__class_Oplus(U_166,U_167,U_168) != c_Groups_Oplus__class_Oplus(U_166,U_167,U_169)
      | ~ class_Groups_Ocancel__semigroup__add(U_166) ),
    inference(definitional_conversion,[status(esa)],[f_57_2]) ).

cnf(f_57_4,plain,
    ( U_168 = U_169
    | c_Groups_Oplus__class_Oplus(U_166,U_167,U_168) != c_Groups_Oplus__class_Oplus(U_166,U_167,U_169)
    | ~ class_Groups_Ocancel__semigroup__add(U_166) ),
    inference(clausify,[status(thm)],[f_57_3]) ).

fof(f_58_1,plain,
    ! [V_ca_2,V_ab_2,V_b_2,T_a] :
      ( ( ( c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) = c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2)
          | V_b_2 != V_ca_2 )
        & ( V_b_2 = V_ca_2
          | c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) != c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2) ) )
      | ~ class_Groups_Ocancel__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__right__cancel]) ).

fof(f_58_2,plain,
    ! [U_173,U_172,U_171,U_170] :
      ( ( ( c_Groups_Oplus__class_Oplus(U_170,U_171,U_172) = c_Groups_Oplus__class_Oplus(U_170,U_173,U_172)
          | U_171 != U_173 )
        & ( U_171 = U_173
          | c_Groups_Oplus__class_Oplus(U_170,U_171,U_172) != c_Groups_Oplus__class_Oplus(U_170,U_173,U_172) ) )
      | ~ class_Groups_Ocancel__semigroup__add(U_170) ),
    inference(variable_rename,[status(thm)],[f_58_1]) ).

fof(f_58_3,plain,
    ( ! [U_172,U_173,U_171,U_170] :
        ( c_Groups_Oplus__class_Oplus(U_170,U_171,U_172) = c_Groups_Oplus__class_Oplus(U_170,U_173,U_172)
        | U_171 != U_173
        | ~ sP17(U_172,U_173,U_171,U_170) )
    & ! [U_172,U_173,U_171,U_170] :
        ( U_171 = U_173
        | c_Groups_Oplus__class_Oplus(U_170,U_171,U_172) != c_Groups_Oplus__class_Oplus(U_170,U_173,U_172)
        | ~ sP17(U_172,U_173,U_171,U_170) )
    & ! [U_172,U_173,U_171,U_170] :
        ( sP17(U_172,U_173,U_171,U_170)
        | ~ class_Groups_Ocancel__semigroup__add(U_170) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP17])],[f_58_2]) ).

cnf(f_58_4,plain,
    ( sP17(U_172,U_173,U_171,U_170)
    | ~ class_Groups_Ocancel__semigroup__add(U_170) ),
    inference(clausify,[status(thm)],[f_58_3]) ).

cnf(f_58_5,plain,
    ( U_171 = U_173
    | c_Groups_Oplus__class_Oplus(U_170,U_171,U_172) != c_Groups_Oplus__class_Oplus(U_170,U_173,U_172)
    | ~ sP17(U_172,U_173,U_171,U_170) ),
    inference(clausify,[status(thm)],[f_58_3]) ).

cnf(f_58_6,plain,
    ( c_Groups_Oplus__class_Oplus(U_170,U_171,U_172) = c_Groups_Oplus__class_Oplus(U_170,U_173,U_172)
    | U_171 != U_173
    | ~ sP17(U_172,U_173,U_171,U_170) ),
    inference(clausify,[status(thm)],[f_58_3]) ).

fof(f_59_1,plain,
    ! [V_ca_2,V_b_2,V_ab_2,T_a] :
      ( ( ( c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_b_2) = c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ca_2)
          | V_b_2 != V_ca_2 )
        & ( V_b_2 = V_ca_2
          | c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_b_2) != c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ca_2) ) )
      | ~ class_Groups_Ocancel__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__left__cancel]) ).

fof(f_59_2,plain,
    ! [U_177,U_176,U_175,U_174] :
      ( ( ( c_Groups_Oplus__class_Oplus(U_174,U_175,U_176) = c_Groups_Oplus__class_Oplus(U_174,U_175,U_177)
          | U_176 != U_177 )
        & ( U_176 = U_177
          | c_Groups_Oplus__class_Oplus(U_174,U_175,U_176) != c_Groups_Oplus__class_Oplus(U_174,U_175,U_177) ) )
      | ~ class_Groups_Ocancel__semigroup__add(U_174) ),
    inference(variable_rename,[status(thm)],[f_59_1]) ).

fof(f_59_3,plain,
    ( ! [U_174,U_177,U_175,U_176] :
        ( c_Groups_Oplus__class_Oplus(U_174,U_175,U_176) = c_Groups_Oplus__class_Oplus(U_174,U_175,U_177)
        | U_176 != U_177
        | ~ sP18(U_174,U_177,U_175,U_176) )
    & ! [U_174,U_177,U_175,U_176] :
        ( U_176 = U_177
        | c_Groups_Oplus__class_Oplus(U_174,U_175,U_176) != c_Groups_Oplus__class_Oplus(U_174,U_175,U_177)
        | ~ sP18(U_174,U_177,U_175,U_176) )
    & ! [U_174,U_177,U_175,U_176] :
        ( sP18(U_174,U_177,U_175,U_176)
        | ~ class_Groups_Ocancel__semigroup__add(U_174) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP18])],[f_59_2]) ).

cnf(f_59_4,plain,
    ( sP18(U_174,U_177,U_175,U_176)
    | ~ class_Groups_Ocancel__semigroup__add(U_174) ),
    inference(clausify,[status(thm)],[f_59_3]) ).

cnf(f_59_5,plain,
    ( U_176 = U_177
    | c_Groups_Oplus__class_Oplus(U_174,U_175,U_176) != c_Groups_Oplus__class_Oplus(U_174,U_175,U_177)
    | ~ sP18(U_174,U_177,U_175,U_176) ),
    inference(clausify,[status(thm)],[f_59_3]) ).

cnf(f_59_6,plain,
    ( c_Groups_Oplus__class_Oplus(U_174,U_175,U_176) = c_Groups_Oplus__class_Oplus(U_174,U_175,U_177)
    | U_176 != U_177
    | ~ sP18(U_174,U_177,U_175,U_176) ),
    inference(clausify,[status(thm)],[f_59_3]) ).

fof(f_60_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
      | ~ class_Groups_Oab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J]) ).

fof(f_60_2,plain,
    ! [U_181,U_180,U_179,U_178] :
      ( c_Groups_Oplus__class_Oplus(U_178,c_Groups_Oplus__class_Oplus(U_178,U_179,U_180),U_181) = c_Groups_Oplus__class_Oplus(U_178,U_179,c_Groups_Oplus__class_Oplus(U_178,U_180,U_181))
      | ~ class_Groups_Oab__semigroup__add(U_178) ),
    inference(variable_rename,[status(thm)],[f_60_1]) ).

fof(f_60_3,plain,
    ! [U_179,U_178,U_181,U_180] :
      ( c_Groups_Oplus__class_Oplus(U_178,c_Groups_Oplus__class_Oplus(U_178,U_179,U_180),U_181) = c_Groups_Oplus__class_Oplus(U_178,U_179,c_Groups_Oplus__class_Oplus(U_178,U_180,U_181))
      | ~ class_Groups_Oab__semigroup__add(U_178) ),
    inference(definitional_conversion,[status(esa)],[f_60_2]) ).

cnf(f_60_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_178,c_Groups_Oplus__class_Oplus(U_178,U_179,U_180),U_181) = c_Groups_Oplus__class_Oplus(U_178,U_179,c_Groups_Oplus__class_Oplus(U_178,U_180,U_181))
    | ~ class_Groups_Oab__semigroup__add(U_178) ),
    inference(clausify,[status(thm)],[f_60_3]) ).

fof(f_61_1,plain,
    ! [V_w,V_z] :
      ( V_z = V_w
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w) ),
    inference(fof_nnf,[status(thm)],[fact_real__le__antisym]) ).

fof(f_61_2,plain,
    ! [U_183,U_182] :
      ( U_182 = U_183
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_183,U_182)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_182,U_183) ),
    inference(variable_rename,[status(thm)],[f_61_1]) ).

fof(f_61_3,plain,
    ! [U_183,U_182] :
      ( U_182 = U_183
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_183,U_182)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_182,U_183) ),
    inference(definitional_conversion,[status(esa)],[f_61_2]) ).

cnf(f_61_4,plain,
    ( U_182 = U_183
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_183,U_182)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_182,U_183) ),
    inference(clausify,[status(thm)],[f_61_3]) ).

fof(f_62_1,plain,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_k)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_j,V_k)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_i,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_real__le__trans]) ).

fof(f_62_2,plain,
    ! [U_186,U_185,U_184] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_184,U_186)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_185,U_186)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_184,U_185) ),
    inference(variable_rename,[status(thm)],[f_62_1]) ).

fof(f_62_3,plain,
    ! [U_184,U_186,U_185] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_184,U_186)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_185,U_186)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_184,U_185) ),
    inference(definitional_conversion,[status(esa)],[f_62_2]) ).

cnf(f_62_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_184,U_186)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_185,U_186)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_184,U_185) ),
    inference(clausify,[status(thm)],[f_62_3]) ).

fof(f_63_1,plain,
    ! [V_w,V_z] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_z)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_z,V_w) ),
    inference(fof_nnf,[status(thm)],[fact_real__le__linear]) ).

fof(f_63_2,plain,
    ! [U_188,U_187] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_188,U_187)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_187,U_188) ),
    inference(variable_rename,[status(thm)],[f_63_1]) ).

fof(f_63_3,plain,
    ! [U_188,U_187] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_188,U_187)
      | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_187,U_188) ),
    inference(definitional_conversion,[status(esa)],[f_63_2]) ).

cnf(f_63_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_188,U_187)
    | c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_187,U_188) ),
    inference(clausify,[status(thm)],[f_63_3]) ).

fof(f_64_1,plain,
    ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_w,V_w),
    inference(fof_nnf,[status(thm)],[fact_real__le__refl]) ).

fof(f_64_2,plain,
    ! [U_189] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_189,U_189),
    inference(variable_rename,[status(thm)],[f_64_1]) ).

fof(f_64_3,plain,
    ! [U_189] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_189,U_189),
    inference(definitional_conversion,[status(esa)],[f_64_2]) ).

cnf(f_64_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_189,U_189),
    inference(clausify,[status(thm)],[f_64_3]) ).

fof(f_65_1,plain,
    ! [V_q_2,V_b_2,V_pa_2,V_ab_2,T_a] :
      ( ( ( c_Polynomial_OpCons(T_a,V_ab_2,V_pa_2) = c_Polynomial_OpCons(T_a,V_b_2,V_q_2)
          | V_pa_2 != V_q_2
          | V_ab_2 != V_b_2 )
        & ( ( V_pa_2 = V_q_2
            & V_ab_2 = V_b_2 )
          | c_Polynomial_OpCons(T_a,V_ab_2,V_pa_2) != c_Polynomial_OpCons(T_a,V_b_2,V_q_2) ) )
      | ~ class_Groups_Ozero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_pCons__eq__iff]) ).

fof(f_65_2,plain,
    ! [U_194,U_193,U_192,U_191,U_190] :
      ( ( ( c_Polynomial_OpCons(U_190,U_191,U_192) = c_Polynomial_OpCons(U_190,U_193,U_194)
          | U_192 != U_194
          | U_191 != U_193 )
        & ( ( U_192 = U_194
            & U_191 = U_193 )
          | c_Polynomial_OpCons(U_190,U_191,U_192) != c_Polynomial_OpCons(U_190,U_193,U_194) ) )
      | ~ class_Groups_Ozero(U_190) ),
    inference(variable_rename,[status(thm)],[f_65_1]) ).

fof(f_65_3,plain,
    ( ! [U_191,U_192,U_193,U_194] :
        ( U_192 = U_194
        | ~ sP19(U_191,U_192,U_193,U_194) )
    & ! [U_191,U_192,U_193,U_194] :
        ( U_191 = U_193
        | ~ sP19(U_191,U_192,U_193,U_194) )
    & ! [U_191,U_190,U_192,U_193,U_194] :
        ( c_Polynomial_OpCons(U_190,U_191,U_192) = c_Polynomial_OpCons(U_190,U_193,U_194)
        | U_192 != U_194
        | U_191 != U_193
        | ~ sP20(U_191,U_190,U_192,U_193,U_194) )
    & ! [U_191,U_190,U_192,U_193,U_194] :
        ( sP19(U_191,U_192,U_193,U_194)
        | c_Polynomial_OpCons(U_190,U_191,U_192) != c_Polynomial_OpCons(U_190,U_193,U_194)
        | ~ sP20(U_191,U_190,U_192,U_193,U_194) )
    & ! [U_191,U_190,U_192,U_193,U_194] :
        ( sP20(U_191,U_190,U_192,U_193,U_194)
        | ~ class_Groups_Ozero(U_190) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP19,sP20])],[f_65_2]) ).

cnf(f_65_4,plain,
    ( sP20(U_191,U_190,U_192,U_193,U_194)
    | ~ class_Groups_Ozero(U_190) ),
    inference(clausify,[status(thm)],[f_65_3]) ).

cnf(f_65_5,plain,
    ( sP19(U_191,U_192,U_193,U_194)
    | c_Polynomial_OpCons(U_190,U_191,U_192) != c_Polynomial_OpCons(U_190,U_193,U_194)
    | ~ sP20(U_191,U_190,U_192,U_193,U_194) ),
    inference(clausify,[status(thm)],[f_65_3]) ).

cnf(f_65_6,plain,
    ( c_Polynomial_OpCons(U_190,U_191,U_192) = c_Polynomial_OpCons(U_190,U_193,U_194)
    | U_192 != U_194
    | U_191 != U_193
    | ~ sP20(U_191,U_190,U_192,U_193,U_194) ),
    inference(clausify,[status(thm)],[f_65_3]) ).

cnf(f_65_7,plain,
    ( U_191 = U_193
    | ~ sP19(U_191,U_192,U_193,U_194) ),
    inference(clausify,[status(thm)],[f_65_3]) ).

cnf(f_65_8,plain,
    ( U_192 = U_194
    | ~ sP19(U_191,U_192,U_193,U_194) ),
    inference(clausify,[status(thm)],[f_65_3]) ).

fof(f_66_1,plain,
    ! [V_q_2,V_pa_2,T_a] :
      ( ( ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,V_q_2)
          | V_pa_2 != V_q_2 )
        & ( V_pa_2 = V_q_2
          | c_Polynomial_Opoly(T_a,V_pa_2) != c_Polynomial_Opoly(T_a,V_q_2) ) )
      | ~ class_Rings_Oidom(T_a)
      | ~ class_Int_Oring__char__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_poly__eq__iff]) ).

fof(f_66_2,plain,
    ! [U_197,U_196,U_195] :
      ( ( ( c_Polynomial_Opoly(U_195,U_196) = c_Polynomial_Opoly(U_195,U_197)
          | U_196 != U_197 )
        & ( U_196 = U_197
          | c_Polynomial_Opoly(U_195,U_196) != c_Polynomial_Opoly(U_195,U_197) ) )
      | ~ class_Rings_Oidom(U_195)
      | ~ class_Int_Oring__char__0(U_195) ),
    inference(variable_rename,[status(thm)],[f_66_1]) ).

fof(f_66_3,plain,
    ( ! [U_196,U_197,U_195] :
        ( c_Polynomial_Opoly(U_195,U_196) = c_Polynomial_Opoly(U_195,U_197)
        | U_196 != U_197
        | ~ sP21(U_196,U_197,U_195) )
    & ! [U_196,U_197,U_195] :
        ( U_196 = U_197
        | c_Polynomial_Opoly(U_195,U_196) != c_Polynomial_Opoly(U_195,U_197)
        | ~ sP21(U_196,U_197,U_195) )
    & ! [U_196,U_197,U_195] :
        ( sP21(U_196,U_197,U_195)
        | ~ class_Rings_Oidom(U_195)
        | ~ class_Int_Oring__char__0(U_195) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP21])],[f_66_2]) ).

cnf(f_66_4,plain,
    ( sP21(U_196,U_197,U_195)
    | ~ class_Rings_Oidom(U_195)
    | ~ class_Int_Oring__char__0(U_195) ),
    inference(clausify,[status(thm)],[f_66_3]) ).

cnf(f_66_5,plain,
    ( U_196 = U_197
    | c_Polynomial_Opoly(U_195,U_196) != c_Polynomial_Opoly(U_195,U_197)
    | ~ sP21(U_196,U_197,U_195) ),
    inference(clausify,[status(thm)],[f_66_3]) ).

cnf(f_66_6,plain,
    ( c_Polynomial_Opoly(U_195,U_196) = c_Polynomial_Opoly(U_195,U_197)
    | U_196 != U_197
    | ~ sP21(U_196,U_197,U_195) ),
    inference(clausify,[status(thm)],[f_66_3]) ).

fof(f_67_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left]) ).

fof(f_67_2,plain,
    ! [U_201,U_200,U_199,U_198] :
      ( c_Orderings_Oord__class_Oless__eq(U_198,U_200,U_201)
      | ~ c_Orderings_Oord__class_Oless__eq(U_198,c_Groups_Oplus__class_Oplus(U_198,U_199,U_200),c_Groups_Oplus__class_Oplus(U_198,U_199,U_201))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_198) ),
    inference(variable_rename,[status(thm)],[f_67_1]) ).

fof(f_67_3,plain,
    ! [U_200,U_199,U_198,U_201] :
      ( c_Orderings_Oord__class_Oless__eq(U_198,U_200,U_201)
      | ~ c_Orderings_Oord__class_Oless__eq(U_198,c_Groups_Oplus__class_Oplus(U_198,U_199,U_200),c_Groups_Oplus__class_Oplus(U_198,U_199,U_201))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_198) ),
    inference(definitional_conversion,[status(esa)],[f_67_2]) ).

cnf(f_67_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_198,U_200,U_201)
    | ~ c_Orderings_Oord__class_Oless__eq(U_198,c_Groups_Oplus__class_Oplus(U_198,U_199,U_200),c_Groups_Oplus__class_Oplus(U_198,U_199,U_201))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_198) ),
    inference(clausify,[status(thm)],[f_67_3]) ).

fof(f_68_1,plain,
    ! [V_b,V_c,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right]) ).

fof(f_68_2,plain,
    ! [U_205,U_204,U_203,U_202] :
      ( c_Orderings_Oord__class_Oless__eq(U_202,U_203,U_205)
      | ~ c_Orderings_Oord__class_Oless__eq(U_202,c_Groups_Oplus__class_Oplus(U_202,U_203,U_204),c_Groups_Oplus__class_Oplus(U_202,U_205,U_204))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_202) ),
    inference(variable_rename,[status(thm)],[f_68_1]) ).

fof(f_68_3,plain,
    ! [U_203,U_205,U_202,U_204] :
      ( c_Orderings_Oord__class_Oless__eq(U_202,U_203,U_205)
      | ~ c_Orderings_Oord__class_Oless__eq(U_202,c_Groups_Oplus__class_Oplus(U_202,U_203,U_204),c_Groups_Oplus__class_Oplus(U_202,U_205,U_204))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_202) ),
    inference(definitional_conversion,[status(esa)],[f_68_2]) ).

cnf(f_68_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_202,U_203,U_205)
    | ~ c_Orderings_Oord__class_Oless__eq(U_202,c_Groups_Oplus__class_Oplus(U_202,U_203,U_204),c_Groups_Oplus__class_Oplus(U_202,U_205,U_204))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_202) ),
    inference(clausify,[status(thm)],[f_68_3]) ).

fof(f_69_1,plain,
    ! [V_ab_2,V_pa_2,T_a] :
      ( ( ( hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_ab_2) = c_Groups_Ozero__class_Ozero(T_a)
          | ( c_Polynomial_Oorder(T_a,V_ab_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
        & ( c_Polynomial_Oorder(T_a,V_ab_2,V_pa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
          | hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_ab_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Rings_Oidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__root]) ).

fof(f_69_2,plain,
    ! [U_208,U_207,U_206] :
      ( ( ( hAPP(c_Polynomial_Opoly(U_206,U_207),U_208) = c_Groups_Ozero__class_Ozero(U_206)
          | ( c_Polynomial_Oorder(U_206,U_208,U_207) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & U_207 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_206)) ) )
        & ( c_Polynomial_Oorder(U_206,U_208,U_207) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | U_207 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_206))
          | hAPP(c_Polynomial_Opoly(U_206,U_207),U_208) != c_Groups_Ozero__class_Ozero(U_206) ) )
      | ~ class_Rings_Oidom(U_206) ),
    inference(variable_rename,[status(thm)],[f_69_1]) ).

fof(f_69_3,plain,
    ( ! [U_208,U_207,U_206] :
        ( c_Polynomial_Oorder(U_206,U_208,U_207) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP22(U_208,U_207,U_206) )
    & ! [U_208,U_207,U_206] :
        ( U_207 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_206))
        | ~ sP22(U_208,U_207,U_206) )
    & ! [U_208,U_207,U_206] :
        ( hAPP(c_Polynomial_Opoly(U_206,U_207),U_208) = c_Groups_Ozero__class_Ozero(U_206)
        | sP22(U_208,U_207,U_206)
        | ~ sP23(U_208,U_207,U_206) )
    & ! [U_208,U_207,U_206] :
        ( c_Polynomial_Oorder(U_206,U_208,U_207) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_207 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_206))
        | hAPP(c_Polynomial_Opoly(U_206,U_207),U_208) != c_Groups_Ozero__class_Ozero(U_206)
        | ~ sP23(U_208,U_207,U_206) )
    & ! [U_208,U_207,U_206] :
        ( sP23(U_208,U_207,U_206)
        | ~ class_Rings_Oidom(U_206) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP22,sP23])],[f_69_2]) ).

cnf(f_69_4,plain,
    ( sP23(U_208,U_207,U_206)
    | ~ class_Rings_Oidom(U_206) ),
    inference(clausify,[status(thm)],[f_69_3]) ).

cnf(f_69_5,plain,
    ( c_Polynomial_Oorder(U_206,U_208,U_207) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_207 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_206))
    | hAPP(c_Polynomial_Opoly(U_206,U_207),U_208) != c_Groups_Ozero__class_Ozero(U_206)
    | ~ sP23(U_208,U_207,U_206) ),
    inference(clausify,[status(thm)],[f_69_3]) ).

cnf(f_69_6,plain,
    ( hAPP(c_Polynomial_Opoly(U_206,U_207),U_208) = c_Groups_Ozero__class_Ozero(U_206)
    | sP22(U_208,U_207,U_206)
    | ~ sP23(U_208,U_207,U_206) ),
    inference(clausify,[status(thm)],[f_69_3]) ).

cnf(f_69_7,plain,
    ( U_207 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_206))
    | ~ sP22(U_208,U_207,U_206) ),
    inference(clausify,[status(thm)],[f_69_3]) ).

cnf(f_69_8,plain,
    ( c_Polynomial_Oorder(U_206,U_208,U_207) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP22(U_208,U_207,U_206) ),
    inference(clausify,[status(thm)],[f_69_3]) ).

fof(f_70_1,plain,
    ! [V_ab_2,T_a] :
      ( ( ( c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a)
          | V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a)
          | c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff]) ).

fof(f_70_2,plain,
    ! [U_210,U_209] :
      ( ( ( c_Groups_Oplus__class_Oplus(U_209,U_210,U_210) = c_Groups_Ozero__class_Ozero(U_209)
          | U_210 != c_Groups_Ozero__class_Ozero(U_209) )
        & ( U_210 = c_Groups_Ozero__class_Ozero(U_209)
          | c_Groups_Oplus__class_Oplus(U_209,U_210,U_210) != c_Groups_Ozero__class_Ozero(U_209) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_209) ),
    inference(variable_rename,[status(thm)],[f_70_1]) ).

fof(f_70_3,plain,
    ( ! [U_210,U_209] :
        ( c_Groups_Oplus__class_Oplus(U_209,U_210,U_210) = c_Groups_Ozero__class_Ozero(U_209)
        | U_210 != c_Groups_Ozero__class_Ozero(U_209)
        | ~ sP24(U_210,U_209) )
    & ! [U_210,U_209] :
        ( U_210 = c_Groups_Ozero__class_Ozero(U_209)
        | c_Groups_Oplus__class_Oplus(U_209,U_210,U_210) != c_Groups_Ozero__class_Ozero(U_209)
        | ~ sP24(U_210,U_209) )
    & ! [U_210,U_209] :
        ( sP24(U_210,U_209)
        | ~ class_Groups_Olinordered__ab__group__add(U_209) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP24])],[f_70_2]) ).

cnf(f_70_4,plain,
    ( sP24(U_210,U_209)
    | ~ class_Groups_Olinordered__ab__group__add(U_209) ),
    inference(clausify,[status(thm)],[f_70_3]) ).

cnf(f_70_5,plain,
    ( U_210 = c_Groups_Ozero__class_Ozero(U_209)
    | c_Groups_Oplus__class_Oplus(U_209,U_210,U_210) != c_Groups_Ozero__class_Ozero(U_209)
    | ~ sP24(U_210,U_209) ),
    inference(clausify,[status(thm)],[f_70_3]) ).

cnf(f_70_6,plain,
    ( c_Groups_Oplus__class_Oplus(U_209,U_210,U_210) = c_Groups_Ozero__class_Ozero(U_209)
    | U_210 != c_Groups_Ozero__class_Ozero(U_209)
    | ~ sP24(U_210,U_209) ),
    inference(clausify,[status(thm)],[f_70_3]) ).

fof(f_71_1,plain,
    ! [V_ab_2,V_b_2,T_a] :
      ( ( ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2)
          | V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a)
          | V_b_2 != c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ab_2) ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__0__iff]) ).

fof(f_71_2,plain,
    ! [U_213,U_212,U_211] :
      ( ( ( U_212 = c_Groups_Oplus__class_Oplus(U_211,U_212,U_213)
          | U_213 != c_Groups_Ozero__class_Ozero(U_211) )
        & ( U_213 = c_Groups_Ozero__class_Ozero(U_211)
          | U_212 != c_Groups_Oplus__class_Oplus(U_211,U_212,U_213) ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_211) ),
    inference(variable_rename,[status(thm)],[f_71_1]) ).

fof(f_71_3,plain,
    ( ! [U_213,U_212,U_211] :
        ( U_212 = c_Groups_Oplus__class_Oplus(U_211,U_212,U_213)
        | U_213 != c_Groups_Ozero__class_Ozero(U_211)
        | ~ sP25(U_213,U_212,U_211) )
    & ! [U_213,U_212,U_211] :
        ( U_213 = c_Groups_Ozero__class_Ozero(U_211)
        | U_212 != c_Groups_Oplus__class_Oplus(U_211,U_212,U_213)
        | ~ sP25(U_213,U_212,U_211) )
    & ! [U_213,U_212,U_211] :
        ( sP25(U_213,U_212,U_211)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_211) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP25])],[f_71_2]) ).

cnf(f_71_4,plain,
    ( sP25(U_213,U_212,U_211)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_211) ),
    inference(clausify,[status(thm)],[f_71_3]) ).

cnf(f_71_5,plain,
    ( U_213 = c_Groups_Ozero__class_Ozero(U_211)
    | U_212 != c_Groups_Oplus__class_Oplus(U_211,U_212,U_213)
    | ~ sP25(U_213,U_212,U_211) ),
    inference(clausify,[status(thm)],[f_71_3]) ).

cnf(f_71_6,plain,
    ( U_212 = c_Groups_Oplus__class_Oplus(U_211,U_212,U_213)
    | U_213 != c_Groups_Ozero__class_Ozero(U_211)
    | ~ sP25(U_213,U_212,U_211) ),
    inference(clausify,[status(thm)],[f_71_3]) ).

fof(f_72_1,plain,
    ! [V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J]) ).

fof(f_72_2,plain,
    ! [U_215,U_214] :
      ( c_Groups_Oplus__class_Oplus(U_214,U_215,c_Groups_Ozero__class_Ozero(U_214)) = U_215
      | ~ class_Rings_Ocomm__semiring__1(U_214) ),
    inference(variable_rename,[status(thm)],[f_72_1]) ).

fof(f_72_3,plain,
    ! [U_215,U_214] :
      ( c_Groups_Oplus__class_Oplus(U_214,U_215,c_Groups_Ozero__class_Ozero(U_214)) = U_215
      | ~ class_Rings_Ocomm__semiring__1(U_214) ),
    inference(definitional_conversion,[status(esa)],[f_72_2]) ).

cnf(f_72_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_214,U_215,c_Groups_Ozero__class_Ozero(U_214)) = U_215
    | ~ class_Rings_Ocomm__semiring__1(U_214) ),
    inference(clausify,[status(thm)],[f_72_3]) ).

fof(f_73_1,plain,
    ! [V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J]) ).

fof(f_73_2,plain,
    ! [U_217,U_216] :
      ( c_Groups_Oplus__class_Oplus(U_216,c_Groups_Ozero__class_Ozero(U_216),U_217) = U_217
      | ~ class_Rings_Ocomm__semiring__1(U_216) ),
    inference(variable_rename,[status(thm)],[f_73_1]) ).

fof(f_73_3,plain,
    ! [U_217,U_216] :
      ( c_Groups_Oplus__class_Oplus(U_216,c_Groups_Ozero__class_Ozero(U_216),U_217) = U_217
      | ~ class_Rings_Ocomm__semiring__1(U_216) ),
    inference(definitional_conversion,[status(esa)],[f_73_2]) ).

cnf(f_73_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_216,c_Groups_Ozero__class_Ozero(U_216),U_217) = U_217
    | ~ class_Rings_Ocomm__semiring__1(U_216) ),
    inference(clausify,[status(thm)],[f_73_3]) ).

fof(f_74_1,plain,
    ! [V_pa_2,V_ab_2,T_a,V_z_2,V_f_2,T_b] :
      ( c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_ab_2,V_pa_2)) = hAPP(hAPP(hAPP(V_f_2,V_ab_2),V_pa_2),c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pa_2))
      | hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2) != V_z_2
      | ~ class_Groups_Ozero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_poly__rec__pCons]) ).

fof(f_74_2,plain,
    ! [U_223,U_222,U_221,U_220,U_219,U_218] :
      ( c_Polynomial_Opoly__rec(U_221,U_218,U_220,U_219,c_Polynomial_OpCons(U_218,U_222,U_223)) = hAPP(hAPP(hAPP(U_219,U_222),U_223),c_Polynomial_Opoly__rec(U_221,U_218,U_220,U_219,U_223))
      | hAPP(hAPP(hAPP(U_219,c_Groups_Ozero__class_Ozero(U_218)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_218))),U_220) != U_220
      | ~ class_Groups_Ozero(U_218) ),
    inference(variable_rename,[status(thm)],[f_74_1]) ).

fof(f_74_3,plain,
    ! [U_218,U_219,U_220,U_221,U_222,U_223] :
      ( c_Polynomial_Opoly__rec(U_221,U_218,U_220,U_219,c_Polynomial_OpCons(U_218,U_222,U_223)) = hAPP(hAPP(hAPP(U_219,U_222),U_223),c_Polynomial_Opoly__rec(U_221,U_218,U_220,U_219,U_223))
      | hAPP(hAPP(hAPP(U_219,c_Groups_Ozero__class_Ozero(U_218)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_218))),U_220) != U_220
      | ~ class_Groups_Ozero(U_218) ),
    inference(definitional_conversion,[status(esa)],[f_74_2]) ).

cnf(f_74_4,plain,
    ( c_Polynomial_Opoly__rec(U_221,U_218,U_220,U_219,c_Polynomial_OpCons(U_218,U_222,U_223)) = hAPP(hAPP(hAPP(U_219,U_222),U_223),c_Polynomial_Opoly__rec(U_221,U_218,U_220,U_219,U_223))
    | hAPP(hAPP(hAPP(U_219,c_Groups_Ozero__class_Ozero(U_218)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_218))),U_220) != U_220
    | ~ class_Groups_Ozero(U_218) ),
    inference(clausify,[status(thm)],[f_74_3]) ).

fof(f_75_1,plain,
    ! [V_pa_2,V_ab_2,V_f_2,V_z_2,T_a,T_b] :
      ( c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_ab_2,V_pa_2)) = hAPP(hAPP(hAPP(V_f_2,V_ab_2),V_pa_2),c_If(T_a,c_fequal(V_pa_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2,c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pa_2)))
      | ~ class_Groups_Ozero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_poly__rec_Osimps]) ).

fof(f_75_2,plain,
    ! [U_229,U_228,U_227,U_226,U_225,U_224] :
      ( c_Polynomial_Opoly__rec(U_225,U_224,U_226,U_227,c_Polynomial_OpCons(U_224,U_228,U_229)) = hAPP(hAPP(hAPP(U_227,U_228),U_229),c_If(U_225,c_fequal(U_229,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_224))),U_226,c_Polynomial_Opoly__rec(U_225,U_224,U_226,U_227,U_229)))
      | ~ class_Groups_Ozero(U_224) ),
    inference(variable_rename,[status(thm)],[f_75_1]) ).

fof(f_75_3,plain,
    ! [U_225,U_224,U_226,U_227,U_228,U_229] :
      ( c_Polynomial_Opoly__rec(U_225,U_224,U_226,U_227,c_Polynomial_OpCons(U_224,U_228,U_229)) = hAPP(hAPP(hAPP(U_227,U_228),U_229),c_If(U_225,c_fequal(U_229,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_224))),U_226,c_Polynomial_Opoly__rec(U_225,U_224,U_226,U_227,U_229)))
      | ~ class_Groups_Ozero(U_224) ),
    inference(definitional_conversion,[status(esa)],[f_75_2]) ).

cnf(f_75_4,plain,
    ( c_Polynomial_Opoly__rec(U_225,U_224,U_226,U_227,c_Polynomial_OpCons(U_224,U_228,U_229)) = hAPP(hAPP(hAPP(U_227,U_228),U_229),c_If(U_225,c_fequal(U_229,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_224))),U_226,c_Polynomial_Opoly__rec(U_225,U_224,U_226,U_227,U_229)))
    | ~ class_Groups_Ozero(U_224) ),
    inference(clausify,[status(thm)],[f_75_3]) ).

fof(f_76_1,plain,
    ! [V_p,V_r] :
    ? [B_z] :
    ! [B_w] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),B_z)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),B_w)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_w),V_r) ),
    inference(fof_nnf,[status(thm)],[fact_poly__minimum__modulus__disc]) ).

fof(f_76_2,plain,
    ! [U_233,U_232] :
    ? [U_231] :
    ! [U_230] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_233),U_231)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_233),U_230)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_230),U_232) ),
    inference(variable_rename,[status(thm)],[f_76_1]) ).

fof(f_76_3,plain,
    ! [U_233,U_232,U_230] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_233),sK4(U_233,U_232))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_233),U_230)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_230),U_232) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_231,sK4(U_233,U_232))],[f_76_2]) ).

fof(f_76_4,plain,
    ! [U_230,U_233,U_232] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_233),sK4(U_233,U_232))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_233),U_230)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_230),U_232) ),
    inference(definitional_conversion,[status(esa)],[f_76_3]) ).

cnf(f_76_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_233),sK4(U_233,U_232))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_233),U_230)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_230),U_232) ),
    inference(clausify,[status(thm)],[f_76_4]) ).

fof(f_77_1,plain,
    ! [V_h,V_a,T_a] :
      ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_offset__poly__single]) ).

fof(f_77_2,plain,
    ! [U_236,U_235,U_234] :
      ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(U_234,c_Polynomial_OpCons(U_234,U_235,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_234))),U_236) = c_Polynomial_OpCons(U_234,U_235,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_234)))
      | ~ class_Rings_Ocomm__semiring__0(U_234) ),
    inference(variable_rename,[status(thm)],[f_77_1]) ).

fof(f_77_3,plain,
    ! [U_234,U_235,U_236] :
      ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(U_234,c_Polynomial_OpCons(U_234,U_235,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_234))),U_236) = c_Polynomial_OpCons(U_234,U_235,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_234)))
      | ~ class_Rings_Ocomm__semiring__0(U_234) ),
    inference(definitional_conversion,[status(esa)],[f_77_2]) ).

cnf(f_77_4,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(U_234,c_Polynomial_OpCons(U_234,U_235,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_234))),U_236) = c_Polynomial_OpCons(U_234,U_235,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_234)))
    | ~ class_Rings_Ocomm__semiring__0(U_234) ),
    inference(clausify,[status(thm)],[f_77_3]) ).

fof(f_78_1,plain,
    ! [T_a,V_z_2,V_f_2,T_b] :
      ( c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))) = V_z_2
      | hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2) != V_z_2
      | ~ class_Groups_Ozero(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_poly__rec__0]) ).

fof(f_78_2,plain,
    ! [U_240,U_239,U_238,U_237] :
      ( c_Polynomial_Opoly__rec(U_240,U_237,U_239,U_238,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_237))) = U_239
      | hAPP(hAPP(hAPP(U_238,c_Groups_Ozero__class_Ozero(U_237)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_237))),U_239) != U_239
      | ~ class_Groups_Ozero(U_237) ),
    inference(variable_rename,[status(thm)],[f_78_1]) ).

fof(f_78_3,plain,
    ! [U_237,U_238,U_239,U_240] :
      ( c_Polynomial_Opoly__rec(U_240,U_237,U_239,U_238,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_237))) = U_239
      | hAPP(hAPP(hAPP(U_238,c_Groups_Ozero__class_Ozero(U_237)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_237))),U_239) != U_239
      | ~ class_Groups_Ozero(U_237) ),
    inference(definitional_conversion,[status(esa)],[f_78_2]) ).

cnf(f_78_4,plain,
    ( c_Polynomial_Opoly__rec(U_240,U_237,U_239,U_238,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_237))) = U_239
    | hAPP(hAPP(hAPP(U_238,c_Groups_Ozero__class_Ozero(U_237)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_237))),U_239) != U_239
    | ~ class_Groups_Ozero(U_237) ),
    inference(clausify,[status(thm)],[f_78_3]) ).

fof(f_79_1,plain,
    ! [V_c,V_p,V_a,T_a] :
      ( c_Polynomial_Osynthetic__div(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_c) = c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_synthetic__div__pCons]) ).

fof(f_79_2,plain,
    ! [U_244,U_243,U_242,U_241] :
      ( c_Polynomial_Osynthetic__div(U_241,c_Polynomial_OpCons(U_241,U_242,U_243),U_244) = c_Polynomial_OpCons(U_241,hAPP(c_Polynomial_Opoly(U_241,U_243),U_244),c_Polynomial_Osynthetic__div(U_241,U_243,U_244))
      | ~ class_Rings_Ocomm__semiring__0(U_241) ),
    inference(variable_rename,[status(thm)],[f_79_1]) ).

fof(f_79_3,plain,
    ! [U_242,U_241,U_243,U_244] :
      ( c_Polynomial_Osynthetic__div(U_241,c_Polynomial_OpCons(U_241,U_242,U_243),U_244) = c_Polynomial_OpCons(U_241,hAPP(c_Polynomial_Opoly(U_241,U_243),U_244),c_Polynomial_Osynthetic__div(U_241,U_243,U_244))
      | ~ class_Rings_Ocomm__semiring__0(U_241) ),
    inference(definitional_conversion,[status(esa)],[f_79_2]) ).

cnf(f_79_4,plain,
    ( c_Polynomial_Osynthetic__div(U_241,c_Polynomial_OpCons(U_241,U_242,U_243),U_244) = c_Polynomial_OpCons(U_241,hAPP(c_Polynomial_Opoly(U_241,U_243),U_244),c_Polynomial_Osynthetic__div(U_241,U_243,U_244))
    | ~ class_Rings_Ocomm__semiring__0(U_241) ),
    inference(clausify,[status(thm)],[f_79_3]) ).

fof(f_80_1,plain,
    ! [V_x,V_h,V_p,T_a] :
      ( hAPP(c_Polynomial_Opoly(T_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),V_x) = hAPP(c_Polynomial_Opoly(T_a,V_p),c_Groups_Oplus__class_Oplus(T_a,V_h,V_x))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_poly__offset__poly]) ).

fof(f_80_2,plain,
    ! [U_248,U_247,U_246,U_245] :
      ( hAPP(c_Polynomial_Opoly(U_245,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(U_245,U_246,U_247)),U_248) = hAPP(c_Polynomial_Opoly(U_245,U_246),c_Groups_Oplus__class_Oplus(U_245,U_247,U_248))
      | ~ class_Rings_Ocomm__semiring__0(U_245) ),
    inference(variable_rename,[status(thm)],[f_80_1]) ).

fof(f_80_3,plain,
    ! [U_245,U_246,U_247,U_248] :
      ( hAPP(c_Polynomial_Opoly(U_245,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(U_245,U_246,U_247)),U_248) = hAPP(c_Polynomial_Opoly(U_245,U_246),c_Groups_Oplus__class_Oplus(U_245,U_247,U_248))
      | ~ class_Rings_Ocomm__semiring__0(U_245) ),
    inference(definitional_conversion,[status(esa)],[f_80_2]) ).

cnf(f_80_4,plain,
    ( hAPP(c_Polynomial_Opoly(U_245,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(U_245,U_246,U_247)),U_248) = hAPP(c_Polynomial_Opoly(U_245,U_246),c_Groups_Oplus__class_Oplus(U_245,U_247,U_248))
    | ~ class_Rings_Ocomm__semiring__0(U_245) ),
    inference(clausify,[status(thm)],[f_80_3]) ).

fof(f_81_1,plain,
    ! [V_c,T_a] :
      ( c_Polynomial_Osynthetic__div(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_c) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_synthetic__div__0]) ).

fof(f_81_2,plain,
    ! [U_250,U_249] :
      ( c_Polynomial_Osynthetic__div(U_249,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_249)),U_250) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_249))
      | ~ class_Rings_Ocomm__semiring__0(U_249) ),
    inference(variable_rename,[status(thm)],[f_81_1]) ).

fof(f_81_3,plain,
    ! [U_249,U_250] :
      ( c_Polynomial_Osynthetic__div(U_249,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_249)),U_250) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_249))
      | ~ class_Rings_Ocomm__semiring__0(U_249) ),
    inference(definitional_conversion,[status(esa)],[f_81_2]) ).

cnf(f_81_4,plain,
    ( c_Polynomial_Osynthetic__div(U_249,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_249)),U_250) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_249))
    | ~ class_Rings_Ocomm__semiring__0(U_249) ),
    inference(clausify,[status(thm)],[f_81_3]) ).

fof(f_82_1,plain,
    ! [V_x,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x))
      | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_norm__ge__zero]) ).

fof(f_82_2,plain,
    ! [U_252,U_251] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_251,U_252))
      | ~ class_RealVector_Oreal__normed__vector(U_251) ),
    inference(variable_rename,[status(thm)],[f_82_1]) ).

fof(f_82_3,plain,
    ! [U_251,U_252] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_251,U_252))
      | ~ class_RealVector_Oreal__normed__vector(U_251) ),
    inference(definitional_conversion,[status(esa)],[f_82_2]) ).

cnf(f_82_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_251,U_252))
    | ~ class_RealVector_Oreal__normed__vector(U_251) ),
    inference(clausify,[status(thm)],[f_82_3]) ).

fof(f_83_1,plain,
    ! [V_h_2,V_pa_2,T_a] :
      ( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_pa_2,V_h_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
          | V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
        & ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
          | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_pa_2,V_h_2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_offset__poly__eq__0__iff]) ).

fof(f_83_2,plain,
    ! [U_255,U_254,U_253] :
      ( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(U_253,U_254,U_255) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_253))
          | U_254 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_253)) )
        & ( U_254 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_253))
          | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(U_253,U_254,U_255) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_253)) ) )
      | ~ class_Rings_Ocomm__semiring__0(U_253) ),
    inference(variable_rename,[status(thm)],[f_83_1]) ).

fof(f_83_3,plain,
    ( ! [U_253,U_254,U_255] :
        ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(U_253,U_254,U_255) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_253))
        | U_254 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_253))
        | ~ sP26(U_253,U_254,U_255) )
    & ! [U_253,U_254,U_255] :
        ( U_254 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_253))
        | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(U_253,U_254,U_255) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_253))
        | ~ sP26(U_253,U_254,U_255) )
    & ! [U_253,U_254,U_255] :
        ( sP26(U_253,U_254,U_255)
        | ~ class_Rings_Ocomm__semiring__0(U_253) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP26])],[f_83_2]) ).

cnf(f_83_4,plain,
    ( sP26(U_253,U_254,U_255)
    | ~ class_Rings_Ocomm__semiring__0(U_253) ),
    inference(clausify,[status(thm)],[f_83_3]) ).

cnf(f_83_5,plain,
    ( U_254 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_253))
    | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(U_253,U_254,U_255) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_253))
    | ~ sP26(U_253,U_254,U_255) ),
    inference(clausify,[status(thm)],[f_83_3]) ).

cnf(f_83_6,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(U_253,U_254,U_255) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_253))
    | U_254 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_253))
    | ~ sP26(U_253,U_254,U_255) ),
    inference(clausify,[status(thm)],[f_83_3]) ).

fof(f_84_1,plain,
    ! [V_h,T_a] :
      ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_offset__poly__0]) ).

fof(f_84_2,plain,
    ! [U_257,U_256] :
      ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(U_256,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_256)),U_257) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_256))
      | ~ class_Rings_Ocomm__semiring__0(U_256) ),
    inference(variable_rename,[status(thm)],[f_84_1]) ).

fof(f_84_3,plain,
    ! [U_257,U_256] :
      ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(U_256,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_256)),U_257) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_256))
      | ~ class_Rings_Ocomm__semiring__0(U_256) ),
    inference(definitional_conversion,[status(esa)],[f_84_2]) ).

cnf(f_84_4,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(U_256,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_256)),U_257) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_256))
    | ~ class_Rings_Ocomm__semiring__0(U_256) ),
    inference(clausify,[status(thm)],[f_84_3]) ).

fof(f_85_1,plain,
    ! [V_c,V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).

fof(f_85_2,plain,
    ! [U_260,U_259,U_258] :
      ( c_Groups_Oplus__class_Oplus(U_258,U_259,U_260) = c_Groups_Oplus__class_Oplus(U_258,U_260,U_259)
      | ~ class_Rings_Ocomm__semiring__1(U_258) ),
    inference(variable_rename,[status(thm)],[f_85_1]) ).

fof(f_85_3,plain,
    ! [U_258,U_259,U_260] :
      ( c_Groups_Oplus__class_Oplus(U_258,U_259,U_260) = c_Groups_Oplus__class_Oplus(U_258,U_260,U_259)
      | ~ class_Rings_Ocomm__semiring__1(U_258) ),
    inference(definitional_conversion,[status(esa)],[f_85_2]) ).

cnf(f_85_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_258,U_259,U_260) = c_Groups_Oplus__class_Oplus(U_258,U_260,U_259)
    | ~ class_Rings_Ocomm__semiring__1(U_258) ),
    inference(clausify,[status(thm)],[f_85_3]) ).

fof(f_86_1,plain,
    ! [V_d,V_c,V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J]) ).

fof(f_86_2,plain,
    ! [U_264,U_263,U_262,U_261] :
      ( c_Groups_Oplus__class_Oplus(U_261,U_262,c_Groups_Oplus__class_Oplus(U_261,U_263,U_264)) = c_Groups_Oplus__class_Oplus(U_261,U_263,c_Groups_Oplus__class_Oplus(U_261,U_262,U_264))
      | ~ class_Rings_Ocomm__semiring__1(U_261) ),
    inference(variable_rename,[status(thm)],[f_86_1]) ).

fof(f_86_3,plain,
    ! [U_262,U_261,U_263,U_264] :
      ( c_Groups_Oplus__class_Oplus(U_261,U_262,c_Groups_Oplus__class_Oplus(U_261,U_263,U_264)) = c_Groups_Oplus__class_Oplus(U_261,U_263,c_Groups_Oplus__class_Oplus(U_261,U_262,U_264))
      | ~ class_Rings_Ocomm__semiring__1(U_261) ),
    inference(definitional_conversion,[status(esa)],[f_86_2]) ).

cnf(f_86_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_261,U_262,c_Groups_Oplus__class_Oplus(U_261,U_263,U_264)) = c_Groups_Oplus__class_Oplus(U_261,U_263,c_Groups_Oplus__class_Oplus(U_261,U_262,U_264))
    | ~ class_Rings_Ocomm__semiring__1(U_261) ),
    inference(clausify,[status(thm)],[f_86_3]) ).

fof(f_87_1,plain,
    ! [V_d,V_c,V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J]) ).

fof(f_87_2,plain,
    ! [U_268,U_267,U_266,U_265] :
      ( c_Groups_Oplus__class_Oplus(U_265,U_266,c_Groups_Oplus__class_Oplus(U_265,U_267,U_268)) = c_Groups_Oplus__class_Oplus(U_265,c_Groups_Oplus__class_Oplus(U_265,U_266,U_267),U_268)
      | ~ class_Rings_Ocomm__semiring__1(U_265) ),
    inference(variable_rename,[status(thm)],[f_87_1]) ).

fof(f_87_3,plain,
    ! [U_266,U_265,U_267,U_268] :
      ( c_Groups_Oplus__class_Oplus(U_265,U_266,c_Groups_Oplus__class_Oplus(U_265,U_267,U_268)) = c_Groups_Oplus__class_Oplus(U_265,c_Groups_Oplus__class_Oplus(U_265,U_266,U_267),U_268)
      | ~ class_Rings_Ocomm__semiring__1(U_265) ),
    inference(definitional_conversion,[status(esa)],[f_87_2]) ).

cnf(f_87_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_265,U_266,c_Groups_Oplus__class_Oplus(U_265,U_267,U_268)) = c_Groups_Oplus__class_Oplus(U_265,c_Groups_Oplus__class_Oplus(U_265,U_266,U_267),U_268)
    | ~ class_Rings_Ocomm__semiring__1(U_265) ),
    inference(clausify,[status(thm)],[f_87_3]) ).

fof(f_88_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J]) ).

fof(f_88_2,plain,
    ! [U_272,U_271,U_270,U_269] :
      ( c_Groups_Oplus__class_Oplus(U_269,c_Groups_Oplus__class_Oplus(U_269,U_270,U_271),U_272) = c_Groups_Oplus__class_Oplus(U_269,U_270,c_Groups_Oplus__class_Oplus(U_269,U_271,U_272))
      | ~ class_Rings_Ocomm__semiring__1(U_269) ),
    inference(variable_rename,[status(thm)],[f_88_1]) ).

fof(f_88_3,plain,
    ! [U_270,U_269,U_271,U_272] :
      ( c_Groups_Oplus__class_Oplus(U_269,c_Groups_Oplus__class_Oplus(U_269,U_270,U_271),U_272) = c_Groups_Oplus__class_Oplus(U_269,U_270,c_Groups_Oplus__class_Oplus(U_269,U_271,U_272))
      | ~ class_Rings_Ocomm__semiring__1(U_269) ),
    inference(definitional_conversion,[status(esa)],[f_88_2]) ).

cnf(f_88_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_269,c_Groups_Oplus__class_Oplus(U_269,U_270,U_271),U_272) = c_Groups_Oplus__class_Oplus(U_269,U_270,c_Groups_Oplus__class_Oplus(U_269,U_271,U_272))
    | ~ class_Rings_Ocomm__semiring__1(U_269) ),
    inference(clausify,[status(thm)],[f_88_3]) ).

fof(f_89_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J]) ).

fof(f_89_2,plain,
    ! [U_276,U_275,U_274,U_273] :
      ( c_Groups_Oplus__class_Oplus(U_273,c_Groups_Oplus__class_Oplus(U_273,U_274,U_275),U_276) = c_Groups_Oplus__class_Oplus(U_273,c_Groups_Oplus__class_Oplus(U_273,U_274,U_276),U_275)
      | ~ class_Rings_Ocomm__semiring__1(U_273) ),
    inference(variable_rename,[status(thm)],[f_89_1]) ).

fof(f_89_3,plain,
    ! [U_274,U_273,U_275,U_276] :
      ( c_Groups_Oplus__class_Oplus(U_273,c_Groups_Oplus__class_Oplus(U_273,U_274,U_275),U_276) = c_Groups_Oplus__class_Oplus(U_273,c_Groups_Oplus__class_Oplus(U_273,U_274,U_276),U_275)
      | ~ class_Rings_Ocomm__semiring__1(U_273) ),
    inference(definitional_conversion,[status(esa)],[f_89_2]) ).

cnf(f_89_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_273,c_Groups_Oplus__class_Oplus(U_273,U_274,U_275),U_276) = c_Groups_Oplus__class_Oplus(U_273,c_Groups_Oplus__class_Oplus(U_273,U_274,U_276),U_275)
    | ~ class_Rings_Ocomm__semiring__1(U_273) ),
    inference(clausify,[status(thm)],[f_89_3]) ).

fof(f_90_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J]) ).

fof(f_90_2,plain,
    ! [U_281,U_280,U_279,U_278,U_277] :
      ( c_Groups_Oplus__class_Oplus(U_277,c_Groups_Oplus__class_Oplus(U_277,U_278,U_279),c_Groups_Oplus__class_Oplus(U_277,U_280,U_281)) = c_Groups_Oplus__class_Oplus(U_277,c_Groups_Oplus__class_Oplus(U_277,U_278,U_280),c_Groups_Oplus__class_Oplus(U_277,U_279,U_281))
      | ~ class_Rings_Ocomm__semiring__1(U_277) ),
    inference(variable_rename,[status(thm)],[f_90_1]) ).

fof(f_90_3,plain,
    ! [U_278,U_277,U_279,U_280,U_281] :
      ( c_Groups_Oplus__class_Oplus(U_277,c_Groups_Oplus__class_Oplus(U_277,U_278,U_279),c_Groups_Oplus__class_Oplus(U_277,U_280,U_281)) = c_Groups_Oplus__class_Oplus(U_277,c_Groups_Oplus__class_Oplus(U_277,U_278,U_280),c_Groups_Oplus__class_Oplus(U_277,U_279,U_281))
      | ~ class_Rings_Ocomm__semiring__1(U_277) ),
    inference(definitional_conversion,[status(esa)],[f_90_2]) ).

cnf(f_90_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_277,c_Groups_Oplus__class_Oplus(U_277,U_278,U_279),c_Groups_Oplus__class_Oplus(U_277,U_280,U_281)) = c_Groups_Oplus__class_Oplus(U_277,c_Groups_Oplus__class_Oplus(U_277,U_278,U_280),c_Groups_Oplus__class_Oplus(U_277,U_279,U_281))
    | ~ class_Rings_Ocomm__semiring__1(U_277) ),
    inference(clausify,[status(thm)],[f_90_3]) ).

fof(f_91_1,plain,
    ! [V_pa_2,T_a] :
      ( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
        & ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
          | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ class_Groups_Ozero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_psize__eq__0__iff]) ).

fof(f_91_2,plain,
    ! [U_283,U_282] :
      ( ( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_282,U_283) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | U_283 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_282)) )
        & ( U_283 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_282))
          | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_282,U_283) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ class_Groups_Ozero(U_282) ),
    inference(variable_rename,[status(thm)],[f_91_1]) ).

fof(f_91_3,plain,
    ( ! [U_282,U_283] :
        ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_282,U_283) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_283 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_282))
        | ~ sP27(U_282,U_283) )
    & ! [U_282,U_283] :
        ( U_283 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_282))
        | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_282,U_283) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP27(U_282,U_283) )
    & ! [U_282,U_283] :
        ( sP27(U_282,U_283)
        | ~ class_Groups_Ozero(U_282) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP27])],[f_91_2]) ).

cnf(f_91_4,plain,
    ( sP27(U_282,U_283)
    | ~ class_Groups_Ozero(U_282) ),
    inference(clausify,[status(thm)],[f_91_3]) ).

cnf(f_91_5,plain,
    ( U_283 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_282))
    | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_282,U_283) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP27(U_282,U_283) ),
    inference(clausify,[status(thm)],[f_91_3]) ).

cnf(f_91_6,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(U_282,U_283) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_283 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_282))
    | ~ sP27(U_282,U_283) ),
    inference(clausify,[status(thm)],[f_91_3]) ).

fof(f_92_1,plain,
    ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n),
    inference(fof_nnf,[status(thm)],[fact_le0]) ).

fof(f_92_2,plain,
    ! [U_284] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_284),
    inference(variable_rename,[status(thm)],[f_92_1]) ).

fof(f_92_3,plain,
    ! [U_284] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_284),
    inference(definitional_conversion,[status(esa)],[f_92_2]) ).

cnf(f_92_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_284),
    inference(clausify,[status(thm)],[f_92_3]) ).

fof(f_93_1,plain,
    ! [V_c,V_p,T_a] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,c_Polynomial_Osynthetic__div(T_a,V_p,V_c))) = c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_synthetic__div__correct]) ).

fof(f_93_2,plain,
    ! [U_287,U_286,U_285] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_285),U_286,c_Polynomial_Osmult(U_285,U_287,c_Polynomial_Osynthetic__div(U_285,U_286,U_287))) = c_Polynomial_OpCons(U_285,hAPP(c_Polynomial_Opoly(U_285,U_286),U_287),c_Polynomial_Osynthetic__div(U_285,U_286,U_287))
      | ~ class_Rings_Ocomm__semiring__0(U_285) ),
    inference(variable_rename,[status(thm)],[f_93_1]) ).

fof(f_93_3,plain,
    ! [U_286,U_285,U_287] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_285),U_286,c_Polynomial_Osmult(U_285,U_287,c_Polynomial_Osynthetic__div(U_285,U_286,U_287))) = c_Polynomial_OpCons(U_285,hAPP(c_Polynomial_Opoly(U_285,U_286),U_287),c_Polynomial_Osynthetic__div(U_285,U_286,U_287))
      | ~ class_Rings_Ocomm__semiring__0(U_285) ),
    inference(definitional_conversion,[status(esa)],[f_93_2]) ).

cnf(f_93_4,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_285),U_286,c_Polynomial_Osmult(U_285,U_287,c_Polynomial_Osynthetic__div(U_285,U_286,U_287))) = c_Polynomial_OpCons(U_285,hAPP(c_Polynomial_Opoly(U_285,U_286),U_287),c_Polynomial_Osynthetic__div(U_285,U_286,U_287))
    | ~ class_Rings_Ocomm__semiring__0(U_285) ),
    inference(clausify,[status(thm)],[f_93_3]) ).

fof(f_94_1,plain,
    ! [V_r,V_q,V_c,V_p,T_a] :
      ( ( V_q = c_Polynomial_Osynthetic__div(T_a,V_p,V_c)
        & V_r = hAPP(c_Polynomial_Opoly(T_a,V_p),V_c) )
      | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,V_q)) != c_Polynomial_OpCons(T_a,V_r,V_q)
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_synthetic__div__unique]) ).

fof(f_94_2,plain,
    ! [U_292,U_291,U_290,U_289,U_288] :
      ( ( U_291 = c_Polynomial_Osynthetic__div(U_288,U_289,U_290)
        & U_292 = hAPP(c_Polynomial_Opoly(U_288,U_289),U_290) )
      | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_288),U_289,c_Polynomial_Osmult(U_288,U_290,U_291)) != c_Polynomial_OpCons(U_288,U_292,U_291)
      | ~ class_Rings_Ocomm__semiring__0(U_288) ),
    inference(variable_rename,[status(thm)],[f_94_1]) ).

fof(f_94_3,plain,
    ( ! [U_290,U_291,U_288,U_289,U_292] :
        ( U_291 = c_Polynomial_Osynthetic__div(U_288,U_289,U_290)
        | ~ sP28(U_290,U_291,U_288,U_289,U_292) )
    & ! [U_290,U_291,U_288,U_289,U_292] :
        ( U_292 = hAPP(c_Polynomial_Opoly(U_288,U_289),U_290)
        | ~ sP28(U_290,U_291,U_288,U_289,U_292) )
    & ! [U_290,U_291,U_288,U_289,U_292] :
        ( sP28(U_290,U_291,U_288,U_289,U_292)
        | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_288),U_289,c_Polynomial_Osmult(U_288,U_290,U_291)) != c_Polynomial_OpCons(U_288,U_292,U_291)
        | ~ class_Rings_Ocomm__semiring__0(U_288) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP28])],[f_94_2]) ).

cnf(f_94_4,plain,
    ( sP28(U_290,U_291,U_288,U_289,U_292)
    | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_288),U_289,c_Polynomial_Osmult(U_288,U_290,U_291)) != c_Polynomial_OpCons(U_288,U_292,U_291)
    | ~ class_Rings_Ocomm__semiring__0(U_288) ),
    inference(clausify,[status(thm)],[f_94_3]) ).

cnf(f_94_5,plain,
    ( U_292 = hAPP(c_Polynomial_Opoly(U_288,U_289),U_290)
    | ~ sP28(U_290,U_291,U_288,U_289,U_292) ),
    inference(clausify,[status(thm)],[f_94_3]) ).

cnf(f_94_6,plain,
    ( U_291 = c_Polynomial_Osynthetic__div(U_288,U_289,U_290)
    | ~ sP28(U_290,U_291,U_288,U_289,U_292) ),
    inference(clausify,[status(thm)],[f_94_3]) ).

fof(f_95_1,plain,
    ! [V_a,T_a] :
      ( c_Polynomial_Omonom(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
      | ~ class_Groups_Ozero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_monom__0]) ).

fof(f_95_2,plain,
    ! [U_294,U_293] :
      ( c_Polynomial_Omonom(U_293,U_294,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(U_293,U_294,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_293)))
      | ~ class_Groups_Ozero(U_293) ),
    inference(variable_rename,[status(thm)],[f_95_1]) ).

fof(f_95_3,plain,
    ! [U_294,U_293] :
      ( c_Polynomial_Omonom(U_293,U_294,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(U_293,U_294,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_293)))
      | ~ class_Groups_Ozero(U_293) ),
    inference(definitional_conversion,[status(esa)],[f_95_2]) ).

cnf(f_95_4,plain,
    ( c_Polynomial_Omonom(U_293,U_294,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(U_293,U_294,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_293)))
    | ~ class_Groups_Ozero(U_293) ),
    inference(clausify,[status(thm)],[f_95_3]) ).

fof(f_96_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d))))
      | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_norm__diff__triangle__ineq]) ).

fof(f_96_2,plain,
    ! [U_299,U_298,U_297,U_296,U_295] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_295,c_Groups_Ominus__class_Ominus(U_295,c_Groups_Oplus__class_Oplus(U_295,U_296,U_297),c_Groups_Oplus__class_Oplus(U_295,U_298,U_299))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_295,c_Groups_Ominus__class_Ominus(U_295,U_296,U_298)),c_RealVector_Onorm__class_Onorm(U_295,c_Groups_Ominus__class_Ominus(U_295,U_297,U_299))))
      | ~ class_RealVector_Oreal__normed__vector(U_295) ),
    inference(variable_rename,[status(thm)],[f_96_1]) ).

fof(f_96_3,plain,
    ! [U_295,U_296,U_297,U_298,U_299] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_295,c_Groups_Ominus__class_Ominus(U_295,c_Groups_Oplus__class_Oplus(U_295,U_296,U_297),c_Groups_Oplus__class_Oplus(U_295,U_298,U_299))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_295,c_Groups_Ominus__class_Ominus(U_295,U_296,U_298)),c_RealVector_Onorm__class_Onorm(U_295,c_Groups_Ominus__class_Ominus(U_295,U_297,U_299))))
      | ~ class_RealVector_Oreal__normed__vector(U_295) ),
    inference(definitional_conversion,[status(esa)],[f_96_2]) ).

cnf(f_96_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_295,c_Groups_Ominus__class_Ominus(U_295,c_Groups_Oplus__class_Oplus(U_295,U_296,U_297),c_Groups_Oplus__class_Oplus(U_295,U_298,U_299))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_295,c_Groups_Ominus__class_Ominus(U_295,U_296,U_298)),c_RealVector_Onorm__class_Onorm(U_295,c_Groups_Ominus__class_Ominus(U_295,U_297,U_299))))
    | ~ class_RealVector_Oreal__normed__vector(U_295) ),
    inference(clausify,[status(thm)],[f_96_3]) ).

fof(f_97_1,plain,
    ! [V_h,V_p,V_a,T_a] :
      ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_offset__poly__pCons]) ).

fof(f_97_2,plain,
    ! [U_303,U_302,U_301,U_300] :
      ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(U_300,c_Polynomial_OpCons(U_300,U_301,U_302),U_303) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_300),c_Polynomial_Osmult(U_300,U_303,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(U_300,U_302,U_303)),c_Polynomial_OpCons(U_300,U_301,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(U_300,U_302,U_303)))
      | ~ class_Rings_Ocomm__semiring__0(U_300) ),
    inference(variable_rename,[status(thm)],[f_97_1]) ).

fof(f_97_3,plain,
    ! [U_301,U_300,U_302,U_303] :
      ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(U_300,c_Polynomial_OpCons(U_300,U_301,U_302),U_303) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_300),c_Polynomial_Osmult(U_300,U_303,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(U_300,U_302,U_303)),c_Polynomial_OpCons(U_300,U_301,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(U_300,U_302,U_303)))
      | ~ class_Rings_Ocomm__semiring__0(U_300) ),
    inference(definitional_conversion,[status(esa)],[f_97_2]) ).

cnf(f_97_4,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(U_300,c_Polynomial_OpCons(U_300,U_301,U_302),U_303) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_300),c_Polynomial_Osmult(U_300,U_303,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(U_300,U_302,U_303)),c_Polynomial_OpCons(U_300,U_301,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(U_300,U_302,U_303)))
    | ~ class_Rings_Ocomm__semiring__0(U_300) ),
    inference(clausify,[status(thm)],[f_97_3]) ).

fof(f_98_1,plain,
    ! [V_a,V_p,V_c,T_a] :
      ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
      | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_offset__poly__eq__0__lemma]) ).

fof(f_98_2,plain,
    ! [U_307,U_306,U_305,U_304] :
      ( U_306 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_304))
      | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_304),c_Polynomial_Osmult(U_304,U_305,U_306),c_Polynomial_OpCons(U_304,U_307,U_306)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_304))
      | ~ class_Rings_Ocomm__semiring__0(U_304) ),
    inference(variable_rename,[status(thm)],[f_98_1]) ).

fof(f_98_3,plain,
    ! [U_305,U_306,U_304,U_307] :
      ( U_306 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_304))
      | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_304),c_Polynomial_Osmult(U_304,U_305,U_306),c_Polynomial_OpCons(U_304,U_307,U_306)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_304))
      | ~ class_Rings_Ocomm__semiring__0(U_304) ),
    inference(definitional_conversion,[status(esa)],[f_98_2]) ).

cnf(f_98_4,plain,
    ( U_306 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_304))
    | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_304),c_Polynomial_Osmult(U_304,U_305,U_306),c_Polynomial_OpCons(U_304,U_307,U_306)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_304))
    | ~ class_Rings_Ocomm__semiring__0(U_304) ),
    inference(clausify,[status(thm)],[f_98_3]) ).

fof(f_99_1,plain,
    ! [V_x,V_p,V_a,T_a] :
      ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_poly__pCons]) ).

fof(f_99_2,plain,
    ! [U_311,U_310,U_309,U_308] :
      ( hAPP(c_Polynomial_Opoly(U_308,c_Polynomial_OpCons(U_308,U_309,U_310)),U_311) = c_Groups_Oplus__class_Oplus(U_308,U_309,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_308),U_311),hAPP(c_Polynomial_Opoly(U_308,U_310),U_311)))
      | ~ class_Rings_Ocomm__semiring__0(U_308) ),
    inference(variable_rename,[status(thm)],[f_99_1]) ).

fof(f_99_3,plain,
    ! [U_311,U_310,U_308,U_309] :
      ( hAPP(c_Polynomial_Opoly(U_308,c_Polynomial_OpCons(U_308,U_309,U_310)),U_311) = c_Groups_Oplus__class_Oplus(U_308,U_309,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_308),U_311),hAPP(c_Polynomial_Opoly(U_308,U_310),U_311)))
      | ~ class_Rings_Ocomm__semiring__0(U_308) ),
    inference(definitional_conversion,[status(esa)],[f_99_2]) ).

cnf(f_99_4,plain,
    ( hAPP(c_Polynomial_Opoly(U_308,c_Polynomial_OpCons(U_308,U_309,U_310)),U_311) = c_Groups_Oplus__class_Oplus(U_308,U_309,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_308),U_311),hAPP(c_Polynomial_Opoly(U_308,U_310),U_311)))
    | ~ class_Rings_Ocomm__semiring__0(U_308) ),
    inference(clausify,[status(thm)],[f_99_3]) ).

fof(f_100_1,plain,
    ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n),
    inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).

fof(f_100_2,plain,
    ! [U_312] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_312),
    inference(variable_rename,[status(thm)],[f_100_1]) ).

fof(f_100_3,plain,
    ! [U_312] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_312),
    inference(definitional_conversion,[status(esa)],[f_100_2]) ).

cnf(f_100_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_312),
    inference(clausify,[status(thm)],[f_100_3]) ).

fof(f_101_1,plain,
    ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_n),
    inference(fof_nnf,[status(thm)],[fact_le__refl]) ).

fof(f_101_2,plain,
    ! [U_313] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_313,U_313),
    inference(variable_rename,[status(thm)],[f_101_1]) ).

fof(f_101_3,plain,
    ! [U_313] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_313,U_313),
    inference(definitional_conversion,[status(esa)],[f_101_2]) ).

cnf(f_101_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_313,U_313),
    inference(clausify,[status(thm)],[f_101_3]) ).

fof(f_102_1,plain,
    ! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)),
    inference(fof_nnf,[status(thm)],[fact_le__square]) ).

fof(f_102_2,plain,
    ! [U_314] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_314,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_314),U_314)),
    inference(variable_rename,[status(thm)],[f_102_1]) ).

fof(f_102_3,plain,
    ! [U_314] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_314,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_314),U_314)),
    inference(definitional_conversion,[status(esa)],[f_102_2]) ).

cnf(f_102_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_314,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_314),U_314)),
    inference(clausify,[status(thm)],[f_102_3]) ).

fof(f_103_1,plain,
    ! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
    inference(fof_nnf,[status(thm)],[fact_le__add2]) ).

fof(f_103_2,plain,
    ! [U_316,U_315] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_315,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_316,U_315)),
    inference(variable_rename,[status(thm)],[f_103_1]) ).

fof(f_103_3,plain,
    ! [U_316,U_315] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_315,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_316,U_315)),
    inference(definitional_conversion,[status(esa)],[f_103_2]) ).

cnf(f_103_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_315,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_316,U_315)),
    inference(clausify,[status(thm)],[f_103_3]) ).

fof(f_104_1,plain,
    ! [V_m,V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)),
    inference(fof_nnf,[status(thm)],[fact_le__add1]) ).

fof(f_104_2,plain,
    ! [U_318,U_317] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_317,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_317,U_318)),
    inference(variable_rename,[status(thm)],[f_104_1]) ).

fof(f_104_3,plain,
    ! [U_318,U_317] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_317,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_317,U_318)),
    inference(definitional_conversion,[status(esa)],[f_104_2]) ).

cnf(f_104_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_317,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_317,U_318)),
    inference(clausify,[status(thm)],[f_104_3]) ).

fof(f_105_1,plain,
    ! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))),
    inference(fof_nnf,[status(thm)],[fact_le__cube]) ).

fof(f_105_2,plain,
    ! [U_319] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_319,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_319),U_319))),
    inference(variable_rename,[status(thm)],[f_105_1]) ).

fof(f_105_3,plain,
    ! [U_319] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_319,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_319),U_319))),
    inference(definitional_conversion,[status(esa)],[f_105_2]) ).

cnf(f_105_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_319,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_319),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_319),U_319))),
    inference(clausify,[status(thm)],[f_105_3]) ).

fof(f_106_1,plain,
    ! [V_n,V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m),
    inference(fof_nnf,[status(thm)],[fact_diff__le__self]) ).

fof(f_106_2,plain,
    ! [U_321,U_320] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_320,U_321),U_320),
    inference(variable_rename,[status(thm)],[f_106_1]) ).

fof(f_106_3,plain,
    ! [U_321,U_320] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_320,U_321),U_320),
    inference(definitional_conversion,[status(esa)],[f_106_2]) ).

cnf(f_106_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_320,U_321),U_320),
    inference(clausify,[status(thm)],[f_106_3]) ).

fof(f_107_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
        | ! [B_k] : V_n_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k) )
      & ( ? [B_k] : V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__iff__add]) ).

fof(f_107_2,plain,
    ! [U_325,U_324] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_324,U_325)
        | ! [U_323] : U_325 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_324,U_323) )
      & ( ? [U_322] : U_325 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_324,U_322)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_324,U_325) ) ),
    inference(variable_rename,[status(thm)],[f_107_1]) ).

fof(f_107_3,plain,
    ( ! [U_329,U_327] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_327,U_329)
        | ! [U_323] : U_329 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_327,U_323) )
    & ! [U_328,U_326] :
        ( ? [U_322] : U_328 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_326,U_322)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_326,U_328) ) ),
    inference(miniscope,[status(thm)],[f_107_2]) ).

fof(f_107_4,plain,
    ( ! [U_329,U_327] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_327,U_329)
        | ! [U_323] : U_329 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_327,U_323) )
    & ! [U_328,U_326] :
        ( U_328 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_326,sK5(U_328,U_326))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_326,U_328) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_322,sK5(U_328,U_326))],[f_107_3]) ).

fof(f_107_5,plain,
    ( ! [U_323,U_329,U_327] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_327,U_329)
        | U_329 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_327,U_323) )
    & ! [U_326,U_328] :
        ( U_328 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_326,sK5(U_328,U_326))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_326,U_328) ) ),
    inference(definitional_conversion,[status(esa)],[f_107_4]) ).

cnf(f_107_6,plain,
    ( U_328 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_326,sK5(U_328,U_326))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_326,U_328) ),
    inference(clausify,[status(thm)],[f_107_5]) ).

cnf(f_107_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_327,U_329)
    | U_329 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_327,U_323) ),
    inference(clausify,[status(thm)],[f_107_5]) ).

fof(f_108_1,plain,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
    inference(fof_nnf,[status(thm)],[fact_nat__le__linear]) ).

fof(f_108_2,plain,
    ! [U_331,U_330] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_331,U_330)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_330,U_331) ),
    inference(variable_rename,[status(thm)],[f_108_1]) ).

fof(f_108_3,plain,
    ! [U_330,U_331] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_331,U_330)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_330,U_331) ),
    inference(definitional_conversion,[status(esa)],[f_108_2]) ).

cnf(f_108_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_331,U_330)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_330,U_331) ),
    inference(clausify,[status(thm)],[f_108_3]) ).

fof(f_109_1,plain,
    ! [V_i,V_j,V_k] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_diff__diff__right]) ).

fof(f_109_2,plain,
    ! [U_334,U_333,U_332] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_334,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_333,U_332)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_334,U_332),U_333)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_332,U_333) ),
    inference(variable_rename,[status(thm)],[f_109_1]) ).

fof(f_109_3,plain,
    ! [U_333,U_332,U_334] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_334,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_333,U_332)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_334,U_332),U_333)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_332,U_333) ),
    inference(definitional_conversion,[status(esa)],[f_109_2]) ).

cnf(f_109_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_334,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_333,U_332)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_334,U_332),U_333)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_332,U_333) ),
    inference(clausify,[status(thm)],[f_109_3]) ).

fof(f_110_1,plain,
    ! [V_i_2,V_k_2,V_j_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__diff__conv]) ).

fof(f_110_2,plain,
    ! [U_337,U_336,U_335] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_335,U_336),U_337)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_335,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_337,U_336)) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_335,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_337,U_336))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_335,U_336),U_337) ) ),
    inference(variable_rename,[status(thm)],[f_110_1]) ).

fof(f_110_3,plain,
    ( ! [U_343,U_341,U_339] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_339,U_341),U_343)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_339,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_343,U_341)) )
    & ! [U_342,U_340,U_338] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_338,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_342,U_340))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_338,U_340),U_342) ) ),
    inference(miniscope,[status(thm)],[f_110_2]) ).

fof(f_110_4,plain,
    ( ! [U_341,U_343,U_339] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_339,U_341),U_343)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_339,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_343,U_341)) )
    & ! [U_338,U_340,U_342] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_338,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_342,U_340))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_338,U_340),U_342) ) ),
    inference(definitional_conversion,[status(esa)],[f_110_3]) ).

cnf(f_110_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_338,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_342,U_340))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_338,U_340),U_342) ),
    inference(clausify,[status(thm)],[f_110_4]) ).

cnf(f_110_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_339,U_341),U_343)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_339,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_343,U_341)) ),
    inference(clausify,[status(thm)],[f_110_4]) ).

fof(f_111_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le]) ).

fof(f_111_2,plain,
    ! [U_346,U_345,U_344] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_344,U_345),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_344,U_346))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_345,U_346) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_345,U_346)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_344,U_345),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_344,U_346)) ) ),
    inference(variable_rename,[status(thm)],[f_111_1]) ).

fof(f_111_3,plain,
    ( ! [U_352,U_350] :
        ( ! [U_348] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_348,U_350),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_348,U_352))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_350,U_352) )
    & ! [U_351,U_349] :
        ( ! [U_347] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_347,U_349),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_347,U_351))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_349,U_351) ) ),
    inference(miniscope,[status(thm)],[f_111_2]) ).

fof(f_111_4,plain,
    ( ! [U_348,U_350,U_352] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_348,U_350),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_348,U_352))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_350,U_352) )
    & ! [U_347,U_349,U_351] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_347,U_349),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_347,U_351))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_349,U_351) ) ),
    inference(definitional_conversion,[status(esa)],[f_111_3]) ).

cnf(f_111_5,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_347,U_349),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_347,U_351))
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_349,U_351) ),
    inference(clausify,[status(thm)],[f_111_4]) ).

cnf(f_111_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_348,U_350),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_348,U_352))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_350,U_352) ),
    inference(clausify,[status(thm)],[f_111_4]) ).

fof(f_112_1,plain,
    ! [V_n,V_b,V_m,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(T_a,V_a,V_m)),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__monom]) ).

fof(f_112_2,plain,
    ! [U_357,U_356,U_355,U_354,U_353] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_353)),c_Polynomial_Omonom(U_353,U_354,U_355)),c_Polynomial_Omonom(U_353,U_356,U_357)) = c_Polynomial_Omonom(U_353,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_353),U_354),U_356),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_355,U_357))
      | ~ class_Rings_Ocomm__semiring__0(U_353) ),
    inference(variable_rename,[status(thm)],[f_112_1]) ).

fof(f_112_3,plain,
    ! [U_353,U_354,U_355,U_356,U_357] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_353)),c_Polynomial_Omonom(U_353,U_354,U_355)),c_Polynomial_Omonom(U_353,U_356,U_357)) = c_Polynomial_Omonom(U_353,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_353),U_354),U_356),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_355,U_357))
      | ~ class_Rings_Ocomm__semiring__0(U_353) ),
    inference(definitional_conversion,[status(esa)],[f_112_2]) ).

cnf(f_112_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_353)),c_Polynomial_Omonom(U_353,U_354,U_355)),c_Polynomial_Omonom(U_353,U_356,U_357)) = c_Polynomial_Omonom(U_353,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_353),U_354),U_356),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_355,U_357))
    | ~ class_Rings_Ocomm__semiring__0(U_353) ),
    inference(clausify,[status(thm)],[f_112_3]) ).

fof(f_113_1,plain,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
      | V_m != V_n ),
    inference(fof_nnf,[status(thm)],[fact_eq__imp__le]) ).

fof(f_113_2,plain,
    ! [U_359,U_358] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_358,U_359)
      | U_358 != U_359 ),
    inference(variable_rename,[status(thm)],[f_113_1]) ).

fof(f_113_3,plain,
    ! [U_359,U_358] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_358,U_359)
      | U_358 != U_359 ),
    inference(definitional_conversion,[status(esa)],[f_113_2]) ).

cnf(f_113_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_358,U_359)
    | U_358 != U_359 ),
    inference(clausify,[status(thm)],[f_113_3]) ).

fof(f_114_1,plain,
    ! [V_m,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_trans__le__add1]) ).

fof(f_114_2,plain,
    ! [U_362,U_361,U_360] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_360,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_361,U_362))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_360,U_361) ),
    inference(variable_rename,[status(thm)],[f_114_1]) ).

fof(f_114_3,plain,
    ! [U_361,U_360,U_362] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_360,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_361,U_362))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_360,U_361) ),
    inference(definitional_conversion,[status(esa)],[f_114_2]) ).

cnf(f_114_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_360,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_361,U_362))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_360,U_361) ),
    inference(clausify,[status(thm)],[f_114_3]) ).

fof(f_115_1,plain,
    ! [V_m,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_trans__le__add2]) ).

fof(f_115_2,plain,
    ! [U_365,U_364,U_363] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_363,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_365,U_364))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_363,U_364) ),
    inference(variable_rename,[status(thm)],[f_115_1]) ).

fof(f_115_3,plain,
    ! [U_364,U_363,U_365] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_363,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_365,U_364))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_363,U_364) ),
    inference(definitional_conversion,[status(esa)],[f_115_2]) ).

cnf(f_115_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_363,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_365,U_364))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_363,U_364) ),
    inference(clausify,[status(thm)],[f_115_3]) ).

fof(f_116_1,plain,
    ! [V_m,V_n,V_k] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n) ),
    inference(fof_nnf,[status(thm)],[fact_le__add__diff]) ).

fof(f_116_2,plain,
    ! [U_368,U_367,U_366] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_368,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_367,U_368),U_366))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_366,U_367) ),
    inference(variable_rename,[status(thm)],[f_116_1]) ).

fof(f_116_3,plain,
    ! [U_367,U_366,U_368] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_368,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_367,U_368),U_366))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_366,U_367) ),
    inference(definitional_conversion,[status(esa)],[f_116_2]) ).

cnf(f_116_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_368,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_367,U_368),U_366))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_366,U_367) ),
    inference(clausify,[status(thm)],[f_116_3]) ).

fof(f_117_1,plain,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_add__le__mono1]) ).

fof(f_117_2,plain,
    ! [U_371,U_370,U_369] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_369,U_371),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_370,U_371))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_369,U_370) ),
    inference(variable_rename,[status(thm)],[f_117_1]) ).

fof(f_117_3,plain,
    ! [U_370,U_369,U_371] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_369,U_371),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_370,U_371))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_369,U_370) ),
    inference(definitional_conversion,[status(esa)],[f_117_2]) ).

cnf(f_117_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_369,U_371),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_370,U_371))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_369,U_370) ),
    inference(clausify,[status(thm)],[f_117_3]) ).

fof(f_118_1,plain,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__mono1]) ).

fof(f_118_2,plain,
    ! [U_374,U_373,U_372] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_372),U_374),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_373),U_374))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_372,U_373) ),
    inference(variable_rename,[status(thm)],[f_118_1]) ).

fof(f_118_3,plain,
    ! [U_372,U_373,U_374] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_372),U_374),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_373),U_374))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_372,U_373) ),
    inference(definitional_conversion,[status(esa)],[f_118_2]) ).

cnf(f_118_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_372),U_374),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_373),U_374))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_372,U_373) ),
    inference(clausify,[status(thm)],[f_118_3]) ).

fof(f_119_1,plain,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__mono2]) ).

fof(f_119_2,plain,
    ! [U_377,U_376,U_375] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_377),U_375),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_377),U_376))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_375,U_376) ),
    inference(variable_rename,[status(thm)],[f_119_1]) ).

fof(f_119_3,plain,
    ! [U_375,U_376,U_377] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_377),U_375),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_377),U_376))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_375,U_376) ),
    inference(definitional_conversion,[status(esa)],[f_119_2]) ).

cnf(f_119_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_377),U_375),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_377),U_376))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_375,U_376) ),
    inference(clausify,[status(thm)],[f_119_3]) ).

fof(f_120_1,plain,
    ! [V_l,V_n,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
    inference(fof_nnf,[status(thm)],[fact_diff__le__mono2]) ).

fof(f_120_2,plain,
    ! [U_380,U_379,U_378] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_380,U_379),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_380,U_378))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_378,U_379) ),
    inference(variable_rename,[status(thm)],[f_120_1]) ).

fof(f_120_3,plain,
    ! [U_378,U_379,U_380] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_380,U_379),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_380,U_378))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_378,U_379) ),
    inference(definitional_conversion,[status(esa)],[f_120_2]) ).

cnf(f_120_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_380,U_379),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_380,U_378))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_378,U_379) ),
    inference(clausify,[status(thm)],[f_120_3]) ).

fof(f_121_1,plain,
    ! [V_l,V_n,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
    inference(fof_nnf,[status(thm)],[fact_diff__le__mono]) ).

fof(f_121_2,plain,
    ! [U_383,U_382,U_381] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_381,U_383),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_382,U_383))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_381,U_382) ),
    inference(variable_rename,[status(thm)],[f_121_1]) ).

fof(f_121_3,plain,
    ! [U_381,U_382,U_383] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_381,U_383),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_382,U_383))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_381,U_382) ),
    inference(definitional_conversion,[status(esa)],[f_121_2]) ).

cnf(f_121_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_381,U_383),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_382,U_383))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_381,U_382) ),
    inference(clausify,[status(thm)],[f_121_3]) ).

fof(f_122_1,plain,
    ! [V_n,V_i] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = V_i
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_n) ),
    inference(fof_nnf,[status(thm)],[fact_diff__diff__cancel]) ).

fof(f_122_2,plain,
    ! [U_385,U_384] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_385,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_385,U_384)) = U_384
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_384,U_385) ),
    inference(variable_rename,[status(thm)],[f_122_1]) ).

fof(f_122_3,plain,
    ! [U_384,U_385] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_385,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_385,U_384)) = U_384
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_384,U_385) ),
    inference(definitional_conversion,[status(esa)],[f_122_2]) ).

cnf(f_122_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_385,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_385,U_384)) = U_384
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_384,U_385) ),
    inference(clausify,[status(thm)],[f_122_3]) ).

fof(f_123_1,plain,
    ! [V_m,V_n] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ),
    inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse]) ).

fof(f_123_2,plain,
    ! [U_387,U_386] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_386,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_387,U_386)) = U_387
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_386,U_387) ),
    inference(variable_rename,[status(thm)],[f_123_1]) ).

fof(f_123_3,plain,
    ! [U_386,U_387] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_386,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_387,U_386)) = U_387
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_386,U_387) ),
    inference(definitional_conversion,[status(esa)],[f_123_2]) ).

cnf(f_123_4,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_386,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_387,U_386)) = U_387
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_386,U_387) ),
    inference(clausify,[status(thm)],[f_123_3]) ).

fof(f_124_1,plain,
    ! [V_i,V_j,V_k] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_add__diff__assoc]) ).

fof(f_124_2,plain,
    ! [U_390,U_389,U_388] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_390,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_389,U_388)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_390,U_389),U_388)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_388,U_389) ),
    inference(variable_rename,[status(thm)],[f_124_1]) ).

fof(f_124_3,plain,
    ! [U_389,U_388,U_390] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_390,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_389,U_388)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_390,U_389),U_388)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_388,U_389) ),
    inference(definitional_conversion,[status(esa)],[f_124_2]) ).

cnf(f_124_4,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_390,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_389,U_388)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_390,U_389),U_388)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_388,U_389) ),
    inference(clausify,[status(thm)],[f_124_3]) ).

fof(f_125_1,plain,
    ! [V_i_2,V_j_2,V_k_2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_j_2) ),
    inference(fof_nnf,[status(thm)],[fact_le__diff__conv2]) ).

fof(f_125_2,plain,
    ! [U_393,U_392,U_391] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_393,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_392,U_391))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_393,U_391),U_392) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_393,U_391),U_392)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_393,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_392,U_391)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_391,U_392) ),
    inference(variable_rename,[status(thm)],[f_125_1]) ).

fof(f_125_3,plain,
    ( ! [U_392,U_391,U_393] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_393,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_392,U_391))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_393,U_391),U_392)
        | ~ sP29(U_392,U_391,U_393) )
    & ! [U_392,U_391,U_393] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_393,U_391),U_392)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_393,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_392,U_391))
        | ~ sP29(U_392,U_391,U_393) )
    & ! [U_392,U_391,U_393] :
        ( sP29(U_392,U_391,U_393)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_391,U_392) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP29])],[f_125_2]) ).

cnf(f_125_4,plain,
    ( sP29(U_392,U_391,U_393)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_391,U_392) ),
    inference(clausify,[status(thm)],[f_125_3]) ).

cnf(f_125_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_393,U_391),U_392)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_393,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_392,U_391))
    | ~ sP29(U_392,U_391,U_393) ),
    inference(clausify,[status(thm)],[f_125_3]) ).

cnf(f_125_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_393,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_392,U_391))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_393,U_391),U_392)
    | ~ sP29(U_392,U_391,U_393) ),
    inference(clausify,[status(thm)],[f_125_3]) ).

fof(f_126_1,plain,
    ! [V_m,V_n] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n) = V_m
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ),
    inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse2]) ).

fof(f_126_2,plain,
    ! [U_395,U_394] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_395,U_394),U_394) = U_395
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_394,U_395) ),
    inference(variable_rename,[status(thm)],[f_126_1]) ).

fof(f_126_3,plain,
    ! [U_394,U_395] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_395,U_394),U_394) = U_395
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_394,U_395) ),
    inference(definitional_conversion,[status(esa)],[f_126_2]) ).

cnf(f_126_4,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_395,U_394),U_394) = U_395
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_394,U_395) ),
    inference(clausify,[status(thm)],[f_126_3]) ).

fof(f_127_1,plain,
    ! [V_k_2,V_j_2,V_i_2] :
      ( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) = V_k_2
          | V_j_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2) )
        & ( V_j_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2)
          | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2) != V_k_2 ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) ),
    inference(fof_nnf,[status(thm)],[fact_le__imp__diff__is__add]) ).

fof(f_127_2,plain,
    ! [U_398,U_397,U_396] :
      ( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_397,U_396) = U_398
          | U_397 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_398,U_396) )
        & ( U_397 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_398,U_396)
          | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_397,U_396) != U_398 ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_396,U_397) ),
    inference(variable_rename,[status(thm)],[f_127_1]) ).

fof(f_127_3,plain,
    ( ! [U_396,U_397,U_398] :
        ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_397,U_396) = U_398
        | U_397 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_398,U_396)
        | ~ sP30(U_396,U_397,U_398) )
    & ! [U_396,U_397,U_398] :
        ( U_397 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_398,U_396)
        | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_397,U_396) != U_398
        | ~ sP30(U_396,U_397,U_398) )
    & ! [U_396,U_397,U_398] :
        ( sP30(U_396,U_397,U_398)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_396,U_397) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP30])],[f_127_2]) ).

cnf(f_127_4,plain,
    ( sP30(U_396,U_397,U_398)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_396,U_397) ),
    inference(clausify,[status(thm)],[f_127_3]) ).

cnf(f_127_5,plain,
    ( U_397 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_398,U_396)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_397,U_396) != U_398
    | ~ sP30(U_396,U_397,U_398) ),
    inference(clausify,[status(thm)],[f_127_3]) ).

cnf(f_127_6,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_397,U_396) = U_398
    | U_397 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_398,U_396)
    | ~ sP30(U_396,U_397,U_398) ),
    inference(clausify,[status(thm)],[f_127_3]) ).

fof(f_128_1,plain,
    ! [V_i,V_j,V_k] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_diff__add__assoc]) ).

fof(f_128_2,plain,
    ! [U_401,U_400,U_399] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_401,U_400),U_399) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_401,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_400,U_399))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_399,U_400) ),
    inference(variable_rename,[status(thm)],[f_128_1]) ).

fof(f_128_3,plain,
    ! [U_400,U_399,U_401] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_401,U_400),U_399) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_401,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_400,U_399))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_399,U_400) ),
    inference(definitional_conversion,[status(esa)],[f_128_2]) ).

cnf(f_128_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_401,U_400),U_399) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_401,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_400,U_399))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_399,U_400) ),
    inference(clausify,[status(thm)],[f_128_3]) ).

fof(f_129_1,plain,
    ! [V_i,V_j,V_k] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_add__diff__assoc2]) ).

fof(f_129_2,plain,
    ! [U_404,U_403,U_402] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_403,U_402),U_404) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_403,U_404),U_402)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_402,U_403) ),
    inference(variable_rename,[status(thm)],[f_129_1]) ).

fof(f_129_3,plain,
    ! [U_403,U_402,U_404] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_403,U_402),U_404) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_403,U_404),U_402)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_402,U_403) ),
    inference(definitional_conversion,[status(esa)],[f_129_2]) ).

cnf(f_129_4,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_403,U_402),U_404) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_403,U_404),U_402)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_402,U_403) ),
    inference(clausify,[status(thm)],[f_129_3]) ).

fof(f_130_1,plain,
    ! [V_i,V_j,V_k] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_diff__add__assoc2]) ).

fof(f_130_2,plain,
    ! [U_407,U_406,U_405] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_406,U_407),U_405) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_406,U_405),U_407)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_405,U_406) ),
    inference(variable_rename,[status(thm)],[f_130_1]) ).

fof(f_130_3,plain,
    ! [U_407,U_406,U_405] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_406,U_407),U_405) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_406,U_405),U_407)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_405,U_406) ),
    inference(definitional_conversion,[status(esa)],[f_130_2]) ).

cnf(f_130_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_406,U_407),U_405) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_406,U_405),U_407)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_405,U_406) ),
    inference(clausify,[status(thm)],[f_130_3]) ).

fof(f_131_1,plain,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_k)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_k)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_le__trans]) ).

fof(f_131_2,plain,
    ! [U_410,U_409,U_408] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_408,U_410)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_409,U_410)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_408,U_409) ),
    inference(variable_rename,[status(thm)],[f_131_1]) ).

fof(f_131_3,plain,
    ! [U_408,U_410,U_409] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_408,U_410)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_409,U_410)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_408,U_409) ),
    inference(definitional_conversion,[status(esa)],[f_131_2]) ).

cnf(f_131_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_408,U_410)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_409,U_410)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_408,U_409) ),
    inference(clausify,[status(thm)],[f_131_3]) ).

fof(f_132_1,plain,
    ! [V_n,V_m] :
      ( V_m = V_n
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
    inference(fof_nnf,[status(thm)],[fact_le__antisym]) ).

fof(f_132_2,plain,
    ! [U_412,U_411] :
      ( U_411 = U_412
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_412,U_411)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_411,U_412) ),
    inference(variable_rename,[status(thm)],[f_132_1]) ).

fof(f_132_3,plain,
    ! [U_412,U_411] :
      ( U_411 = U_412
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_412,U_411)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_411,U_412) ),
    inference(definitional_conversion,[status(esa)],[f_132_2]) ).

cnf(f_132_4,plain,
    ( U_411 = U_412
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_412,U_411)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_411,U_412) ),
    inference(clausify,[status(thm)],[f_132_3]) ).

fof(f_133_1,plain,
    ! [V_l,V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_add__le__mono]) ).

fof(f_133_2,plain,
    ! [U_416,U_415,U_414,U_413] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_413,U_415),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_414,U_416))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_415,U_416)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_413,U_414) ),
    inference(variable_rename,[status(thm)],[f_133_1]) ).

fof(f_133_3,plain,
    ! [U_414,U_415,U_416,U_413] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_413,U_415),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_414,U_416))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_415,U_416)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_413,U_414) ),
    inference(definitional_conversion,[status(esa)],[f_133_2]) ).

cnf(f_133_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_413,U_415),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_414,U_416))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_415,U_416)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_413,U_414) ),
    inference(clausify,[status(thm)],[f_133_3]) ).

fof(f_134_1,plain,
    ! [V_l,V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_l)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__mono]) ).

fof(f_134_2,plain,
    ! [U_420,U_419,U_418,U_417] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_417),U_419),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_418),U_420))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_419,U_420)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_417,U_418) ),
    inference(variable_rename,[status(thm)],[f_134_1]) ).

fof(f_134_3,plain,
    ! [U_418,U_417,U_419,U_420] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_417),U_419),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_418),U_420))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_419,U_420)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_417,U_418) ),
    inference(definitional_conversion,[status(esa)],[f_134_2]) ).

cnf(f_134_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_417),U_419),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_418),U_420))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_419,U_420)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_417,U_418) ),
    inference(clausify,[status(thm)],[f_134_3]) ).

fof(f_135_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)
          | V_m_2 != V_n_2 )
        & ( V_m_2 = V_n_2
          | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2) ),
    inference(fof_nnf,[status(thm)],[fact_eq__diff__iff]) ).

fof(f_135_2,plain,
    ! [U_423,U_422,U_421] :
      ( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_422,U_421) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_423,U_421)
          | U_422 != U_423 )
        & ( U_422 = U_423
          | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_422,U_421) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_423,U_421) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_421,U_423)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_421,U_422) ),
    inference(variable_rename,[status(thm)],[f_135_1]) ).

fof(f_135_3,plain,
    ( ! [U_423,U_421,U_422] :
        ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_422,U_421) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_423,U_421)
        | U_422 != U_423
        | ~ sP31(U_423,U_421,U_422) )
    & ! [U_423,U_421,U_422] :
        ( U_422 = U_423
        | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_422,U_421) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_423,U_421)
        | ~ sP31(U_423,U_421,U_422) )
    & ! [U_423,U_421,U_422] :
        ( sP31(U_423,U_421,U_422)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_421,U_423)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_421,U_422) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP31])],[f_135_2]) ).

cnf(f_135_4,plain,
    ( sP31(U_423,U_421,U_422)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_421,U_423)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_421,U_422) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_5,plain,
    ( U_422 = U_423
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_422,U_421) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_423,U_421)
    | ~ sP31(U_423,U_421,U_422) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

cnf(f_135_6,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_422,U_421) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_423,U_421)
    | U_422 != U_423
    | ~ sP31(U_423,U_421,U_422) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

fof(f_136_1,plain,
    ! [V_n,V_m,V_k] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_m) ),
    inference(fof_nnf,[status(thm)],[fact_Nat_Odiff__diff__eq]) ).

fof(f_136_2,plain,
    ! [U_426,U_425,U_424] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_425,U_424),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_426,U_424)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_425,U_426)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_424,U_426)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_424,U_425) ),
    inference(variable_rename,[status(thm)],[f_136_1]) ).

fof(f_136_3,plain,
    ! [U_425,U_426,U_424] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_425,U_424),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_426,U_424)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_425,U_426)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_424,U_426)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_424,U_425) ),
    inference(definitional_conversion,[status(esa)],[f_136_2]) ).

cnf(f_136_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_425,U_424),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_426,U_424)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_425,U_426)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_424,U_426)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_424,U_425) ),
    inference(clausify,[status(thm)],[f_136_3]) ).

fof(f_137_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2) ),
    inference(fof_nnf,[status(thm)],[fact_le__diff__iff]) ).

fof(f_137_2,plain,
    ! [U_429,U_428,U_427] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_428,U_427),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_429,U_427))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_428,U_429) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_428,U_429)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_428,U_427),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_429,U_427)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_427,U_429)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_427,U_428) ),
    inference(variable_rename,[status(thm)],[f_137_1]) ).

fof(f_137_3,plain,
    ( ! [U_429,U_428,U_427] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_428,U_427),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_429,U_427))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_428,U_429)
        | ~ sP32(U_429,U_428,U_427) )
    & ! [U_429,U_428,U_427] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_428,U_429)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_428,U_427),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_429,U_427))
        | ~ sP32(U_429,U_428,U_427) )
    & ! [U_429,U_428,U_427] :
        ( sP32(U_429,U_428,U_427)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_427,U_429)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_427,U_428) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP32])],[f_137_2]) ).

cnf(f_137_4,plain,
    ( sP32(U_429,U_428,U_427)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_427,U_429)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_427,U_428) ),
    inference(clausify,[status(thm)],[f_137_3]) ).

cnf(f_137_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_428,U_429)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_428,U_427),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_429,U_427))
    | ~ sP32(U_429,U_428,U_427) ),
    inference(clausify,[status(thm)],[f_137_3]) ).

cnf(f_137_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_428,U_427),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_429,U_427))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_428,U_429)
    | ~ sP32(U_429,U_428,U_427) ),
    inference(clausify,[status(thm)],[f_137_3]) ).

fof(f_138_1,plain,
    ! [V_n,V_k,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n) ),
    inference(fof_nnf,[status(thm)],[fact_add__leD2]) ).

fof(f_138_2,plain,
    ! [U_432,U_431,U_430] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_431,U_432)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_430,U_431),U_432) ),
    inference(variable_rename,[status(thm)],[f_138_1]) ).

fof(f_138_3,plain,
    ! [U_432,U_431] :
      ( ! [U_430] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_430,U_431),U_432)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_431,U_432) ),
    inference(miniscope,[status(thm)],[f_138_2]) ).

fof(f_138_4,plain,
    ! [U_432,U_430,U_431] :
      ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_430,U_431),U_432)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_431,U_432) ),
    inference(definitional_conversion,[status(esa)],[f_138_3]) ).

cnf(f_138_5,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_430,U_431),U_432)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_431,U_432) ),
    inference(clausify,[status(thm)],[f_138_4]) ).

fof(f_139_1,plain,
    ! [V_n,V_k,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n) ),
    inference(fof_nnf,[status(thm)],[fact_add__leD1]) ).

fof(f_139_2,plain,
    ! [U_435,U_434,U_433] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_433,U_435)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_433,U_434),U_435) ),
    inference(variable_rename,[status(thm)],[f_139_1]) ).

fof(f_139_3,plain,
    ! [U_435,U_434,U_433] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_433,U_435)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_433,U_434),U_435) ),
    inference(definitional_conversion,[status(esa)],[f_139_2]) ).

cnf(f_139_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_433,U_435)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_433,U_434),U_435) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

fof(f_140_1,plain,
    ! [V_n,V_k,V_m] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
        & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n) ),
    inference(fof_nnf,[status(thm)],[fact_add__leE]) ).

fof(f_140_2,plain,
    ! [U_438,U_437,U_436] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_437,U_438)
        & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_436,U_438) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_436,U_437),U_438) ),
    inference(variable_rename,[status(thm)],[f_140_1]) ).

fof(f_140_3,plain,
    ( ! [U_437,U_436,U_438] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_437,U_438)
        | ~ sP33(U_437,U_436,U_438) )
    & ! [U_437,U_436,U_438] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_436,U_438)
        | ~ sP33(U_437,U_436,U_438) )
    & ! [U_437,U_436,U_438] :
        ( sP33(U_437,U_436,U_438)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_436,U_437),U_438) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP33])],[f_140_2]) ).

cnf(f_140_4,plain,
    ( sP33(U_437,U_436,U_438)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_436,U_437),U_438) ),
    inference(clausify,[status(thm)],[f_140_3]) ).

cnf(f_140_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_436,U_438)
    | ~ sP33(U_437,U_436,U_438) ),
    inference(clausify,[status(thm)],[f_140_3]) ).

cnf(f_140_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_437,U_438)
    | ~ sP33(U_437,U_436,U_438) ),
    inference(clausify,[status(thm)],[f_140_3]) ).

fof(f_141_1,plain,
    ! [V_ry,V_rx,V_ly,V_lx,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_ry))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J]) ).

fof(f_141_2,plain,
    ! [U_443,U_442,U_441,U_440,U_439] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_439),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_439),U_440),U_441)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_439),U_442),U_443)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_439),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_439),U_440),U_442)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_439),U_441),U_443))
      | ~ class_Rings_Ocomm__semiring__1(U_439) ),
    inference(variable_rename,[status(thm)],[f_141_1]) ).

fof(f_141_3,plain,
    ! [U_439,U_440,U_441,U_442,U_443] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_439),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_439),U_440),U_441)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_439),U_442),U_443)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_439),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_439),U_440),U_442)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_439),U_441),U_443))
      | ~ class_Rings_Ocomm__semiring__1(U_439) ),
    inference(definitional_conversion,[status(esa)],[f_141_2]) ).

cnf(f_141_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_439),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_439),U_440),U_441)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_439),U_442),U_443)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_439),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_439),U_440),U_442)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_439),U_441),U_443))
    | ~ class_Rings_Ocomm__semiring__1(U_439) ),
    inference(clausify,[status(thm)],[f_141_3]) ).

fof(f_142_1,plain,
    ! [V_ry,V_rx,V_ly,V_lx,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J]) ).

fof(f_142_2,plain,
    ! [U_448,U_447,U_446,U_445,U_444] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_444),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_444),U_445),U_446)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_444),U_447),U_448)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_444),U_447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_444),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_444),U_445),U_446)),U_448))
      | ~ class_Rings_Ocomm__semiring__1(U_444) ),
    inference(variable_rename,[status(thm)],[f_142_1]) ).

fof(f_142_3,plain,
    ! [U_444,U_445,U_446,U_447,U_448] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_444),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_444),U_445),U_446)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_444),U_447),U_448)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_444),U_447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_444),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_444),U_445),U_446)),U_448))
      | ~ class_Rings_Ocomm__semiring__1(U_444) ),
    inference(definitional_conversion,[status(esa)],[f_142_2]) ).

cnf(f_142_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_444),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_444),U_445),U_446)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_444),U_447),U_448)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_444),U_447),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_444),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_444),U_445),U_446)),U_448))
    | ~ class_Rings_Ocomm__semiring__1(U_444) ),
    inference(clausify,[status(thm)],[f_142_3]) ).

fof(f_143_1,plain,
    ! [V_ry,V_rx,V_ly,V_lx,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J]) ).

fof(f_143_2,plain,
    ! [U_453,U_452,U_451,U_450,U_449] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_449),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_449),U_450),U_451)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_449),U_452),U_453)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_449),U_450),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_449),U_451),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_449),U_452),U_453)))
      | ~ class_Rings_Ocomm__semiring__1(U_449) ),
    inference(variable_rename,[status(thm)],[f_143_1]) ).

fof(f_143_3,plain,
    ! [U_453,U_452,U_449,U_450,U_451] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_449),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_449),U_450),U_451)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_449),U_452),U_453)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_449),U_450),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_449),U_451),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_449),U_452),U_453)))
      | ~ class_Rings_Ocomm__semiring__1(U_449) ),
    inference(definitional_conversion,[status(esa)],[f_143_2]) ).

cnf(f_143_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_449),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_449),U_450),U_451)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_449),U_452),U_453)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_449),U_450),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_449),U_451),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_449),U_452),U_453)))
    | ~ class_Rings_Ocomm__semiring__1(U_449) ),
    inference(clausify,[status(thm)],[f_143_3]) ).

fof(f_144_1,plain,
    ! [V_rx,V_ly,V_lx,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ly)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J]) ).

fof(f_144_2,plain,
    ! [U_457,U_456,U_455,U_454] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_454),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_454),U_455),U_456)),U_457) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_454),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_454),U_455),U_457)),U_456)
      | ~ class_Rings_Ocomm__semiring__1(U_454) ),
    inference(variable_rename,[status(thm)],[f_144_1]) ).

fof(f_144_3,plain,
    ! [U_454,U_455,U_456,U_457] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_454),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_454),U_455),U_456)),U_457) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_454),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_454),U_455),U_457)),U_456)
      | ~ class_Rings_Ocomm__semiring__1(U_454) ),
    inference(definitional_conversion,[status(esa)],[f_144_2]) ).

cnf(f_144_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_454),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_454),U_455),U_456)),U_457) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_454),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_454),U_455),U_457)),U_456)
    | ~ class_Rings_Ocomm__semiring__1(U_454) ),
    inference(clausify,[status(thm)],[f_144_3]) ).

fof(f_145_1,plain,
    ! [V_rx,V_ly,V_lx,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J]) ).

fof(f_145_2,plain,
    ! [U_461,U_460,U_459,U_458] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_458),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_458),U_459),U_460)),U_461) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_458),U_459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_458),U_460),U_461))
      | ~ class_Rings_Ocomm__semiring__1(U_458) ),
    inference(variable_rename,[status(thm)],[f_145_1]) ).

fof(f_145_3,plain,
    ! [U_458,U_459,U_460,U_461] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_458),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_458),U_459),U_460)),U_461) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_458),U_459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_458),U_460),U_461))
      | ~ class_Rings_Ocomm__semiring__1(U_458) ),
    inference(definitional_conversion,[status(esa)],[f_145_2]) ).

cnf(f_145_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_458),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_458),U_459),U_460)),U_461) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_458),U_459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_458),U_460),U_461))
    | ~ class_Rings_Ocomm__semiring__1(U_458) ),
    inference(clausify,[status(thm)],[f_145_3]) ).

fof(f_146_1,plain,
    ! [V_ry,V_rx,V_lx,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),V_ry)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J]) ).

fof(f_146_2,plain,
    ! [U_465,U_464,U_463,U_462] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_462),U_463),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_462),U_464),U_465)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_462),U_463),U_464)),U_465)
      | ~ class_Rings_Ocomm__semiring__1(U_462) ),
    inference(variable_rename,[status(thm)],[f_146_1]) ).

fof(f_146_3,plain,
    ! [U_462,U_463,U_464,U_465] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_462),U_463),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_462),U_464),U_465)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_462),U_463),U_464)),U_465)
      | ~ class_Rings_Ocomm__semiring__1(U_462) ),
    inference(definitional_conversion,[status(esa)],[f_146_2]) ).

cnf(f_146_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_462),U_463),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_462),U_464),U_465)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_462),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_462),U_463),U_464)),U_465)
    | ~ class_Rings_Ocomm__semiring__1(U_462) ),
    inference(clausify,[status(thm)],[f_146_3]) ).

fof(f_147_1,plain,
    ! [V_ry,V_rx,V_lx,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ry))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J]) ).

fof(f_147_2,plain,
    ! [U_469,U_468,U_467,U_466] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_466),U_467),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_466),U_468),U_469)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_466),U_468),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_466),U_467),U_469))
      | ~ class_Rings_Ocomm__semiring__1(U_466) ),
    inference(variable_rename,[status(thm)],[f_147_1]) ).

fof(f_147_3,plain,
    ! [U_466,U_467,U_468,U_469] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_466),U_467),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_466),U_468),U_469)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_466),U_468),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_466),U_467),U_469))
      | ~ class_Rings_Ocomm__semiring__1(U_466) ),
    inference(definitional_conversion,[status(esa)],[f_147_2]) ).

cnf(f_147_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_466),U_467),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_466),U_468),U_469)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_466),U_468),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_466),U_467),U_469))
    | ~ class_Rings_Ocomm__semiring__1(U_466) ),
    inference(clausify,[status(thm)],[f_147_3]) ).

fof(f_148_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J]) ).

fof(f_148_2,plain,
    ! [U_472,U_471,U_470] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_470),U_471),U_472) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_470),U_472),U_471)
      | ~ class_Rings_Ocomm__semiring__1(U_470) ),
    inference(variable_rename,[status(thm)],[f_148_1]) ).

fof(f_148_3,plain,
    ! [U_470,U_471,U_472] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_470),U_471),U_472) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_470),U_472),U_471)
      | ~ class_Rings_Ocomm__semiring__1(U_470) ),
    inference(definitional_conversion,[status(esa)],[f_148_2]) ).

cnf(f_148_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_470),U_471),U_472) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_470),U_472),U_471)
    | ~ class_Rings_Ocomm__semiring__1(U_470) ),
    inference(clausify,[status(thm)],[f_148_3]) ).

fof(f_149_1,plain,
    ! [V_b,V_a,V_y,V_x,T_a] :
      ( c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)))
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult_Oprod__diff__prod]) ).

fof(f_149_2,plain,
    ! [U_477,U_476,U_475,U_474,U_473] :
      ( c_Groups_Ominus__class_Ominus(U_473,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_473),U_474),U_475),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_473),U_476),U_477)) = c_Groups_Oplus__class_Oplus(U_473,c_Groups_Oplus__class_Oplus(U_473,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_473),c_Groups_Ominus__class_Ominus(U_473,U_474,U_476)),c_Groups_Ominus__class_Ominus(U_473,U_475,U_477)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_473),c_Groups_Ominus__class_Ominus(U_473,U_474,U_476)),U_477)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_473),U_476),c_Groups_Ominus__class_Ominus(U_473,U_475,U_477)))
      | ~ class_RealVector_Oreal__normed__algebra(U_473) ),
    inference(variable_rename,[status(thm)],[f_149_1]) ).

fof(f_149_3,plain,
    ! [U_473,U_474,U_475,U_476,U_477] :
      ( c_Groups_Ominus__class_Ominus(U_473,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_473),U_474),U_475),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_473),U_476),U_477)) = c_Groups_Oplus__class_Oplus(U_473,c_Groups_Oplus__class_Oplus(U_473,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_473),c_Groups_Ominus__class_Ominus(U_473,U_474,U_476)),c_Groups_Ominus__class_Ominus(U_473,U_475,U_477)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_473),c_Groups_Ominus__class_Ominus(U_473,U_474,U_476)),U_477)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_473),U_476),c_Groups_Ominus__class_Ominus(U_473,U_475,U_477)))
      | ~ class_RealVector_Oreal__normed__algebra(U_473) ),
    inference(definitional_conversion,[status(esa)],[f_149_2]) ).

cnf(f_149_4,plain,
    ( c_Groups_Ominus__class_Ominus(U_473,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_473),U_474),U_475),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_473),U_476),U_477)) = c_Groups_Oplus__class_Oplus(U_473,c_Groups_Oplus__class_Oplus(U_473,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_473),c_Groups_Ominus__class_Ominus(U_473,U_474,U_476)),c_Groups_Ominus__class_Ominus(U_473,U_475,U_477)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_473),c_Groups_Ominus__class_Ominus(U_473,U_474,U_476)),U_477)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_473),U_476),c_Groups_Ominus__class_Ominus(U_473,U_475,U_477)))
    | ~ class_RealVector_Oreal__normed__algebra(U_473) ),
    inference(clausify,[status(thm)],[f_149_3]) ).

fof(f_150_1,plain,
    ! [V_b,V_a,V_y,V_x,T_a] :
      ( c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b))
      | ~ class_Rings_Oring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__diff__mult]) ).

fof(f_150_2,plain,
    ! [U_482,U_481,U_480,U_479,U_478] :
      ( c_Groups_Ominus__class_Ominus(U_478,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_478),U_479),U_480),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_478),U_481),U_482)) = c_Groups_Oplus__class_Oplus(U_478,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_478),U_479),c_Groups_Ominus__class_Ominus(U_478,U_480,U_482)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_478),c_Groups_Ominus__class_Ominus(U_478,U_479,U_481)),U_482))
      | ~ class_Rings_Oring(U_478) ),
    inference(variable_rename,[status(thm)],[f_150_1]) ).

fof(f_150_3,plain,
    ! [U_478,U_479,U_480,U_481,U_482] :
      ( c_Groups_Ominus__class_Ominus(U_478,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_478),U_479),U_480),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_478),U_481),U_482)) = c_Groups_Oplus__class_Oplus(U_478,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_478),U_479),c_Groups_Ominus__class_Ominus(U_478,U_480,U_482)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_478),c_Groups_Ominus__class_Ominus(U_478,U_479,U_481)),U_482))
      | ~ class_Rings_Oring(U_478) ),
    inference(definitional_conversion,[status(esa)],[f_150_2]) ).

cnf(f_150_4,plain,
    ( c_Groups_Ominus__class_Ominus(U_478,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_478),U_479),U_480),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_478),U_481),U_482)) = c_Groups_Oplus__class_Oplus(U_478,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_478),U_479),c_Groups_Ominus__class_Ominus(U_478,U_480,U_482)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_478),c_Groups_Ominus__class_Ominus(U_478,U_479,U_481)),U_482))
    | ~ class_Rings_Oring(U_478) ),
    inference(clausify,[status(thm)],[f_150_3]) ).

fof(f_151_1,plain,
    ! [V_db_2,V_ca_2,V_b_2,V_ab_2,T_a] :
      ( ( ( V_ab_2 = V_b_2
          | V_ca_2 != V_db_2 )
        & ( V_ca_2 = V_db_2
          | V_ab_2 != V_b_2 ) )
      | c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2) != c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_db_2)
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq]) ).

fof(f_151_2,plain,
    ! [U_487,U_486,U_485,U_484,U_483] :
      ( ( ( U_484 = U_485
          | U_486 != U_487 )
        & ( U_486 = U_487
          | U_484 != U_485 ) )
      | c_Groups_Ominus__class_Ominus(U_483,U_484,U_485) != c_Groups_Ominus__class_Ominus(U_483,U_486,U_487)
      | ~ class_Groups_Oab__group__add(U_483) ),
    inference(variable_rename,[status(thm)],[f_151_1]) ).

fof(f_151_3,plain,
    ( ! [U_485,U_486,U_487,U_484] :
        ( U_484 = U_485
        | U_486 != U_487
        | ~ sP34(U_485,U_486,U_487,U_484) )
    & ! [U_485,U_486,U_487,U_484] :
        ( U_486 = U_487
        | U_484 != U_485
        | ~ sP34(U_485,U_486,U_487,U_484) )
    & ! [U_485,U_486,U_487,U_483,U_484] :
        ( sP34(U_485,U_486,U_487,U_484)
        | c_Groups_Ominus__class_Ominus(U_483,U_484,U_485) != c_Groups_Ominus__class_Ominus(U_483,U_486,U_487)
        | ~ class_Groups_Oab__group__add(U_483) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP34])],[f_151_2]) ).

cnf(f_151_4,plain,
    ( sP34(U_485,U_486,U_487,U_484)
    | c_Groups_Ominus__class_Ominus(U_483,U_484,U_485) != c_Groups_Ominus__class_Ominus(U_483,U_486,U_487)
    | ~ class_Groups_Oab__group__add(U_483) ),
    inference(clausify,[status(thm)],[f_151_3]) ).

cnf(f_151_5,plain,
    ( U_486 = U_487
    | U_484 != U_485
    | ~ sP34(U_485,U_486,U_487,U_484) ),
    inference(clausify,[status(thm)],[f_151_3]) ).

cnf(f_151_6,plain,
    ( U_484 = U_485
    | U_486 != U_487
    | ~ sP34(U_485,U_486,U_487,U_484) ),
    inference(clausify,[status(thm)],[f_151_3]) ).

fof(f_152_1,plain,
    ! [V_b,V_n,V_a,T_a] :
      ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_n)
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__monom]) ).

fof(f_152_2,plain,
    ! [U_491,U_490,U_489,U_488] :
      ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_488),c_Polynomial_Omonom(U_488,U_489,U_490),c_Polynomial_Omonom(U_488,U_491,U_490)) = c_Polynomial_Omonom(U_488,c_Groups_Ominus__class_Ominus(U_488,U_489,U_491),U_490)
      | ~ class_Groups_Oab__group__add(U_488) ),
    inference(variable_rename,[status(thm)],[f_152_1]) ).

fof(f_152_3,plain,
    ! [U_491,U_490,U_489,U_488] :
      ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_488),c_Polynomial_Omonom(U_488,U_489,U_490),c_Polynomial_Omonom(U_488,U_491,U_490)) = c_Polynomial_Omonom(U_488,c_Groups_Ominus__class_Ominus(U_488,U_489,U_491),U_490)
      | ~ class_Groups_Oab__group__add(U_488) ),
    inference(definitional_conversion,[status(esa)],[f_152_2]) ).

cnf(f_152_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_488),c_Polynomial_Omonom(U_488,U_489,U_490),c_Polynomial_Omonom(U_488,U_491,U_490)) = c_Polynomial_Omonom(U_488,c_Groups_Ominus__class_Ominus(U_488,U_489,U_491),U_490)
    | ~ class_Groups_Oab__group__add(U_488) ),
    inference(clausify,[status(thm)],[f_152_3]) ).

fof(f_153_1,plain,
    ! [V_b_2,V_n_2,V_ab_2,T_a] :
      ( ( ( c_Polynomial_Omonom(T_a,V_ab_2,V_n_2) = c_Polynomial_Omonom(T_a,V_b_2,V_n_2)
          | V_ab_2 != V_b_2 )
        & ( V_ab_2 = V_b_2
          | c_Polynomial_Omonom(T_a,V_ab_2,V_n_2) != c_Polynomial_Omonom(T_a,V_b_2,V_n_2) ) )
      | ~ class_Groups_Ozero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_monom__eq__iff]) ).

fof(f_153_2,plain,
    ! [U_495,U_494,U_493,U_492] :
      ( ( ( c_Polynomial_Omonom(U_492,U_493,U_494) = c_Polynomial_Omonom(U_492,U_495,U_494)
          | U_493 != U_495 )
        & ( U_493 = U_495
          | c_Polynomial_Omonom(U_492,U_493,U_494) != c_Polynomial_Omonom(U_492,U_495,U_494) ) )
      | ~ class_Groups_Ozero(U_492) ),
    inference(variable_rename,[status(thm)],[f_153_1]) ).

fof(f_153_3,plain,
    ( ! [U_492,U_494,U_493,U_495] :
        ( c_Polynomial_Omonom(U_492,U_493,U_494) = c_Polynomial_Omonom(U_492,U_495,U_494)
        | U_493 != U_495
        | ~ sP35(U_492,U_494,U_493,U_495) )
    & ! [U_492,U_494,U_493,U_495] :
        ( U_493 = U_495
        | c_Polynomial_Omonom(U_492,U_493,U_494) != c_Polynomial_Omonom(U_492,U_495,U_494)
        | ~ sP35(U_492,U_494,U_493,U_495) )
    & ! [U_492,U_494,U_493,U_495] :
        ( sP35(U_492,U_494,U_493,U_495)
        | ~ class_Groups_Ozero(U_492) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP35])],[f_153_2]) ).

cnf(f_153_4,plain,
    ( sP35(U_492,U_494,U_493,U_495)
    | ~ class_Groups_Ozero(U_492) ),
    inference(clausify,[status(thm)],[f_153_3]) ).

cnf(f_153_5,plain,
    ( U_493 = U_495
    | c_Polynomial_Omonom(U_492,U_493,U_494) != c_Polynomial_Omonom(U_492,U_495,U_494)
    | ~ sP35(U_492,U_494,U_493,U_495) ),
    inference(clausify,[status(thm)],[f_153_3]) ).

cnf(f_153_6,plain,
    ( c_Polynomial_Omonom(U_492,U_493,U_494) = c_Polynomial_Omonom(U_492,U_495,U_494)
    | U_493 != U_495
    | ~ sP35(U_492,U_494,U_493,U_495) ),
    inference(clausify,[status(thm)],[f_153_3]) ).

fof(f_154_1,plain,
    ! [V_ya,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),V_ya) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya))
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__left_Odiff]) ).

fof(f_154_2,plain,
    ! [U_499,U_498,U_497,U_496] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_496),c_Groups_Ominus__class_Ominus(U_496,U_497,U_498)),U_499) = c_Groups_Ominus__class_Ominus(U_496,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_496),U_497),U_499),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_496),U_498),U_499))
      | ~ class_RealVector_Oreal__normed__algebra(U_496) ),
    inference(variable_rename,[status(thm)],[f_154_1]) ).

fof(f_154_3,plain,
    ! [U_497,U_499,U_498,U_496] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_496),c_Groups_Ominus__class_Ominus(U_496,U_497,U_498)),U_499) = c_Groups_Ominus__class_Ominus(U_496,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_496),U_497),U_499),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_496),U_498),U_499))
      | ~ class_RealVector_Oreal__normed__algebra(U_496) ),
    inference(definitional_conversion,[status(esa)],[f_154_2]) ).

cnf(f_154_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_496),c_Groups_Ominus__class_Ominus(U_496,U_497,U_498)),U_499) = c_Groups_Ominus__class_Ominus(U_496,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_496),U_497),U_499),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_496),U_498),U_499))
    | ~ class_RealVector_Oreal__normed__algebra(U_496) ),
    inference(clausify,[status(thm)],[f_154_3]) ).

fof(f_155_1,plain,
    ! [V_b,V_a_H,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H)),V_b) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b))
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult_Odiff__left]) ).

fof(f_155_2,plain,
    ! [U_503,U_502,U_501,U_500] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_500),c_Groups_Ominus__class_Ominus(U_500,U_501,U_502)),U_503) = c_Groups_Ominus__class_Ominus(U_500,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_500),U_501),U_503),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_500),U_502),U_503))
      | ~ class_RealVector_Oreal__normed__algebra(U_500) ),
    inference(variable_rename,[status(thm)],[f_155_1]) ).

fof(f_155_3,plain,
    ! [U_500,U_501,U_502,U_503] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_500),c_Groups_Ominus__class_Ominus(U_500,U_501,U_502)),U_503) = c_Groups_Ominus__class_Ominus(U_500,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_500),U_501),U_503),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_500),U_502),U_503))
      | ~ class_RealVector_Oreal__normed__algebra(U_500) ),
    inference(definitional_conversion,[status(esa)],[f_155_2]) ).

cnf(f_155_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_500),c_Groups_Ominus__class_Ominus(U_500,U_501,U_502)),U_503) = c_Groups_Ominus__class_Ominus(U_500,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_500),U_501),U_503),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_500),U_502),U_503))
    | ~ class_RealVector_Oreal__normed__algebra(U_500) ),
    inference(clausify,[status(thm)],[f_155_3]) ).

fof(f_156_1,plain,
    ! [V_p,V_b,V_a,T_a] :
      ( c_Polynomial_Osmult(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_p) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_b,V_p))
      | ~ class_Rings_Ocomm__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_smult__diff__left]) ).

fof(f_156_2,plain,
    ! [U_507,U_506,U_505,U_504] :
      ( c_Polynomial_Osmult(U_504,c_Groups_Ominus__class_Ominus(U_504,U_505,U_506),U_507) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_504),c_Polynomial_Osmult(U_504,U_505,U_507),c_Polynomial_Osmult(U_504,U_506,U_507))
      | ~ class_Rings_Ocomm__ring(U_504) ),
    inference(variable_rename,[status(thm)],[f_156_1]) ).

fof(f_156_3,plain,
    ! [U_504,U_505,U_506,U_507] :
      ( c_Polynomial_Osmult(U_504,c_Groups_Ominus__class_Ominus(U_504,U_505,U_506),U_507) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_504),c_Polynomial_Osmult(U_504,U_505,U_507),c_Polynomial_Osmult(U_504,U_506,U_507))
      | ~ class_Rings_Ocomm__ring(U_504) ),
    inference(definitional_conversion,[status(esa)],[f_156_2]) ).

cnf(f_156_4,plain,
    ( c_Polynomial_Osmult(U_504,c_Groups_Ominus__class_Ominus(U_504,U_505,U_506),U_507) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_504),c_Polynomial_Osmult(U_504,U_505,U_507),c_Polynomial_Osmult(U_504,U_506,U_507))
    | ~ class_Rings_Ocomm__ring(U_504) ),
    inference(clausify,[status(thm)],[f_156_3]) ).

fof(f_157_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
      | ~ class_Groups_Oab__semigroup__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ab__semigroup__mult__class_Omult__ac_I1_J]) ).

fof(f_157_2,plain,
    ! [U_511,U_510,U_509,U_508] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_508),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_508),U_509),U_510)),U_511) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_508),U_509),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_508),U_510),U_511))
      | ~ class_Groups_Oab__semigroup__mult(U_508) ),
    inference(variable_rename,[status(thm)],[f_157_1]) ).

fof(f_157_3,plain,
    ! [U_508,U_509,U_510,U_511] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_508),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_508),U_509),U_510)),U_511) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_508),U_509),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_508),U_510),U_511))
      | ~ class_Groups_Oab__semigroup__mult(U_508) ),
    inference(definitional_conversion,[status(esa)],[f_157_2]) ).

cnf(f_157_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_508),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_508),U_509),U_510)),U_511) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_508),U_509),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_508),U_510),U_511))
    | ~ class_Groups_Oab__semigroup__mult(U_508) ),
    inference(clausify,[status(thm)],[f_157_3]) ).

fof(f_158_1,plain,
    ! [V_q,V_p,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_Osmult(T_a,V_a,V_p)),V_q) = c_Polynomial_Osmult(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__smult__left]) ).

fof(f_158_2,plain,
    ! [U_515,U_514,U_513,U_512] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_512)),c_Polynomial_Osmult(U_512,U_513,U_514)),U_515) = c_Polynomial_Osmult(U_512,U_513,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_512)),U_514),U_515))
      | ~ class_Rings_Ocomm__semiring__0(U_512) ),
    inference(variable_rename,[status(thm)],[f_158_1]) ).

fof(f_158_3,plain,
    ! [U_512,U_513,U_514,U_515] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_512)),c_Polynomial_Osmult(U_512,U_513,U_514)),U_515) = c_Polynomial_Osmult(U_512,U_513,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_512)),U_514),U_515))
      | ~ class_Rings_Ocomm__semiring__0(U_512) ),
    inference(definitional_conversion,[status(esa)],[f_158_2]) ).

cnf(f_158_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_512)),c_Polynomial_Osmult(U_512,U_513,U_514)),U_515) = c_Polynomial_Osmult(U_512,U_513,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_512)),U_514),U_515))
    | ~ class_Rings_Ocomm__semiring__0(U_512) ),
    inference(clausify,[status(thm)],[f_158_3]) ).

fof(f_159_1,plain,
    ! [V_y,V_x,V_xa,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y))
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__right_Odiff]) ).

fof(f_159_2,plain,
    ! [U_519,U_518,U_517,U_516] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_516),U_517),c_Groups_Ominus__class_Ominus(U_516,U_518,U_519)) = c_Groups_Ominus__class_Ominus(U_516,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_516),U_517),U_518),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_516),U_517),U_519))
      | ~ class_RealVector_Oreal__normed__algebra(U_516) ),
    inference(variable_rename,[status(thm)],[f_159_1]) ).

fof(f_159_3,plain,
    ! [U_516,U_517,U_518,U_519] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_516),U_517),c_Groups_Ominus__class_Ominus(U_516,U_518,U_519)) = c_Groups_Ominus__class_Ominus(U_516,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_516),U_517),U_518),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_516),U_517),U_519))
      | ~ class_RealVector_Oreal__normed__algebra(U_516) ),
    inference(definitional_conversion,[status(esa)],[f_159_2]) ).

cnf(f_159_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_516),U_517),c_Groups_Ominus__class_Ominus(U_516,U_518,U_519)) = c_Groups_Ominus__class_Ominus(U_516,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_516),U_517),U_518),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_516),U_517),U_519))
    | ~ class_RealVector_Oreal__normed__algebra(U_516) ),
    inference(clausify,[status(thm)],[f_159_3]) ).

fof(f_160_1,plain,
    ! [V_b_H,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H)) = c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H))
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult_Odiff__right]) ).

fof(f_160_2,plain,
    ! [U_523,U_522,U_521,U_520] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_520),U_521),c_Groups_Ominus__class_Ominus(U_520,U_522,U_523)) = c_Groups_Ominus__class_Ominus(U_520,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_520),U_521),U_522),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_520),U_521),U_523))
      | ~ class_RealVector_Oreal__normed__algebra(U_520) ),
    inference(variable_rename,[status(thm)],[f_160_1]) ).

fof(f_160_3,plain,
    ! [U_520,U_521,U_522,U_523] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_520),U_521),c_Groups_Ominus__class_Ominus(U_520,U_522,U_523)) = c_Groups_Ominus__class_Ominus(U_520,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_520),U_521),U_522),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_520),U_521),U_523))
      | ~ class_RealVector_Oreal__normed__algebra(U_520) ),
    inference(definitional_conversion,[status(esa)],[f_160_2]) ).

cnf(f_160_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_520),U_521),c_Groups_Ominus__class_Ominus(U_520,U_522,U_523)) = c_Groups_Ominus__class_Ominus(U_520,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_520),U_521),U_522),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_520),U_521),U_523))
    | ~ class_RealVector_Oreal__normed__algebra(U_520) ),
    inference(clausify,[status(thm)],[f_160_3]) ).

fof(f_161_1,plain,
    ! [V_q,V_p,V_a,T_a] :
      ( c_Polynomial_Osmult(T_a,V_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_a,V_q))
      | ~ class_Rings_Ocomm__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_smult__diff__right]) ).

fof(f_161_2,plain,
    ! [U_527,U_526,U_525,U_524] :
      ( c_Polynomial_Osmult(U_524,U_525,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_524),U_526,U_527)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_524),c_Polynomial_Osmult(U_524,U_525,U_526),c_Polynomial_Osmult(U_524,U_525,U_527))
      | ~ class_Rings_Ocomm__ring(U_524) ),
    inference(variable_rename,[status(thm)],[f_161_1]) ).

fof(f_161_3,plain,
    ! [U_525,U_524,U_526,U_527] :
      ( c_Polynomial_Osmult(U_524,U_525,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_524),U_526,U_527)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_524),c_Polynomial_Osmult(U_524,U_525,U_526),c_Polynomial_Osmult(U_524,U_525,U_527))
      | ~ class_Rings_Ocomm__ring(U_524) ),
    inference(definitional_conversion,[status(esa)],[f_161_2]) ).

cnf(f_161_4,plain,
    ( c_Polynomial_Osmult(U_524,U_525,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_524),U_526,U_527)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_524),c_Polynomial_Osmult(U_524,U_525,U_526),c_Polynomial_Osmult(U_524,U_525,U_527))
    | ~ class_Rings_Ocomm__ring(U_524) ),
    inference(clausify,[status(thm)],[f_161_3]) ).

fof(f_162_1,plain,
    ! [V_p,V_b,V_a,T_a] :
      ( c_Polynomial_Osmult(T_a,V_a,c_Polynomial_Osmult(T_a,V_b,V_p)) = c_Polynomial_Osmult(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_p)
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_smult__smult]) ).

fof(f_162_2,plain,
    ! [U_531,U_530,U_529,U_528] :
      ( c_Polynomial_Osmult(U_528,U_529,c_Polynomial_Osmult(U_528,U_530,U_531)) = c_Polynomial_Osmult(U_528,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_528),U_529),U_530),U_531)
      | ~ class_Rings_Ocomm__semiring__0(U_528) ),
    inference(variable_rename,[status(thm)],[f_162_1]) ).

fof(f_162_3,plain,
    ! [U_528,U_529,U_530,U_531] :
      ( c_Polynomial_Osmult(U_528,U_529,c_Polynomial_Osmult(U_528,U_530,U_531)) = c_Polynomial_Osmult(U_528,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_528),U_529),U_530),U_531)
      | ~ class_Rings_Ocomm__semiring__0(U_528) ),
    inference(definitional_conversion,[status(esa)],[f_162_2]) ).

cnf(f_162_4,plain,
    ( c_Polynomial_Osmult(U_528,U_529,c_Polynomial_Osmult(U_528,U_530,U_531)) = c_Polynomial_Osmult(U_528,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_528),U_529),U_530),U_531)
    | ~ class_Rings_Ocomm__semiring__0(U_528) ),
    inference(clausify,[status(thm)],[f_162_3]) ).

fof(f_163_1,plain,
    ! [V_n,V_b,V_a,T_a] :
      ( c_Polynomial_Osmult(T_a,V_a,c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_n)
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_smult__monom]) ).

fof(f_163_2,plain,
    ! [U_535,U_534,U_533,U_532] :
      ( c_Polynomial_Osmult(U_532,U_533,c_Polynomial_Omonom(U_532,U_534,U_535)) = c_Polynomial_Omonom(U_532,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_532),U_533),U_534),U_535)
      | ~ class_Rings_Ocomm__semiring__0(U_532) ),
    inference(variable_rename,[status(thm)],[f_163_1]) ).

fof(f_163_3,plain,
    ! [U_532,U_533,U_534,U_535] :
      ( c_Polynomial_Osmult(U_532,U_533,c_Polynomial_Omonom(U_532,U_534,U_535)) = c_Polynomial_Omonom(U_532,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_532),U_533),U_534),U_535)
      | ~ class_Rings_Ocomm__semiring__0(U_532) ),
    inference(definitional_conversion,[status(esa)],[f_163_2]) ).

cnf(f_163_4,plain,
    ( c_Polynomial_Osmult(U_532,U_533,c_Polynomial_Omonom(U_532,U_534,U_535)) = c_Polynomial_Omonom(U_532,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_532),U_533),U_534),U_535)
    | ~ class_Rings_Ocomm__semiring__0(U_532) ),
    inference(clausify,[status(thm)],[f_163_3]) ).

fof(f_164_1,plain,
    ! [V_q,V_a,V_p,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_Osmult(T_a,V_a,V_q)) = c_Polynomial_Osmult(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__smult__right]) ).

fof(f_164_2,plain,
    ! [U_539,U_538,U_537,U_536] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_536)),U_537),c_Polynomial_Osmult(U_536,U_538,U_539)) = c_Polynomial_Osmult(U_536,U_538,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_536)),U_537),U_539))
      | ~ class_Rings_Ocomm__semiring__0(U_536) ),
    inference(variable_rename,[status(thm)],[f_164_1]) ).

fof(f_164_3,plain,
    ! [U_536,U_537,U_538,U_539] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_536)),U_537),c_Polynomial_Osmult(U_536,U_538,U_539)) = c_Polynomial_Osmult(U_536,U_538,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_536)),U_537),U_539))
      | ~ class_Rings_Ocomm__semiring__0(U_536) ),
    inference(definitional_conversion,[status(esa)],[f_164_2]) ).

cnf(f_164_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_536)),U_537),c_Polynomial_Osmult(U_536,U_538,U_539)) = c_Polynomial_Osmult(U_536,U_538,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_536)),U_537),U_539))
    | ~ class_Rings_Ocomm__semiring__0(U_536) ),
    inference(clausify,[status(thm)],[f_164_3]) ).

fof(f_165_1,plain,
    ! [V_q,V_b,V_p,V_a,T_a] :
      ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q)) = c_Polynomial_OpCons(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q))
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__pCons]) ).

fof(f_165_2,plain,
    ! [U_544,U_543,U_542,U_541,U_540] :
      ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_540),c_Polynomial_OpCons(U_540,U_541,U_542),c_Polynomial_OpCons(U_540,U_543,U_544)) = c_Polynomial_OpCons(U_540,c_Groups_Ominus__class_Ominus(U_540,U_541,U_543),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_540),U_542,U_544))
      | ~ class_Groups_Oab__group__add(U_540) ),
    inference(variable_rename,[status(thm)],[f_165_1]) ).

fof(f_165_3,plain,
    ! [U_541,U_540,U_542,U_543,U_544] :
      ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_540),c_Polynomial_OpCons(U_540,U_541,U_542),c_Polynomial_OpCons(U_540,U_543,U_544)) = c_Polynomial_OpCons(U_540,c_Groups_Ominus__class_Ominus(U_540,U_541,U_543),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_540),U_542,U_544))
      | ~ class_Groups_Oab__group__add(U_540) ),
    inference(definitional_conversion,[status(esa)],[f_165_2]) ).

cnf(f_165_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_540),c_Polynomial_OpCons(U_540,U_541,U_542),c_Polynomial_OpCons(U_540,U_543,U_544)) = c_Polynomial_OpCons(U_540,c_Groups_Ominus__class_Ominus(U_540,U_541,U_543),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_540),U_542,U_544))
    | ~ class_Groups_Oab__group__add(U_540) ),
    inference(clausify,[status(thm)],[f_165_3]) ).

fof(f_166_1,plain,
    ! [V_y,V_x,T_a] :
      ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y))
      | ~ class_RealVector_Oreal__normed__div__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_norm__mult]) ).

fof(f_166_2,plain,
    ! [U_547,U_546,U_545] :
      ( c_RealVector_Onorm__class_Onorm(U_545,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_545),U_546),U_547)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_545,U_546)),c_RealVector_Onorm__class_Onorm(U_545,U_547))
      | ~ class_RealVector_Oreal__normed__div__algebra(U_545) ),
    inference(variable_rename,[status(thm)],[f_166_1]) ).

fof(f_166_3,plain,
    ! [U_545,U_546,U_547] :
      ( c_RealVector_Onorm__class_Onorm(U_545,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_545),U_546),U_547)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_545,U_546)),c_RealVector_Onorm__class_Onorm(U_545,U_547))
      | ~ class_RealVector_Oreal__normed__div__algebra(U_545) ),
    inference(definitional_conversion,[status(esa)],[f_166_2]) ).

cnf(f_166_4,plain,
    ( c_RealVector_Onorm__class_Onorm(U_545,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_545),U_546),U_547)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_545,U_546)),c_RealVector_Onorm__class_Onorm(U_545,U_547))
    | ~ class_RealVector_Oreal__normed__div__algebra(U_545) ),
    inference(clausify,[status(thm)],[f_166_3]) ).

fof(f_167_1,plain,
    ! [V_p,V_b,V_a,T_a] :
      ( c_Polynomial_Osmult(T_a,V_a,c_Polynomial_OpCons(T_a,V_b,V_p)) = c_Polynomial_OpCons(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Polynomial_Osmult(T_a,V_a,V_p))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_smult__pCons]) ).

fof(f_167_2,plain,
    ! [U_551,U_550,U_549,U_548] :
      ( c_Polynomial_Osmult(U_548,U_549,c_Polynomial_OpCons(U_548,U_550,U_551)) = c_Polynomial_OpCons(U_548,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_548),U_549),U_550),c_Polynomial_Osmult(U_548,U_549,U_551))
      | ~ class_Rings_Ocomm__semiring__0(U_548) ),
    inference(variable_rename,[status(thm)],[f_167_1]) ).

fof(f_167_3,plain,
    ! [U_548,U_549,U_550,U_551] :
      ( c_Polynomial_Osmult(U_548,U_549,c_Polynomial_OpCons(U_548,U_550,U_551)) = c_Polynomial_OpCons(U_548,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_548),U_549),U_550),c_Polynomial_Osmult(U_548,U_549,U_551))
      | ~ class_Rings_Ocomm__semiring__0(U_548) ),
    inference(definitional_conversion,[status(esa)],[f_167_2]) ).

cnf(f_167_4,plain,
    ( c_Polynomial_Osmult(U_548,U_549,c_Polynomial_OpCons(U_548,U_550,U_551)) = c_Polynomial_OpCons(U_548,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_548),U_549),U_550),c_Polynomial_Osmult(U_548,U_549,U_551))
    | ~ class_Rings_Ocomm__semiring__0(U_548) ),
    inference(clausify,[status(thm)],[f_167_3]) ).

fof(f_168_1,plain,
    ! [V_x,V_q,V_p,T_a] :
      ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))
      | ~ class_Rings_Ocomm__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_poly__diff]) ).

fof(f_168_2,plain,
    ! [U_555,U_554,U_553,U_552] :
      ( hAPP(c_Polynomial_Opoly(U_552,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_552),U_553,U_554)),U_555) = c_Groups_Ominus__class_Ominus(U_552,hAPP(c_Polynomial_Opoly(U_552,U_553),U_555),hAPP(c_Polynomial_Opoly(U_552,U_554),U_555))
      | ~ class_Rings_Ocomm__ring(U_552) ),
    inference(variable_rename,[status(thm)],[f_168_1]) ).

fof(f_168_3,plain,
    ! [U_552,U_553,U_554,U_555] :
      ( hAPP(c_Polynomial_Opoly(U_552,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_552),U_553,U_554)),U_555) = c_Groups_Ominus__class_Ominus(U_552,hAPP(c_Polynomial_Opoly(U_552,U_553),U_555),hAPP(c_Polynomial_Opoly(U_552,U_554),U_555))
      | ~ class_Rings_Ocomm__ring(U_552) ),
    inference(definitional_conversion,[status(esa)],[f_168_2]) ).

cnf(f_168_4,plain,
    ( hAPP(c_Polynomial_Opoly(U_552,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_552),U_553,U_554)),U_555) = c_Groups_Ominus__class_Ominus(U_552,hAPP(c_Polynomial_Opoly(U_552,U_553),U_555),hAPP(c_Polynomial_Opoly(U_552,U_554),U_555))
    | ~ class_Rings_Ocomm__ring(U_552) ),
    inference(clausify,[status(thm)],[f_168_3]) ).

fof(f_169_1,plain,
    ! [V_x,V_p,V_a,T_a] :
      ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Osmult(T_a,V_a,V_p)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_poly__smult]) ).

fof(f_169_2,plain,
    ! [U_559,U_558,U_557,U_556] :
      ( hAPP(c_Polynomial_Opoly(U_556,c_Polynomial_Osmult(U_556,U_557,U_558)),U_559) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_556),U_557),hAPP(c_Polynomial_Opoly(U_556,U_558),U_559))
      | ~ class_Rings_Ocomm__semiring__0(U_556) ),
    inference(variable_rename,[status(thm)],[f_169_1]) ).

fof(f_169_3,plain,
    ! [U_556,U_557,U_558,U_559] :
      ( hAPP(c_Polynomial_Opoly(U_556,c_Polynomial_Osmult(U_556,U_557,U_558)),U_559) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_556),U_557),hAPP(c_Polynomial_Opoly(U_556,U_558),U_559))
      | ~ class_Rings_Ocomm__semiring__0(U_556) ),
    inference(definitional_conversion,[status(esa)],[f_169_2]) ).

cnf(f_169_4,plain,
    ( hAPP(c_Polynomial_Opoly(U_556,c_Polynomial_Osmult(U_556,U_557,U_558)),U_559) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_556),U_557),hAPP(c_Polynomial_Opoly(U_556,U_558),U_559))
    | ~ class_Rings_Ocomm__semiring__0(U_556) ),
    inference(clausify,[status(thm)],[f_169_3]) ).

fof(f_170_1,plain,
    ! [V_n,V_m] :
      ( V_m = V_n
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_nnf,[status(thm)],[fact_diffs0__imp__equal]) ).

fof(f_170_2,plain,
    ! [U_561,U_560] :
      ( U_560 = U_561
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_561,U_560) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_560,U_561) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_170_1]) ).

fof(f_170_3,plain,
    ! [U_561,U_560] :
      ( U_560 = U_561
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_561,U_560) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_560,U_561) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_170_2]) ).

cnf(f_170_4,plain,
    ( U_560 = U_561
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_561,U_560) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_560,U_561) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_170_3]) ).

fof(f_171_1,plain,
    ! [V_n,V_m] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
    inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq_H]) ).

fof(f_171_2,plain,
    ! [U_563,U_562] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_562,U_563) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_562,U_563) ),
    inference(variable_rename,[status(thm)],[f_171_1]) ).

fof(f_171_3,plain,
    ! [U_562,U_563] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_562,U_563) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_562,U_563) ),
    inference(definitional_conversion,[status(esa)],[f_171_2]) ).

cnf(f_171_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_562,U_563) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_562,U_563) ),
    inference(clausify,[status(thm)],[f_171_3]) ).

fof(f_172_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
        | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq]) ).

fof(f_172_2,plain,
    ! [U_565,U_564] :
      ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_564,U_565) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_564,U_565) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_564,U_565)
        | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_564,U_565) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_172_1]) ).

fof(f_172_3,plain,
    ( ! [U_569,U_567] :
        ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_567,U_569) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_567,U_569) )
    & ! [U_568,U_566] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_566,U_568)
        | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_566,U_568) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_172_2]) ).

fof(f_172_4,plain,
    ( ! [U_569,U_567] :
        ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_567,U_569) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_567,U_569) )
    & ! [U_566,U_568] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_566,U_568)
        | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_566,U_568) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_172_3]) ).

cnf(f_172_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_566,U_568)
    | c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_566,U_568) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_172_4]) ).

cnf(f_172_6,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_567,U_569) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_567,U_569) ),
    inference(clausify,[status(thm)],[f_172_4]) ).

fof(f_173_1,plain,
    ! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_diff__add__0]) ).

fof(f_173_2,plain,
    ! [U_571,U_570] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_570,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_570,U_571)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_173_1]) ).

fof(f_173_3,plain,
    ! [U_570,U_571] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_570,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_570,U_571)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_173_2]) ).

cnf(f_173_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_570,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_570,U_571)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_173_3]) ).

fof(f_174_1,plain,
    ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_diff__self__eq__0]) ).

fof(f_174_2,plain,
    ! [U_572] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_572,U_572) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_174_1]) ).

fof(f_174_3,plain,
    ! [U_572] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_572,U_572) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_174_2]) ).

cnf(f_174_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_572,U_572) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_174_3]) ).

fof(f_175_1,plain,
    ! [V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
    inference(fof_nnf,[status(thm)],[fact_minus__nat_Odiff__0]) ).

fof(f_175_2,plain,
    ! [U_573] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_573,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_573,
    inference(variable_rename,[status(thm)],[f_175_1]) ).

fof(f_175_3,plain,
    ! [U_573] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_573,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_573,
    inference(definitional_conversion,[status(esa)],[f_175_2]) ).

cnf(f_175_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_573,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_573,
    inference(clausify,[status(thm)],[f_175_3]) ).

fof(f_176_1,plain,
    ! [V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_diff__0__eq__0]) ).

fof(f_176_2,plain,
    ! [U_574] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_574) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_176_1]) ).

fof(f_176_3,plain,
    ! [U_574] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_574) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_176_2]) ).

cnf(f_176_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_574) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_176_3]) ).

fof(f_177_1,plain,
    ! [V_x,V_q,V_p,T_a] :
      ( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_poly__mult]) ).

fof(f_177_2,plain,
    ! [U_578,U_577,U_576,U_575] :
      ( hAPP(c_Polynomial_Opoly(U_575,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_575)),U_576),U_577)),U_578) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_575),hAPP(c_Polynomial_Opoly(U_575,U_576),U_578)),hAPP(c_Polynomial_Opoly(U_575,U_577),U_578))
      | ~ class_Rings_Ocomm__semiring__0(U_575) ),
    inference(variable_rename,[status(thm)],[f_177_1]) ).

fof(f_177_3,plain,
    ! [U_575,U_576,U_577,U_578] :
      ( hAPP(c_Polynomial_Opoly(U_575,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_575)),U_576),U_577)),U_578) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_575),hAPP(c_Polynomial_Opoly(U_575,U_576),U_578)),hAPP(c_Polynomial_Opoly(U_575,U_577),U_578))
      | ~ class_Rings_Ocomm__semiring__0(U_575) ),
    inference(definitional_conversion,[status(esa)],[f_177_2]) ).

cnf(f_177_4,plain,
    ( hAPP(c_Polynomial_Opoly(U_575,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_575)),U_576),U_577)),U_578) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_575),hAPP(c_Polynomial_Opoly(U_575,U_576),U_578)),hAPP(c_Polynomial_Opoly(U_575,U_577),U_578))
    | ~ class_Rings_Ocomm__semiring__0(U_575) ),
    inference(clausify,[status(thm)],[f_177_3]) ).

fof(f_178_1,plain,
    ! [V_n_2,V_k_2,V_m_2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)
        | ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_m_2 != V_n_2 ) )
      & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_m_2 = V_n_2
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__cancel2]) ).

fof(f_178_2,plain,
    ! [U_581,U_580,U_579] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_579),U_580) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_581),U_580)
        | ( U_580 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_579 != U_581 ) )
      & ( U_580 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_579 = U_581
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_579),U_580) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_581),U_580) ) ),
    inference(variable_rename,[status(thm)],[f_178_1]) ).

fof(f_178_3,plain,
    ( ! [U_587,U_585,U_583] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_583),U_585) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_587),U_585)
        | ( U_585 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_583 != U_587 ) )
    & ! [U_586,U_584,U_582] :
        ( U_584 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_582 = U_586
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_582),U_584) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_586),U_584) ) ),
    inference(miniscope,[status(thm)],[f_178_2]) ).

fof(f_178_4,plain,
    ( ! [U_585,U_587,U_583] :
        ( U_585 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP36(U_585,U_587,U_583) )
    & ! [U_585,U_587,U_583] :
        ( U_583 != U_587
        | ~ sP36(U_585,U_587,U_583) )
    & ! [U_585,U_587,U_583] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_583),U_585) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_587),U_585)
        | sP36(U_585,U_587,U_583) )
    & ! [U_584,U_582,U_586] :
        ( U_584 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_582 = U_586
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_582),U_584) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_586),U_584) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP36])],[f_178_3]) ).

cnf(f_178_5,plain,
    ( U_584 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_582 = U_586
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_582),U_584) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_586),U_584) ),
    inference(clausify,[status(thm)],[f_178_4]) ).

cnf(f_178_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_583),U_585) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_587),U_585)
    | sP36(U_585,U_587,U_583) ),
    inference(clausify,[status(thm)],[f_178_4]) ).

cnf(f_178_7,plain,
    ( U_583 != U_587
    | ~ sP36(U_585,U_587,U_583) ),
    inference(clausify,[status(thm)],[f_178_4]) ).

cnf(f_178_8,plain,
    ( U_585 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP36(U_585,U_587,U_583) ),
    inference(clausify,[status(thm)],[f_178_4]) ).

fof(f_179_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
        | ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_m_2 != V_n_2 ) )
      & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_m_2 = V_n_2
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__cancel1]) ).

fof(f_179_2,plain,
    ! [U_590,U_589,U_588] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_588),U_589) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_588),U_590)
        | ( U_588 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_589 != U_590 ) )
      & ( U_588 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_589 = U_590
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_588),U_589) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_588),U_590) ) ),
    inference(variable_rename,[status(thm)],[f_179_1]) ).

fof(f_179_3,plain,
    ( ! [U_596,U_594,U_592] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_592),U_594) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_592),U_596)
        | ( U_592 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_594 != U_596 ) )
    & ! [U_595,U_593,U_591] :
        ( U_591 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_593 = U_595
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_591),U_593) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_591),U_595) ) ),
    inference(miniscope,[status(thm)],[f_179_2]) ).

fof(f_179_4,plain,
    ( ! [U_594,U_592,U_596] :
        ( U_592 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP37(U_594,U_592,U_596) )
    & ! [U_594,U_592,U_596] :
        ( U_594 != U_596
        | ~ sP37(U_594,U_592,U_596) )
    & ! [U_594,U_592,U_596] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_592),U_594) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_592),U_596)
        | sP37(U_594,U_592,U_596) )
    & ! [U_593,U_595,U_591] :
        ( U_591 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_593 = U_595
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_591),U_593) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_591),U_595) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP37])],[f_179_3]) ).

cnf(f_179_5,plain,
    ( U_591 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_593 = U_595
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_591),U_593) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_591),U_595) ),
    inference(clausify,[status(thm)],[f_179_4]) ).

cnf(f_179_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_592),U_594) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_592),U_596)
    | sP37(U_594,U_592,U_596) ),
    inference(clausify,[status(thm)],[f_179_4]) ).

cnf(f_179_7,plain,
    ( U_594 != U_596
    | ~ sP37(U_594,U_592,U_596) ),
    inference(clausify,[status(thm)],[f_179_4]) ).

cnf(f_179_8,plain,
    ( U_592 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP37(U_594,U_592,U_596) ),
    inference(clausify,[status(thm)],[f_179_4]) ).

fof(f_180_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__is__0]) ).

fof(f_180_2,plain,
    ! [U_598,U_597] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_597),U_598) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( U_598 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_597 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_598 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_597 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_597),U_598) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_180_1]) ).

fof(f_180_3,plain,
    ( ! [U_602,U_600] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_600),U_602) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( U_602 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_600 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_601,U_599] :
        ( U_601 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_599 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_599),U_601) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_180_2]) ).

fof(f_180_4,plain,
    ( ! [U_602,U_600] :
        ( U_602 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP38(U_602,U_600) )
    & ! [U_602,U_600] :
        ( U_600 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP38(U_602,U_600) )
    & ! [U_602,U_600] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_600),U_602) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sP38(U_602,U_600) )
    & ! [U_601,U_599] :
        ( U_601 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_599 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_599),U_601) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP38])],[f_180_3]) ).

cnf(f_180_5,plain,
    ( U_601 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_599 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_599),U_601) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_180_4]) ).

cnf(f_180_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_600),U_602) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sP38(U_602,U_600) ),
    inference(clausify,[status(thm)],[f_180_4]) ).

cnf(f_180_7,plain,
    ( U_600 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP38(U_602,U_600) ),
    inference(clausify,[status(thm)],[f_180_4]) ).

cnf(f_180_8,plain,
    ( U_602 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP38(U_602,U_600) ),
    inference(clausify,[status(thm)],[f_180_4]) ).

fof(f_181_1,plain,
    ! [V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_mult__0__right]) ).

fof(f_181_2,plain,
    ! [U_603] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_603),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_181_1]) ).

fof(f_181_3,plain,
    ! [U_603] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_603),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_181_2]) ).

cnf(f_181_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_603),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_181_3]) ).

fof(f_182_1,plain,
    ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_mult__0]) ).

fof(f_182_2,plain,
    ! [U_604] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_604) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_182_1]) ).

fof(f_182_3,plain,
    ! [U_604] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_604) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_182_2]) ).

cnf(f_182_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_604) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_182_3]) ).

fof(f_183_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)))
      | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq2]) ).

fof(f_183_2,plain,
    ! [U_607,U_606,U_605] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_605,U_606),c_RealVector_Onorm__class_Onorm(U_605,U_607)),c_RealVector_Onorm__class_Onorm(U_605,c_Groups_Ominus__class_Ominus(U_605,U_606,U_607)))
      | ~ class_RealVector_Oreal__normed__vector(U_605) ),
    inference(variable_rename,[status(thm)],[f_183_1]) ).

fof(f_183_3,plain,
    ! [U_605,U_606,U_607] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_605,U_606),c_RealVector_Onorm__class_Onorm(U_605,U_607)),c_RealVector_Onorm__class_Onorm(U_605,c_Groups_Ominus__class_Ominus(U_605,U_606,U_607)))
      | ~ class_RealVector_Oreal__normed__vector(U_605) ),
    inference(definitional_conversion,[status(esa)],[f_183_2]) ).

cnf(f_183_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_605,U_606),c_RealVector_Onorm__class_Onorm(U_605,U_607)),c_RealVector_Onorm__class_Onorm(U_605,c_Groups_Ominus__class_Ominus(U_605,U_606,U_607)))
    | ~ class_RealVector_Oreal__normed__vector(U_605) ),
    inference(clausify,[status(thm)],[f_183_3]) ).

fof(f_184_1,plain,
    ! [V_y,V_x,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),c_RealVector_Onorm__class_Onorm(T_a,V_y)))
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_norm__mult__ineq]) ).

fof(f_184_2,plain,
    ! [U_610,U_609,U_608] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_608,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_608),U_609),U_610)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_608,U_609)),c_RealVector_Onorm__class_Onorm(U_608,U_610)))
      | ~ class_RealVector_Oreal__normed__algebra(U_608) ),
    inference(variable_rename,[status(thm)],[f_184_1]) ).

fof(f_184_3,plain,
    ! [U_608,U_609,U_610] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_608,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_608),U_609),U_610)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_608,U_609)),c_RealVector_Onorm__class_Onorm(U_608,U_610)))
      | ~ class_RealVector_Oreal__normed__algebra(U_608) ),
    inference(definitional_conversion,[status(esa)],[f_184_2]) ).

cnf(f_184_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_608,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_608),U_609),U_610)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_608,U_609)),c_RealVector_Onorm__class_Onorm(U_608,U_610)))
    | ~ class_RealVector_Oreal__normed__algebra(U_608) ),
    inference(clausify,[status(thm)],[f_184_3]) ).

fof(f_185_1,plain,
    ! [V_a,T_a] :
      ( c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__0__right]) ).

fof(f_185_2,plain,
    ! [U_612,U_611] :
      ( c_Groups_Ominus__class_Ominus(U_611,U_612,c_Groups_Ozero__class_Ozero(U_611)) = U_612
      | ~ class_Groups_Ogroup__add(U_611) ),
    inference(variable_rename,[status(thm)],[f_185_1]) ).

fof(f_185_3,plain,
    ! [U_612,U_611] :
      ( c_Groups_Ominus__class_Ominus(U_611,U_612,c_Groups_Ozero__class_Ozero(U_611)) = U_612
      | ~ class_Groups_Ogroup__add(U_611) ),
    inference(definitional_conversion,[status(esa)],[f_185_2]) ).

cnf(f_185_4,plain,
    ( c_Groups_Ominus__class_Ominus(U_611,U_612,c_Groups_Ozero__class_Ozero(U_611)) = U_612
    | ~ class_Groups_Ogroup__add(U_611) ),
    inference(clausify,[status(thm)],[f_185_3]) ).

fof(f_186_1,plain,
    ! [V_a,T_a] :
      ( c_Groups_Ominus__class_Ominus(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__self]) ).

fof(f_186_2,plain,
    ! [U_614,U_613] :
      ( c_Groups_Ominus__class_Ominus(U_613,U_614,U_614) = c_Groups_Ozero__class_Ozero(U_613)
      | ~ class_Groups_Ogroup__add(U_613) ),
    inference(variable_rename,[status(thm)],[f_186_1]) ).

fof(f_186_3,plain,
    ! [U_613,U_614] :
      ( c_Groups_Ominus__class_Ominus(U_613,U_614,U_614) = c_Groups_Ozero__class_Ozero(U_613)
      | ~ class_Groups_Ogroup__add(U_613) ),
    inference(definitional_conversion,[status(esa)],[f_186_2]) ).

cnf(f_186_4,plain,
    ( c_Groups_Ominus__class_Ominus(U_613,U_614,U_614) = c_Groups_Ozero__class_Ozero(U_613)
    | ~ class_Groups_Ogroup__add(U_613) ),
    inference(clausify,[status(thm)],[f_186_3]) ).

fof(f_187_1,plain,
    ! [V_b_2,V_ab_2,T_a] :
      ( ( ( V_ab_2 = V_b_2
          | c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2) != c_Groups_Ozero__class_Ozero(T_a) )
        & ( c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
          | V_ab_2 != V_b_2 ) )
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0]) ).

fof(f_187_2,plain,
    ! [U_617,U_616,U_615] :
      ( ( ( U_616 = U_617
          | c_Groups_Ominus__class_Ominus(U_615,U_616,U_617) != c_Groups_Ozero__class_Ozero(U_615) )
        & ( c_Groups_Ominus__class_Ominus(U_615,U_616,U_617) = c_Groups_Ozero__class_Ozero(U_615)
          | U_616 != U_617 ) )
      | ~ class_Groups_Oab__group__add(U_615) ),
    inference(variable_rename,[status(thm)],[f_187_1]) ).

fof(f_187_3,plain,
    ( ! [U_615,U_616,U_617] :
        ( U_616 = U_617
        | c_Groups_Ominus__class_Ominus(U_615,U_616,U_617) != c_Groups_Ozero__class_Ozero(U_615)
        | ~ sP39(U_615,U_616,U_617) )
    & ! [U_615,U_616,U_617] :
        ( c_Groups_Ominus__class_Ominus(U_615,U_616,U_617) = c_Groups_Ozero__class_Ozero(U_615)
        | U_616 != U_617
        | ~ sP39(U_615,U_616,U_617) )
    & ! [U_615,U_616,U_617] :
        ( sP39(U_615,U_616,U_617)
        | ~ class_Groups_Oab__group__add(U_615) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP39])],[f_187_2]) ).

cnf(f_187_4,plain,
    ( sP39(U_615,U_616,U_617)
    | ~ class_Groups_Oab__group__add(U_615) ),
    inference(clausify,[status(thm)],[f_187_3]) ).

cnf(f_187_5,plain,
    ( c_Groups_Ominus__class_Ominus(U_615,U_616,U_617) = c_Groups_Ozero__class_Ozero(U_615)
    | U_616 != U_617
    | ~ sP39(U_615,U_616,U_617) ),
    inference(clausify,[status(thm)],[f_187_3]) ).

cnf(f_187_6,plain,
    ( U_616 = U_617
    | c_Groups_Ominus__class_Ominus(U_615,U_616,U_617) != c_Groups_Ozero__class_Ozero(U_615)
    | ~ sP39(U_615,U_616,U_617) ),
    inference(clausify,[status(thm)],[f_187_3]) ).

fof(f_188_1,plain,
    ! [V_b_2,V_ab_2,T_a] :
      ( ( ( c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
          | V_ab_2 != V_b_2 )
        & ( V_ab_2 = V_b_2
          | c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_right__minus__eq]) ).

fof(f_188_2,plain,
    ! [U_620,U_619,U_618] :
      ( ( ( c_Groups_Ominus__class_Ominus(U_618,U_619,U_620) = c_Groups_Ozero__class_Ozero(U_618)
          | U_619 != U_620 )
        & ( U_619 = U_620
          | c_Groups_Ominus__class_Ominus(U_618,U_619,U_620) != c_Groups_Ozero__class_Ozero(U_618) ) )
      | ~ class_Groups_Ogroup__add(U_618) ),
    inference(variable_rename,[status(thm)],[f_188_1]) ).

fof(f_188_3,plain,
    ( ! [U_620,U_619,U_618] :
        ( c_Groups_Ominus__class_Ominus(U_618,U_619,U_620) = c_Groups_Ozero__class_Ozero(U_618)
        | U_619 != U_620
        | ~ sP40(U_620,U_619,U_618) )
    & ! [U_620,U_619,U_618] :
        ( U_619 = U_620
        | c_Groups_Ominus__class_Ominus(U_618,U_619,U_620) != c_Groups_Ozero__class_Ozero(U_618)
        | ~ sP40(U_620,U_619,U_618) )
    & ! [U_620,U_619,U_618] :
        ( sP40(U_620,U_619,U_618)
        | ~ class_Groups_Ogroup__add(U_618) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP40])],[f_188_2]) ).

cnf(f_188_4,plain,
    ( sP40(U_620,U_619,U_618)
    | ~ class_Groups_Ogroup__add(U_618) ),
    inference(clausify,[status(thm)],[f_188_3]) ).

cnf(f_188_5,plain,
    ( U_619 = U_620
    | c_Groups_Ominus__class_Ominus(U_618,U_619,U_620) != c_Groups_Ozero__class_Ozero(U_618)
    | ~ sP40(U_620,U_619,U_618) ),
    inference(clausify,[status(thm)],[f_188_3]) ).

cnf(f_188_6,plain,
    ( c_Groups_Ominus__class_Ominus(U_618,U_619,U_620) = c_Groups_Ozero__class_Ozero(U_618)
    | U_619 != U_620
    | ~ sP40(U_620,U_619,U_618) ),
    inference(clausify,[status(thm)],[f_188_3]) ).

fof(f_189_1,plain,
    ! [V_db_2,V_ca_2,V_b_2,V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2,V_db_2) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2,V_db_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2) ) )
      | c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2) != c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_db_2)
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq]) ).

fof(f_189_2,plain,
    ! [U_625,U_624,U_623,U_622,U_621] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_621,U_622,U_623)
          | ~ c_Orderings_Oord__class_Oless__eq(U_621,U_624,U_625) )
        & ( c_Orderings_Oord__class_Oless__eq(U_621,U_624,U_625)
          | ~ c_Orderings_Oord__class_Oless__eq(U_621,U_622,U_623) ) )
      | c_Groups_Ominus__class_Ominus(U_621,U_622,U_623) != c_Groups_Ominus__class_Ominus(U_621,U_624,U_625)
      | ~ class_Groups_Oordered__ab__group__add(U_621) ),
    inference(variable_rename,[status(thm)],[f_189_1]) ).

fof(f_189_3,plain,
    ( ! [U_624,U_623,U_621,U_622,U_625] :
        ( c_Orderings_Oord__class_Oless__eq(U_621,U_622,U_623)
        | ~ c_Orderings_Oord__class_Oless__eq(U_621,U_624,U_625)
        | ~ sP41(U_624,U_623,U_621,U_622,U_625) )
    & ! [U_624,U_623,U_621,U_622,U_625] :
        ( c_Orderings_Oord__class_Oless__eq(U_621,U_624,U_625)
        | ~ c_Orderings_Oord__class_Oless__eq(U_621,U_622,U_623)
        | ~ sP41(U_624,U_623,U_621,U_622,U_625) )
    & ! [U_624,U_623,U_621,U_622,U_625] :
        ( sP41(U_624,U_623,U_621,U_622,U_625)
        | c_Groups_Ominus__class_Ominus(U_621,U_622,U_623) != c_Groups_Ominus__class_Ominus(U_621,U_624,U_625)
        | ~ class_Groups_Oordered__ab__group__add(U_621) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP41])],[f_189_2]) ).

cnf(f_189_4,plain,
    ( sP41(U_624,U_623,U_621,U_622,U_625)
    | c_Groups_Ominus__class_Ominus(U_621,U_622,U_623) != c_Groups_Ominus__class_Ominus(U_621,U_624,U_625)
    | ~ class_Groups_Oordered__ab__group__add(U_621) ),
    inference(clausify,[status(thm)],[f_189_3]) ).

cnf(f_189_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_621,U_624,U_625)
    | ~ c_Orderings_Oord__class_Oless__eq(U_621,U_622,U_623)
    | ~ sP41(U_624,U_623,U_621,U_622,U_625) ),
    inference(clausify,[status(thm)],[f_189_3]) ).

cnf(f_189_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_621,U_622,U_623)
    | ~ c_Orderings_Oord__class_Oless__eq(U_621,U_624,U_625)
    | ~ sP41(U_624,U_623,U_621,U_622,U_625) ),
    inference(clausify,[status(thm)],[f_189_3]) ).

fof(f_190_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = V_a
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__diff__cancel]) ).

fof(f_190_2,plain,
    ! [U_628,U_627,U_626] :
      ( c_Groups_Ominus__class_Ominus(U_626,c_Groups_Oplus__class_Oplus(U_626,U_627,U_628),U_628) = U_627
      | ~ class_Groups_Ogroup__add(U_626) ),
    inference(variable_rename,[status(thm)],[f_190_1]) ).

fof(f_190_3,plain,
    ! [U_627,U_628,U_626] :
      ( c_Groups_Ominus__class_Ominus(U_626,c_Groups_Oplus__class_Oplus(U_626,U_627,U_628),U_628) = U_627
      | ~ class_Groups_Ogroup__add(U_626) ),
    inference(definitional_conversion,[status(esa)],[f_190_2]) ).

cnf(f_190_4,plain,
    ( c_Groups_Ominus__class_Ominus(U_626,c_Groups_Oplus__class_Oplus(U_626,U_627,U_628),U_628) = U_627
    | ~ class_Groups_Ogroup__add(U_626) ),
    inference(clausify,[status(thm)],[f_190_3]) ).

fof(f_191_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b) = V_a
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__add__cancel]) ).

fof(f_191_2,plain,
    ! [U_631,U_630,U_629] :
      ( c_Groups_Oplus__class_Oplus(U_629,c_Groups_Ominus__class_Ominus(U_629,U_630,U_631),U_631) = U_630
      | ~ class_Groups_Ogroup__add(U_629) ),
    inference(variable_rename,[status(thm)],[f_191_1]) ).

fof(f_191_3,plain,
    ! [U_630,U_629,U_631] :
      ( c_Groups_Oplus__class_Oplus(U_629,c_Groups_Ominus__class_Ominus(U_629,U_630,U_631),U_631) = U_630
      | ~ class_Groups_Ogroup__add(U_629) ),
    inference(definitional_conversion,[status(esa)],[f_191_2]) ).

cnf(f_191_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_629,c_Groups_Ominus__class_Ominus(U_629,U_630,U_631),U_631) = U_630
    | ~ class_Groups_Ogroup__add(U_629) ),
    inference(clausify,[status(thm)],[f_191_3]) ).

fof(f_192_1,plain,
    ! [V_b,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult_Ozero__left]) ).

fof(f_192_2,plain,
    ! [U_633,U_632] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_632),c_Groups_Ozero__class_Ozero(U_632)),U_633) = c_Groups_Ozero__class_Ozero(U_632)
      | ~ class_RealVector_Oreal__normed__algebra(U_632) ),
    inference(variable_rename,[status(thm)],[f_192_1]) ).

fof(f_192_3,plain,
    ! [U_632,U_633] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_632),c_Groups_Ozero__class_Ozero(U_632)),U_633) = c_Groups_Ozero__class_Ozero(U_632)
      | ~ class_RealVector_Oreal__normed__algebra(U_632) ),
    inference(definitional_conversion,[status(esa)],[f_192_2]) ).

cnf(f_192_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_632),c_Groups_Ozero__class_Ozero(U_632)),U_633) = c_Groups_Ozero__class_Ozero(U_632)
    | ~ class_RealVector_Oreal__normed__algebra(U_632) ),
    inference(clausify,[status(thm)],[f_192_3]) ).

fof(f_193_1,plain,
    ! [V_y,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__left_Ozero]) ).

fof(f_193_2,plain,
    ! [U_635,U_634] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_634),c_Groups_Ozero__class_Ozero(U_634)),U_635) = c_Groups_Ozero__class_Ozero(U_634)
      | ~ class_RealVector_Oreal__normed__algebra(U_634) ),
    inference(variable_rename,[status(thm)],[f_193_1]) ).

fof(f_193_3,plain,
    ! [U_634,U_635] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_634),c_Groups_Ozero__class_Ozero(U_634)),U_635) = c_Groups_Ozero__class_Ozero(U_634)
      | ~ class_RealVector_Oreal__normed__algebra(U_634) ),
    inference(definitional_conversion,[status(esa)],[f_193_2]) ).

cnf(f_193_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_634),c_Groups_Ozero__class_Ozero(U_634)),U_635) = c_Groups_Ozero__class_Ozero(U_634)
    | ~ class_RealVector_Oreal__normed__algebra(U_634) ),
    inference(clausify,[status(thm)],[f_193_3]) ).

fof(f_194_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult_Ozero__right]) ).

fof(f_194_2,plain,
    ! [U_637,U_636] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_636),U_637),c_Groups_Ozero__class_Ozero(U_636)) = c_Groups_Ozero__class_Ozero(U_636)
      | ~ class_RealVector_Oreal__normed__algebra(U_636) ),
    inference(variable_rename,[status(thm)],[f_194_1]) ).

fof(f_194_3,plain,
    ! [U_636,U_637] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_636),U_637),c_Groups_Ozero__class_Ozero(U_636)) = c_Groups_Ozero__class_Ozero(U_636)
      | ~ class_RealVector_Oreal__normed__algebra(U_636) ),
    inference(definitional_conversion,[status(esa)],[f_194_2]) ).

cnf(f_194_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_636),U_637),c_Groups_Ozero__class_Ozero(U_636)) = c_Groups_Ozero__class_Ozero(U_636)
    | ~ class_RealVector_Oreal__normed__algebra(U_636) ),
    inference(clausify,[status(thm)],[f_194_3]) ).

fof(f_195_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__right_Ozero]) ).

fof(f_195_2,plain,
    ! [U_639,U_638] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_638),U_639),c_Groups_Ozero__class_Ozero(U_638)) = c_Groups_Ozero__class_Ozero(U_638)
      | ~ class_RealVector_Oreal__normed__algebra(U_638) ),
    inference(variable_rename,[status(thm)],[f_195_1]) ).

fof(f_195_3,plain,
    ! [U_638,U_639] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_638),U_639),c_Groups_Ozero__class_Ozero(U_638)) = c_Groups_Ozero__class_Ozero(U_638)
      | ~ class_RealVector_Oreal__normed__algebra(U_638) ),
    inference(definitional_conversion,[status(esa)],[f_195_2]) ).

cnf(f_195_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_638),U_639),c_Groups_Ozero__class_Ozero(U_638)) = c_Groups_Ozero__class_Ozero(U_638)
    | ~ class_RealVector_Oreal__normed__algebra(U_638) ),
    inference(clausify,[status(thm)],[f_195_3]) ).

fof(f_196_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J]) ).

fof(f_196_2,plain,
    ! [U_641,U_640] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_640),c_Groups_Ozero__class_Ozero(U_640)),U_641) = c_Groups_Ozero__class_Ozero(U_640)
      | ~ class_Rings_Ocomm__semiring__1(U_640) ),
    inference(variable_rename,[status(thm)],[f_196_1]) ).

fof(f_196_3,plain,
    ! [U_640,U_641] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_640),c_Groups_Ozero__class_Ozero(U_640)),U_641) = c_Groups_Ozero__class_Ozero(U_640)
      | ~ class_Rings_Ocomm__semiring__1(U_640) ),
    inference(definitional_conversion,[status(esa)],[f_196_2]) ).

cnf(f_196_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_640),c_Groups_Ozero__class_Ozero(U_640)),U_641) = c_Groups_Ozero__class_Ozero(U_640)
    | ~ class_Rings_Ocomm__semiring__1(U_640) ),
    inference(clausify,[status(thm)],[f_196_3]) ).

fof(f_197_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J]) ).

fof(f_197_2,plain,
    ! [U_643,U_642] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_642),U_643),c_Groups_Ozero__class_Ozero(U_642)) = c_Groups_Ozero__class_Ozero(U_642)
      | ~ class_Rings_Ocomm__semiring__1(U_642) ),
    inference(variable_rename,[status(thm)],[f_197_1]) ).

fof(f_197_3,plain,
    ! [U_642,U_643] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_642),U_643),c_Groups_Ozero__class_Ozero(U_642)) = c_Groups_Ozero__class_Ozero(U_642)
      | ~ class_Rings_Ocomm__semiring__1(U_642) ),
    inference(definitional_conversion,[status(esa)],[f_197_2]) ).

cnf(f_197_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_642),U_643),c_Groups_Ozero__class_Ozero(U_642)) = c_Groups_Ozero__class_Ozero(U_642)
    | ~ class_Rings_Ocomm__semiring__1(U_642) ),
    inference(clausify,[status(thm)],[f_197_3]) ).

fof(f_198_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_a))
      | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_norm__minus__commute]) ).

fof(f_198_2,plain,
    ! [U_646,U_645,U_644] :
      ( c_RealVector_Onorm__class_Onorm(U_644,c_Groups_Ominus__class_Ominus(U_644,U_645,U_646)) = c_RealVector_Onorm__class_Onorm(U_644,c_Groups_Ominus__class_Ominus(U_644,U_646,U_645))
      | ~ class_RealVector_Oreal__normed__vector(U_644) ),
    inference(variable_rename,[status(thm)],[f_198_1]) ).

fof(f_198_3,plain,
    ! [U_644,U_645,U_646] :
      ( c_RealVector_Onorm__class_Onorm(U_644,c_Groups_Ominus__class_Ominus(U_644,U_645,U_646)) = c_RealVector_Onorm__class_Onorm(U_644,c_Groups_Ominus__class_Ominus(U_644,U_646,U_645))
      | ~ class_RealVector_Oreal__normed__vector(U_644) ),
    inference(definitional_conversion,[status(esa)],[f_198_2]) ).

cnf(f_198_4,plain,
    ( c_RealVector_Onorm__class_Onorm(U_644,c_Groups_Ominus__class_Ominus(U_644,U_645,U_646)) = c_RealVector_Onorm__class_Onorm(U_644,c_Groups_Ominus__class_Ominus(U_644,U_646,U_645))
    | ~ class_RealVector_Oreal__normed__vector(U_644) ),
    inference(clausify,[status(thm)],[f_198_3]) ).

fof(f_199_1,plain,
    ! [V_ya,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),V_ya) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya))
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__left_Oadd]) ).

fof(f_199_2,plain,
    ! [U_650,U_649,U_648,U_647] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_647),c_Groups_Oplus__class_Oplus(U_647,U_648,U_649)),U_650) = c_Groups_Oplus__class_Oplus(U_647,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_647),U_648),U_650),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_647),U_649),U_650))
      | ~ class_RealVector_Oreal__normed__algebra(U_647) ),
    inference(variable_rename,[status(thm)],[f_199_1]) ).

fof(f_199_3,plain,
    ! [U_647,U_648,U_649,U_650] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_647),c_Groups_Oplus__class_Oplus(U_647,U_648,U_649)),U_650) = c_Groups_Oplus__class_Oplus(U_647,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_647),U_648),U_650),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_647),U_649),U_650))
      | ~ class_RealVector_Oreal__normed__algebra(U_647) ),
    inference(definitional_conversion,[status(esa)],[f_199_2]) ).

cnf(f_199_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_647),c_Groups_Oplus__class_Oplus(U_647,U_648,U_649)),U_650) = c_Groups_Oplus__class_Oplus(U_647,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_647),U_648),U_650),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_647),U_649),U_650))
    | ~ class_RealVector_Oreal__normed__algebra(U_647) ),
    inference(clausify,[status(thm)],[f_199_3]) ).

fof(f_200_1,plain,
    ! [V_b,V_a_H,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H)),V_b) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_H),V_b))
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult_Oadd__left]) ).

fof(f_200_2,plain,
    ! [U_654,U_653,U_652,U_651] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_651),c_Groups_Oplus__class_Oplus(U_651,U_652,U_653)),U_654) = c_Groups_Oplus__class_Oplus(U_651,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_651),U_652),U_654),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_651),U_653),U_654))
      | ~ class_RealVector_Oreal__normed__algebra(U_651) ),
    inference(variable_rename,[status(thm)],[f_200_1]) ).

fof(f_200_3,plain,
    ! [U_651,U_652,U_653,U_654] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_651),c_Groups_Oplus__class_Oplus(U_651,U_652,U_653)),U_654) = c_Groups_Oplus__class_Oplus(U_651,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_651),U_652),U_654),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_651),U_653),U_654))
      | ~ class_RealVector_Oreal__normed__algebra(U_651) ),
    inference(definitional_conversion,[status(esa)],[f_200_2]) ).

cnf(f_200_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_651),c_Groups_Oplus__class_Oplus(U_651,U_652,U_653)),U_654) = c_Groups_Oplus__class_Oplus(U_651,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_651),U_652),U_654),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_651),U_653),U_654))
    | ~ class_RealVector_Oreal__normed__algebra(U_651) ),
    inference(clausify,[status(thm)],[f_200_3]) ).

fof(f_201_1,plain,
    ! [V_y,V_x,V_xa,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y))
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__right_Oadd]) ).

fof(f_201_2,plain,
    ! [U_658,U_657,U_656,U_655] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_655),U_656),c_Groups_Oplus__class_Oplus(U_655,U_657,U_658)) = c_Groups_Oplus__class_Oplus(U_655,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_655),U_656),U_657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_655),U_656),U_658))
      | ~ class_RealVector_Oreal__normed__algebra(U_655) ),
    inference(variable_rename,[status(thm)],[f_201_1]) ).

fof(f_201_3,plain,
    ! [U_655,U_656,U_657,U_658] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_655),U_656),c_Groups_Oplus__class_Oplus(U_655,U_657,U_658)) = c_Groups_Oplus__class_Oplus(U_655,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_655),U_656),U_657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_655),U_656),U_658))
      | ~ class_RealVector_Oreal__normed__algebra(U_655) ),
    inference(definitional_conversion,[status(esa)],[f_201_2]) ).

cnf(f_201_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_655),U_656),c_Groups_Oplus__class_Oplus(U_655,U_657,U_658)) = c_Groups_Oplus__class_Oplus(U_655,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_655),U_656),U_657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_655),U_656),U_658))
    | ~ class_RealVector_Oreal__normed__algebra(U_655) ),
    inference(clausify,[status(thm)],[f_201_3]) ).

fof(f_202_1,plain,
    ! [V_b_H,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b_H))
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult_Oadd__right]) ).

fof(f_202_2,plain,
    ! [U_662,U_661,U_660,U_659] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_659),U_660),c_Groups_Oplus__class_Oplus(U_659,U_661,U_662)) = c_Groups_Oplus__class_Oplus(U_659,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_659),U_660),U_661),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_659),U_660),U_662))
      | ~ class_RealVector_Oreal__normed__algebra(U_659) ),
    inference(variable_rename,[status(thm)],[f_202_1]) ).

fof(f_202_3,plain,
    ! [U_659,U_660,U_661,U_662] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_659),U_660),c_Groups_Oplus__class_Oplus(U_659,U_661,U_662)) = c_Groups_Oplus__class_Oplus(U_659,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_659),U_660),U_661),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_659),U_660),U_662))
      | ~ class_RealVector_Oreal__normed__algebra(U_659) ),
    inference(definitional_conversion,[status(esa)],[f_202_2]) ).

cnf(f_202_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_659),U_660),c_Groups_Oplus__class_Oplus(U_659,U_661,U_662)) = c_Groups_Oplus__class_Oplus(U_659,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_659),U_660),U_661),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_659),U_660),U_662))
    | ~ class_RealVector_Oreal__normed__algebra(U_659) ),
    inference(clausify,[status(thm)],[f_202_3]) ).

fof(f_203_1,plain,
    ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] :
      ( ( ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))
          | ( V_y_2 != V_z_2
            & V_w_2 != V_x_2 ) )
        & ( V_y_2 = V_z_2
          | V_w_2 = V_x_2
          | c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2)) ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_crossproduct__eq]) ).

fof(f_203_2,plain,
    ! [U_667,U_666,U_665,U_664,U_663] :
      ( ( ( c_Groups_Oplus__class_Oplus(U_663,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_664),U_665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_666),U_667)) = c_Groups_Oplus__class_Oplus(U_663,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_664),U_667),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_666),U_665))
          | ( U_665 != U_667
            & U_664 != U_666 ) )
        & ( U_665 = U_667
          | U_664 = U_666
          | c_Groups_Oplus__class_Oplus(U_663,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_664),U_665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_666),U_667)) != c_Groups_Oplus__class_Oplus(U_663,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_664),U_667),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_666),U_665)) ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_663) ),
    inference(variable_rename,[status(thm)],[f_203_1]) ).

fof(f_203_3,plain,
    ( ! [U_664,U_665,U_666,U_667] :
        ( U_665 != U_667
        | ~ sP42(U_664,U_665,U_666,U_667) )
    & ! [U_664,U_665,U_666,U_667] :
        ( U_664 != U_666
        | ~ sP42(U_664,U_665,U_666,U_667) )
    & ! [U_663,U_664,U_665,U_666,U_667] :
        ( c_Groups_Oplus__class_Oplus(U_663,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_664),U_665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_666),U_667)) = c_Groups_Oplus__class_Oplus(U_663,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_664),U_667),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_666),U_665))
        | sP42(U_664,U_665,U_666,U_667)
        | ~ sP43(U_663,U_664,U_665,U_666,U_667) )
    & ! [U_663,U_664,U_665,U_666,U_667] :
        ( U_665 = U_667
        | U_664 = U_666
        | c_Groups_Oplus__class_Oplus(U_663,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_664),U_665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_666),U_667)) != c_Groups_Oplus__class_Oplus(U_663,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_664),U_667),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_666),U_665))
        | ~ sP43(U_663,U_664,U_665,U_666,U_667) )
    & ! [U_663,U_664,U_665,U_666,U_667] :
        ( sP43(U_663,U_664,U_665,U_666,U_667)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_663) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP42,sP43])],[f_203_2]) ).

cnf(f_203_4,plain,
    ( sP43(U_663,U_664,U_665,U_666,U_667)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_663) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

cnf(f_203_5,plain,
    ( U_665 = U_667
    | U_664 = U_666
    | c_Groups_Oplus__class_Oplus(U_663,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_664),U_665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_666),U_667)) != c_Groups_Oplus__class_Oplus(U_663,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_664),U_667),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_666),U_665))
    | ~ sP43(U_663,U_664,U_665,U_666,U_667) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

cnf(f_203_6,plain,
    ( c_Groups_Oplus__class_Oplus(U_663,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_664),U_665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_666),U_667)) = c_Groups_Oplus__class_Oplus(U_663,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_664),U_667),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_666),U_665))
    | sP42(U_664,U_665,U_666,U_667)
    | ~ sP43(U_663,U_664,U_665,U_666,U_667) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

cnf(f_203_7,plain,
    ( U_664 != U_666
    | ~ sP42(U_664,U_665,U_666,U_667) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

cnf(f_203_8,plain,
    ( U_665 != U_667
    | ~ sP42(U_664,U_665,U_666,U_667) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

fof(f_204_1,plain,
    ! [V_b,V_m,V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_m)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J]) ).

fof(f_204_2,plain,
    ! [U_671,U_670,U_669,U_668] :
      ( c_Groups_Oplus__class_Oplus(U_668,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_668),U_669),U_670),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_668),U_671),U_670)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_668),c_Groups_Oplus__class_Oplus(U_668,U_669,U_671)),U_670)
      | ~ class_Rings_Ocomm__semiring__1(U_668) ),
    inference(variable_rename,[status(thm)],[f_204_1]) ).

fof(f_204_3,plain,
    ! [U_669,U_671,U_670,U_668] :
      ( c_Groups_Oplus__class_Oplus(U_668,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_668),U_669),U_670),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_668),U_671),U_670)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_668),c_Groups_Oplus__class_Oplus(U_668,U_669,U_671)),U_670)
      | ~ class_Rings_Ocomm__semiring__1(U_668) ),
    inference(definitional_conversion,[status(esa)],[f_204_2]) ).

cnf(f_204_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_668,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_668),U_669),U_670),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_668),U_671),U_670)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_668),c_Groups_Oplus__class_Oplus(U_668,U_669,U_671)),U_670)
    | ~ class_Rings_Ocomm__semiring__1(U_668) ),
    inference(clausify,[status(thm)],[f_204_3]) ).

fof(f_205_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J]) ).

fof(f_205_2,plain,
    ! [U_675,U_674,U_673,U_672] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_672),c_Groups_Oplus__class_Oplus(U_672,U_673,U_674)),U_675) = c_Groups_Oplus__class_Oplus(U_672,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_672),U_673),U_675),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_672),U_674),U_675))
      | ~ class_Rings_Ocomm__semiring__1(U_672) ),
    inference(variable_rename,[status(thm)],[f_205_1]) ).

fof(f_205_3,plain,
    ! [U_674,U_672,U_673,U_675] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_672),c_Groups_Oplus__class_Oplus(U_672,U_673,U_674)),U_675) = c_Groups_Oplus__class_Oplus(U_672,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_672),U_673),U_675),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_672),U_674),U_675))
      | ~ class_Rings_Ocomm__semiring__1(U_672) ),
    inference(definitional_conversion,[status(esa)],[f_205_2]) ).

cnf(f_205_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_672),c_Groups_Oplus__class_Oplus(U_672,U_673,U_674)),U_675) = c_Groups_Oplus__class_Oplus(U_672,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_672),U_673),U_675),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_672),U_674),U_675))
    | ~ class_Rings_Ocomm__semiring__1(U_672) ),
    inference(clausify,[status(thm)],[f_205_3]) ).

fof(f_206_1,plain,
    ! [V_db_2,V_ca_2,V_b_2,V_ab_2,T_a] :
      ( ( ( ( V_ca_2 != V_db_2
            & V_ab_2 != V_b_2 )
          | c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_db_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_db_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)) )
        & ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_db_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_db_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))
          | V_ca_2 = V_db_2
          | V_ab_2 = V_b_2 ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq]) ).

fof(f_206_2,plain,
    ! [U_680,U_679,U_678,U_677,U_676] :
      ( ( ( ( U_679 != U_680
            & U_677 != U_678 )
          | c_Groups_Oplus__class_Oplus(U_676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_677),U_679),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_678),U_680)) = c_Groups_Oplus__class_Oplus(U_676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_677),U_680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_678),U_679)) )
        & ( c_Groups_Oplus__class_Oplus(U_676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_677),U_679),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_678),U_680)) != c_Groups_Oplus__class_Oplus(U_676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_677),U_680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_678),U_679))
          | U_679 = U_680
          | U_677 = U_678 ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_676) ),
    inference(variable_rename,[status(thm)],[f_206_1]) ).

fof(f_206_3,plain,
    ( ! [U_677,U_678,U_679,U_680] :
        ( U_679 != U_680
        | ~ sP44(U_677,U_678,U_679,U_680) )
    & ! [U_677,U_678,U_679,U_680] :
        ( U_677 != U_678
        | ~ sP44(U_677,U_678,U_679,U_680) )
    & ! [U_676,U_677,U_678,U_679,U_680] :
        ( sP44(U_677,U_678,U_679,U_680)
        | c_Groups_Oplus__class_Oplus(U_676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_677),U_679),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_678),U_680)) = c_Groups_Oplus__class_Oplus(U_676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_677),U_680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_678),U_679))
        | ~ sP45(U_676,U_677,U_678,U_679,U_680) )
    & ! [U_676,U_677,U_678,U_679,U_680] :
        ( c_Groups_Oplus__class_Oplus(U_676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_677),U_679),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_678),U_680)) != c_Groups_Oplus__class_Oplus(U_676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_677),U_680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_678),U_679))
        | U_679 = U_680
        | U_677 = U_678
        | ~ sP45(U_676,U_677,U_678,U_679,U_680) )
    & ! [U_676,U_677,U_678,U_679,U_680] :
        ( sP45(U_676,U_677,U_678,U_679,U_680)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_676) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP44,sP45])],[f_206_2]) ).

cnf(f_206_4,plain,
    ( sP45(U_676,U_677,U_678,U_679,U_680)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_676) ),
    inference(clausify,[status(thm)],[f_206_3]) ).

cnf(f_206_5,plain,
    ( c_Groups_Oplus__class_Oplus(U_676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_677),U_679),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_678),U_680)) != c_Groups_Oplus__class_Oplus(U_676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_677),U_680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_678),U_679))
    | U_679 = U_680
    | U_677 = U_678
    | ~ sP45(U_676,U_677,U_678,U_679,U_680) ),
    inference(clausify,[status(thm)],[f_206_3]) ).

cnf(f_206_6,plain,
    ( sP44(U_677,U_678,U_679,U_680)
    | c_Groups_Oplus__class_Oplus(U_676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_677),U_679),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_678),U_680)) = c_Groups_Oplus__class_Oplus(U_676,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_677),U_680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_676),U_678),U_679))
    | ~ sP45(U_676,U_677,U_678,U_679,U_680) ),
    inference(clausify,[status(thm)],[f_206_3]) ).

cnf(f_206_7,plain,
    ( U_677 != U_678
    | ~ sP44(U_677,U_678,U_679,U_680) ),
    inference(clausify,[status(thm)],[f_206_3]) ).

cnf(f_206_8,plain,
    ( U_679 != U_680
    | ~ sP44(U_677,U_678,U_679,U_680) ),
    inference(clausify,[status(thm)],[f_206_3]) ).

fof(f_207_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Oplus__class_Oplus(T_a,V_y,V_z)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J]) ).

fof(f_207_2,plain,
    ! [U_684,U_683,U_682,U_681] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_681),U_682),c_Groups_Oplus__class_Oplus(U_681,U_683,U_684)) = c_Groups_Oplus__class_Oplus(U_681,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_681),U_682),U_683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_681),U_682),U_684))
      | ~ class_Rings_Ocomm__semiring__1(U_681) ),
    inference(variable_rename,[status(thm)],[f_207_1]) ).

fof(f_207_3,plain,
    ! [U_682,U_684,U_683,U_681] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_681),U_682),c_Groups_Oplus__class_Oplus(U_681,U_683,U_684)) = c_Groups_Oplus__class_Oplus(U_681,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_681),U_682),U_683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_681),U_682),U_684))
      | ~ class_Rings_Ocomm__semiring__1(U_681) ),
    inference(definitional_conversion,[status(esa)],[f_207_2]) ).

cnf(f_207_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_681),U_682),c_Groups_Oplus__class_Oplus(U_681,U_683,U_684)) = c_Groups_Oplus__class_Oplus(U_681,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_681),U_682),U_683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_681),U_682),U_684))
    | ~ class_Rings_Ocomm__semiring__1(U_681) ),
    inference(clausify,[status(thm)],[f_207_3]) ).

fof(f_208_1,plain,
    ! [V_p,T_a] :
      ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__poly__code_I2_J]) ).

fof(f_208_2,plain,
    ! [U_686,U_685] :
      ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_685),U_686,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_685))) = U_686
      | ~ class_Groups_Oab__group__add(U_685) ),
    inference(variable_rename,[status(thm)],[f_208_1]) ).

fof(f_208_3,plain,
    ! [U_686,U_685] :
      ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_685),U_686,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_685))) = U_686
      | ~ class_Groups_Oab__group__add(U_685) ),
    inference(definitional_conversion,[status(esa)],[f_208_2]) ).

cnf(f_208_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_685),U_686,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_685))) = U_686
    | ~ class_Groups_Oab__group__add(U_685) ),
    inference(clausify,[status(thm)],[f_208_3]) ).

fof(f_209_1,plain,
    ! [V_b_2,V_ab_2,V_ca_2] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_ab_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_b_2)
          | V_ab_2 != V_b_2 )
        & ( V_ab_2 = V_b_2
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_ab_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_b_2) ) )
      | V_ca_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(fof_nnf,[status(thm)],[fact_real__mult__left__cancel]) ).

fof(f_209_2,plain,
    ! [U_689,U_688,U_687] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_687),U_688) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_687),U_689)
          | U_688 != U_689 )
        & ( U_688 = U_689
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_687),U_688) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_687),U_689) ) )
      | U_687 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(variable_rename,[status(thm)],[f_209_1]) ).

fof(f_209_3,plain,
    ( ! [U_687,U_688,U_689] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_687),U_688) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_687),U_689)
        | U_688 != U_689
        | ~ sP46(U_687,U_688,U_689) )
    & ! [U_687,U_688,U_689] :
        ( U_688 = U_689
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_687),U_688) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_687),U_689)
        | ~ sP46(U_687,U_688,U_689) )
    & ! [U_687,U_688,U_689] :
        ( sP46(U_687,U_688,U_689)
        | U_687 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP46])],[f_209_2]) ).

cnf(f_209_4,plain,
    ( sP46(U_687,U_688,U_689)
    | U_687 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(clausify,[status(thm)],[f_209_3]) ).

cnf(f_209_5,plain,
    ( U_688 = U_689
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_687),U_688) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_687),U_689)
    | ~ sP46(U_687,U_688,U_689) ),
    inference(clausify,[status(thm)],[f_209_3]) ).

cnf(f_209_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_687),U_688) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_687),U_689)
    | U_688 != U_689
    | ~ sP46(U_687,U_688,U_689) ),
    inference(clausify,[status(thm)],[f_209_3]) ).

fof(f_210_1,plain,
    ! [V_b_2,V_ab_2,V_ca_2] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ab_2),V_ca_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_ca_2)
          | V_ab_2 != V_b_2 )
        & ( V_ab_2 = V_b_2
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ab_2),V_ca_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_ca_2) ) )
      | V_ca_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(fof_nnf,[status(thm)],[fact_real__mult__right__cancel]) ).

fof(f_210_2,plain,
    ! [U_692,U_691,U_690] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_691),U_690) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_692),U_690)
          | U_691 != U_692 )
        & ( U_691 = U_692
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_691),U_690) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_692),U_690) ) )
      | U_690 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(variable_rename,[status(thm)],[f_210_1]) ).

fof(f_210_3,plain,
    ( ! [U_691,U_692,U_690] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_691),U_690) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_692),U_690)
        | U_691 != U_692
        | ~ sP47(U_691,U_692,U_690) )
    & ! [U_691,U_692,U_690] :
        ( U_691 = U_692
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_691),U_690) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_692),U_690)
        | ~ sP47(U_691,U_692,U_690) )
    & ! [U_691,U_692,U_690] :
        ( sP47(U_691,U_692,U_690)
        | U_690 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP47])],[f_210_2]) ).

cnf(f_210_4,plain,
    ( sP47(U_691,U_692,U_690)
    | U_690 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(clausify,[status(thm)],[f_210_3]) ).

cnf(f_210_5,plain,
    ( U_691 = U_692
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_691),U_690) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_692),U_690)
    | ~ sP47(U_691,U_692,U_690) ),
    inference(clausify,[status(thm)],[f_210_3]) ).

cnf(f_210_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_691),U_690) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_692),U_690)
    | U_691 != U_692
    | ~ sP47(U_691,U_692,U_690) ),
    inference(clausify,[status(thm)],[f_210_3]) ).

fof(f_211_1,plain,
    ! [V_a,T_a] :
      ( c_Polynomial_Osmult(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_smult__0__right]) ).

fof(f_211_2,plain,
    ! [U_694,U_693] :
      ( c_Polynomial_Osmult(U_693,U_694,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_693))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_693))
      | ~ class_Rings_Ocomm__semiring__0(U_693) ),
    inference(variable_rename,[status(thm)],[f_211_1]) ).

fof(f_211_3,plain,
    ! [U_694,U_693] :
      ( c_Polynomial_Osmult(U_693,U_694,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_693))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_693))
      | ~ class_Rings_Ocomm__semiring__0(U_693) ),
    inference(definitional_conversion,[status(esa)],[f_211_2]) ).

cnf(f_211_4,plain,
    ( c_Polynomial_Osmult(U_693,U_694,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_693))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_693))
    | ~ class_Rings_Ocomm__semiring__0(U_693) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

fof(f_212_1,plain,
    ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_z1,V_z2)),V_w) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_w)),
    inference(fof_nnf,[status(thm)],[fact_real__add__mult__distrib]) ).

fof(f_212_2,plain,
    ! [U_697,U_696,U_695] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_695,U_696)),U_697) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_695),U_697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_696),U_697)),
    inference(variable_rename,[status(thm)],[f_212_1]) ).

fof(f_212_3,plain,
    ! [U_695,U_696,U_697] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_695,U_696)),U_697) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_695),U_697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_696),U_697)),
    inference(definitional_conversion,[status(esa)],[f_212_2]) ).

cnf(f_212_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_695,U_696)),U_697) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_695),U_697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_696),U_697)),
    inference(clausify,[status(thm)],[f_212_3]) ).

fof(f_213_1,plain,
    ! [V_q,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__poly__0__left]) ).

fof(f_213_2,plain,
    ! [U_699,U_698] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_698)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_698))),U_699) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_698))
      | ~ class_Rings_Ocomm__semiring__0(U_698) ),
    inference(variable_rename,[status(thm)],[f_213_1]) ).

fof(f_213_3,plain,
    ! [U_698,U_699] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_698)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_698))),U_699) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_698))
      | ~ class_Rings_Ocomm__semiring__0(U_698) ),
    inference(definitional_conversion,[status(esa)],[f_213_2]) ).

cnf(f_213_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_698)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_698))),U_699) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_698))
    | ~ class_Rings_Ocomm__semiring__0(U_698) ),
    inference(clausify,[status(thm)],[f_213_3]) ).

fof(f_214_1,plain,
    ! [V_p,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__poly__0__right]) ).

fof(f_214_2,plain,
    ! [U_701,U_700] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_700)),U_701),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_700))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_700))
      | ~ class_Rings_Ocomm__semiring__0(U_700) ),
    inference(variable_rename,[status(thm)],[f_214_1]) ).

fof(f_214_3,plain,
    ! [U_700,U_701] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_700)),U_701),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_700))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_700))
      | ~ class_Rings_Ocomm__semiring__0(U_700) ),
    inference(definitional_conversion,[status(esa)],[f_214_2]) ).

cnf(f_214_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_700)),U_701),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_700))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_700))
    | ~ class_Rings_Ocomm__semiring__0(U_700) ),
    inference(clausify,[status(thm)],[f_214_3]) ).

fof(f_215_1,plain,
    ! [V_q,V_p,V_a,T_a] :
      ( c_Polynomial_Osmult(T_a,V_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_a,V_q))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_smult__add__right]) ).

fof(f_215_2,plain,
    ! [U_705,U_704,U_703,U_702] :
      ( c_Polynomial_Osmult(U_702,U_703,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_702),U_704,U_705)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_702),c_Polynomial_Osmult(U_702,U_703,U_704),c_Polynomial_Osmult(U_702,U_703,U_705))
      | ~ class_Rings_Ocomm__semiring__0(U_702) ),
    inference(variable_rename,[status(thm)],[f_215_1]) ).

fof(f_215_3,plain,
    ! [U_702,U_703,U_704,U_705] :
      ( c_Polynomial_Osmult(U_702,U_703,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_702),U_704,U_705)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_702),c_Polynomial_Osmult(U_702,U_703,U_704),c_Polynomial_Osmult(U_702,U_703,U_705))
      | ~ class_Rings_Ocomm__semiring__0(U_702) ),
    inference(definitional_conversion,[status(esa)],[f_215_2]) ).

cnf(f_215_4,plain,
    ( c_Polynomial_Osmult(U_702,U_703,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_702),U_704,U_705)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_702),c_Polynomial_Osmult(U_702,U_703,U_704),c_Polynomial_Osmult(U_702,U_703,U_705))
    | ~ class_Rings_Ocomm__semiring__0(U_702) ),
    inference(clausify,[status(thm)],[f_215_3]) ).

fof(f_216_1,plain,
    ! [V_r,V_q,V_p,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_r) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),V_r))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__poly__add__left]) ).

fof(f_216_2,plain,
    ! [U_709,U_708,U_707,U_706] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_706)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_706),U_707,U_708)),U_709) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_706)),U_707),U_709),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_706)),U_708),U_709))
      | ~ class_Rings_Ocomm__semiring__0(U_706) ),
    inference(variable_rename,[status(thm)],[f_216_1]) ).

fof(f_216_3,plain,
    ! [U_706,U_707,U_708,U_709] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_706)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_706),U_707,U_708)),U_709) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_706)),U_707),U_709),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_706)),U_708),U_709))
      | ~ class_Rings_Ocomm__semiring__0(U_706) ),
    inference(definitional_conversion,[status(esa)],[f_216_2]) ).

cnf(f_216_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_706)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_706),U_707,U_708)),U_709) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_706)),U_707),U_709),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_706)),U_708),U_709))
    | ~ class_Rings_Ocomm__semiring__0(U_706) ),
    inference(clausify,[status(thm)],[f_216_3]) ).

fof(f_217_1,plain,
    ! [V_q,V_a,V_p,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Polynomial_OpCons(T_a,V_a,V_q)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__pCons__right]) ).

fof(f_217_2,plain,
    ! [U_713,U_712,U_711,U_710] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_710)),U_711),c_Polynomial_OpCons(U_710,U_712,U_713)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_710),c_Polynomial_Osmult(U_710,U_712,U_711),c_Polynomial_OpCons(U_710,c_Groups_Ozero__class_Ozero(U_710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_710)),U_711),U_713)))
      | ~ class_Rings_Ocomm__semiring__0(U_710) ),
    inference(variable_rename,[status(thm)],[f_217_1]) ).

fof(f_217_3,plain,
    ! [U_710,U_711,U_712,U_713] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_710)),U_711),c_Polynomial_OpCons(U_710,U_712,U_713)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_710),c_Polynomial_Osmult(U_710,U_712,U_711),c_Polynomial_OpCons(U_710,c_Groups_Ozero__class_Ozero(U_710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_710)),U_711),U_713)))
      | ~ class_Rings_Ocomm__semiring__0(U_710) ),
    inference(definitional_conversion,[status(esa)],[f_217_2]) ).

cnf(f_217_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_710)),U_711),c_Polynomial_OpCons(U_710,U_712,U_713)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_710),c_Polynomial_Osmult(U_710,U_712,U_711),c_Polynomial_OpCons(U_710,c_Groups_Ozero__class_Ozero(U_710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_710)),U_711),U_713)))
    | ~ class_Rings_Ocomm__semiring__0(U_710) ),
    inference(clausify,[status(thm)],[f_217_3]) ).

fof(f_218_1,plain,
    ! [V_q,V_p,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,V_a,V_p)),V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_q),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__pCons__left]) ).

fof(f_218_2,plain,
    ! [U_717,U_716,U_715,U_714] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_714)),c_Polynomial_OpCons(U_714,U_715,U_716)),U_717) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_714),c_Polynomial_Osmult(U_714,U_715,U_717),c_Polynomial_OpCons(U_714,c_Groups_Ozero__class_Ozero(U_714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_714)),U_716),U_717)))
      | ~ class_Rings_Ocomm__semiring__0(U_714) ),
    inference(variable_rename,[status(thm)],[f_218_1]) ).

fof(f_218_3,plain,
    ! [U_714,U_715,U_716,U_717] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_714)),c_Polynomial_OpCons(U_714,U_715,U_716)),U_717) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_714),c_Polynomial_Osmult(U_714,U_715,U_717),c_Polynomial_OpCons(U_714,c_Groups_Ozero__class_Ozero(U_714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_714)),U_716),U_717)))
      | ~ class_Rings_Ocomm__semiring__0(U_714) ),
    inference(definitional_conversion,[status(esa)],[f_218_2]) ).

cnf(f_218_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_714)),c_Polynomial_OpCons(U_714,U_715,U_716)),U_717) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_714),c_Polynomial_Osmult(U_714,U_715,U_717),c_Polynomial_OpCons(U_714,c_Groups_Ozero__class_Ozero(U_714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_714)),U_716),U_717)))
    | ~ class_Rings_Ocomm__semiring__0(U_714) ),
    inference(clausify,[status(thm)],[f_218_3]) ).

fof(f_219_1,plain,
    ! [V_b_2,V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__iff__diff__le__0]) ).

fof(f_219_2,plain,
    ! [U_720,U_719,U_718] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_718,U_719,U_720)
          | ~ c_Orderings_Oord__class_Oless__eq(U_718,c_Groups_Ominus__class_Ominus(U_718,U_719,U_720),c_Groups_Ozero__class_Ozero(U_718)) )
        & ( c_Orderings_Oord__class_Oless__eq(U_718,c_Groups_Ominus__class_Ominus(U_718,U_719,U_720),c_Groups_Ozero__class_Ozero(U_718))
          | ~ c_Orderings_Oord__class_Oless__eq(U_718,U_719,U_720) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_718) ),
    inference(variable_rename,[status(thm)],[f_219_1]) ).

fof(f_219_3,plain,
    ( ! [U_719,U_720,U_718] :
        ( c_Orderings_Oord__class_Oless__eq(U_718,U_719,U_720)
        | ~ c_Orderings_Oord__class_Oless__eq(U_718,c_Groups_Ominus__class_Ominus(U_718,U_719,U_720),c_Groups_Ozero__class_Ozero(U_718))
        | ~ sP48(U_719,U_720,U_718) )
    & ! [U_719,U_720,U_718] :
        ( c_Orderings_Oord__class_Oless__eq(U_718,c_Groups_Ominus__class_Ominus(U_718,U_719,U_720),c_Groups_Ozero__class_Ozero(U_718))
        | ~ c_Orderings_Oord__class_Oless__eq(U_718,U_719,U_720)
        | ~ sP48(U_719,U_720,U_718) )
    & ! [U_719,U_720,U_718] :
        ( sP48(U_719,U_720,U_718)
        | ~ class_Groups_Oordered__ab__group__add(U_718) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP48])],[f_219_2]) ).

cnf(f_219_4,plain,
    ( sP48(U_719,U_720,U_718)
    | ~ class_Groups_Oordered__ab__group__add(U_718) ),
    inference(clausify,[status(thm)],[f_219_3]) ).

cnf(f_219_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_718,c_Groups_Ominus__class_Ominus(U_718,U_719,U_720),c_Groups_Ozero__class_Ozero(U_718))
    | ~ c_Orderings_Oord__class_Oless__eq(U_718,U_719,U_720)
    | ~ sP48(U_719,U_720,U_718) ),
    inference(clausify,[status(thm)],[f_219_3]) ).

cnf(f_219_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_718,U_719,U_720)
    | ~ c_Orderings_Oord__class_Oless__eq(U_718,c_Groups_Ominus__class_Ominus(U_718,U_719,U_720),c_Groups_Ozero__class_Ozero(U_718))
    | ~ sP48(U_719,U_720,U_718) ),
    inference(clausify,[status(thm)],[f_219_3]) ).

fof(f_220_1,plain,
    ! [V_d,V_c,V_b,V_a,V_r,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != c_Groups_Oplus__class_Oplus(T_a,V_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d))
      | V_c = V_d
      | V_a != V_b
      | V_r = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__scale__eq__noteq]) ).

fof(f_220_2,plain,
    ! [U_726,U_725,U_724,U_723,U_722,U_721] :
      ( c_Groups_Oplus__class_Oplus(U_721,U_723,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_721),U_722),U_725)) != c_Groups_Oplus__class_Oplus(U_721,U_724,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_721),U_722),U_726))
      | U_725 = U_726
      | U_723 != U_724
      | U_722 = c_Groups_Ozero__class_Ozero(U_721)
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_721) ),
    inference(variable_rename,[status(thm)],[f_220_1]) ).

fof(f_220_3,plain,
    ! [U_722,U_723,U_724,U_725,U_726,U_721] :
      ( c_Groups_Oplus__class_Oplus(U_721,U_723,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_721),U_722),U_725)) != c_Groups_Oplus__class_Oplus(U_721,U_724,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_721),U_722),U_726))
      | U_725 = U_726
      | U_723 != U_724
      | U_722 = c_Groups_Ozero__class_Ozero(U_721)
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_721) ),
    inference(definitional_conversion,[status(esa)],[f_220_2]) ).

cnf(f_220_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_721,U_723,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_721),U_722),U_725)) != c_Groups_Oplus__class_Oplus(U_721,U_724,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_721),U_722),U_726))
    | U_725 = U_726
    | U_723 != U_724
    | U_722 = c_Groups_Ozero__class_Ozero(U_721)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_721) ),
    inference(clausify,[status(thm)],[f_220_3]) ).

fof(f_221_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_real__le__eq__diff]) ).

fof(f_221_2,plain,
    ! [U_728,U_727] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_727,U_728)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_727,U_728),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_727,U_728),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_727,U_728) ) ),
    inference(variable_rename,[status(thm)],[f_221_1]) ).

fof(f_221_3,plain,
    ( ! [U_732,U_730] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_730,U_732)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_730,U_732),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
    & ! [U_731,U_729] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_729,U_731),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_729,U_731) ) ),
    inference(miniscope,[status(thm)],[f_221_2]) ).

fof(f_221_4,plain,
    ( ! [U_730,U_732] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_730,U_732)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_730,U_732),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
    & ! [U_731,U_729] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_729,U_731),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_729,U_731) ) ),
    inference(definitional_conversion,[status(esa)],[f_221_3]) ).

cnf(f_221_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_729,U_731),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_729,U_731) ),
    inference(clausify,[status(thm)],[f_221_4]) ).

cnf(f_221_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_730,U_732)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_730,U_732),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(clausify,[status(thm)],[f_221_4]) ).

fof(f_222_1,plain,
    ! [V_p,T_a] :
      ( c_Polynomial_Osmult(T_a,c_Groups_Ozero__class_Ozero(T_a),V_p) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_smult__0__left]) ).

fof(f_222_2,plain,
    ! [U_734,U_733] :
      ( c_Polynomial_Osmult(U_733,c_Groups_Ozero__class_Ozero(U_733),U_734) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_733))
      | ~ class_Rings_Ocomm__semiring__0(U_733) ),
    inference(variable_rename,[status(thm)],[f_222_1]) ).

fof(f_222_3,plain,
    ! [U_734,U_733] :
      ( c_Polynomial_Osmult(U_733,c_Groups_Ozero__class_Ozero(U_733),U_734) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_733))
      | ~ class_Rings_Ocomm__semiring__0(U_733) ),
    inference(definitional_conversion,[status(esa)],[f_222_2]) ).

cnf(f_222_4,plain,
    ( c_Polynomial_Osmult(U_733,c_Groups_Ozero__class_Ozero(U_733),U_734) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_733))
    | ~ class_Rings_Ocomm__semiring__0(U_733) ),
    inference(clausify,[status(thm)],[f_222_3]) ).

fof(f_223_1,plain,
    ! [V_pa_2,V_ab_2,T_a] :
      ( ( ( c_Polynomial_Osmult(T_a,V_ab_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
          | ( V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
            & V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
        & ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
          | V_ab_2 = c_Groups_Ozero__class_Ozero(T_a)
          | c_Polynomial_Osmult(T_a,V_ab_2,V_pa_2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
      | ~ class_Rings_Oidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_smult__eq__0__iff]) ).

fof(f_223_2,plain,
    ! [U_737,U_736,U_735] :
      ( ( ( c_Polynomial_Osmult(U_735,U_736,U_737) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_735))
          | ( U_737 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_735))
            & U_736 != c_Groups_Ozero__class_Ozero(U_735) ) )
        & ( U_737 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_735))
          | U_736 = c_Groups_Ozero__class_Ozero(U_735)
          | c_Polynomial_Osmult(U_735,U_736,U_737) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_735)) ) )
      | ~ class_Rings_Oidom(U_735) ),
    inference(variable_rename,[status(thm)],[f_223_1]) ).

fof(f_223_3,plain,
    ( ! [U_735,U_736,U_737] :
        ( U_737 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_735))
        | ~ sP49(U_735,U_736,U_737) )
    & ! [U_735,U_736,U_737] :
        ( U_736 != c_Groups_Ozero__class_Ozero(U_735)
        | ~ sP49(U_735,U_736,U_737) )
    & ! [U_735,U_736,U_737] :
        ( c_Polynomial_Osmult(U_735,U_736,U_737) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_735))
        | sP49(U_735,U_736,U_737)
        | ~ sP50(U_735,U_736,U_737) )
    & ! [U_735,U_736,U_737] :
        ( U_737 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_735))
        | U_736 = c_Groups_Ozero__class_Ozero(U_735)
        | c_Polynomial_Osmult(U_735,U_736,U_737) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_735))
        | ~ sP50(U_735,U_736,U_737) )
    & ! [U_735,U_736,U_737] :
        ( sP50(U_735,U_736,U_737)
        | ~ class_Rings_Oidom(U_735) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP49,sP50])],[f_223_2]) ).

cnf(f_223_4,plain,
    ( sP50(U_735,U_736,U_737)
    | ~ class_Rings_Oidom(U_735) ),
    inference(clausify,[status(thm)],[f_223_3]) ).

cnf(f_223_5,plain,
    ( U_737 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_735))
    | U_736 = c_Groups_Ozero__class_Ozero(U_735)
    | c_Polynomial_Osmult(U_735,U_736,U_737) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_735))
    | ~ sP50(U_735,U_736,U_737) ),
    inference(clausify,[status(thm)],[f_223_3]) ).

cnf(f_223_6,plain,
    ( c_Polynomial_Osmult(U_735,U_736,U_737) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_735))
    | sP49(U_735,U_736,U_737)
    | ~ sP50(U_735,U_736,U_737) ),
    inference(clausify,[status(thm)],[f_223_3]) ).

cnf(f_223_7,plain,
    ( U_736 != c_Groups_Ozero__class_Ozero(U_735)
    | ~ sP49(U_735,U_736,U_737) ),
    inference(clausify,[status(thm)],[f_223_3]) ).

cnf(f_223_8,plain,
    ( U_737 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_735))
    | ~ sP49(U_735,U_736,U_737) ),
    inference(clausify,[status(thm)],[f_223_3]) ).

fof(f_224_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | V_y_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | V_x_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
          & V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(fof_nnf,[status(thm)],[fact_real__two__squares__add__zero__iff]) ).

fof(f_224_2,plain,
    ! [U_739,U_738] :
      ( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_738),U_738),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_739),U_739)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_739 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_738 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( ( U_739 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
          & U_738 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_738),U_738),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_739),U_739)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(variable_rename,[status(thm)],[f_224_1]) ).

fof(f_224_3,plain,
    ( ! [U_743,U_741] :
        ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_741),U_741),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_743),U_743)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_743 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_741 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
    & ! [U_742,U_740] :
        ( ( U_742 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
          & U_740 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_740),U_740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_742),U_742)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(miniscope,[status(thm)],[f_224_2]) ).

fof(f_224_4,plain,
    ( ! [U_740,U_742] :
        ( U_742 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | ~ sP51(U_740,U_742) )
    & ! [U_740,U_742] :
        ( U_740 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | ~ sP51(U_740,U_742) )
    & ! [U_743,U_741] :
        ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_741),U_741),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_743),U_743)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_743 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_741 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
    & ! [U_740,U_742] :
        ( sP51(U_740,U_742)
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_740),U_740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_742),U_742)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP51])],[f_224_3]) ).

cnf(f_224_5,plain,
    ( sP51(U_740,U_742)
    | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_740),U_740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_742),U_742)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(clausify,[status(thm)],[f_224_4]) ).

cnf(f_224_6,plain,
    ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_741),U_741),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_743),U_743)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | U_743 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | U_741 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(clausify,[status(thm)],[f_224_4]) ).

cnf(f_224_7,plain,
    ( U_740 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ sP51(U_740,U_742) ),
    inference(clausify,[status(thm)],[f_224_4]) ).

cnf(f_224_8,plain,
    ( U_742 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ sP51(U_740,U_742) ),
    inference(clausify,[status(thm)],[f_224_4]) ).

fof(f_225_1,plain,
    ! [V_a,V_p,V_c,T_a] :
      ( V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
      | c_Polynomial_Osmult(T_a,V_c,V_p) != c_Polynomial_OpCons(T_a,V_a,V_p)
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_synthetic__div__unique__lemma]) ).

fof(f_225_2,plain,
    ! [U_747,U_746,U_745,U_744] :
      ( U_746 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_744))
      | c_Polynomial_Osmult(U_744,U_745,U_746) != c_Polynomial_OpCons(U_744,U_747,U_746)
      | ~ class_Rings_Ocomm__semiring__0(U_744) ),
    inference(variable_rename,[status(thm)],[f_225_1]) ).

fof(f_225_3,plain,
    ! [U_747,U_744,U_745,U_746] :
      ( U_746 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_744))
      | c_Polynomial_Osmult(U_744,U_745,U_746) != c_Polynomial_OpCons(U_744,U_747,U_746)
      | ~ class_Rings_Ocomm__semiring__0(U_744) ),
    inference(definitional_conversion,[status(esa)],[f_225_2]) ).

cnf(f_225_4,plain,
    ( U_746 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_744))
    | c_Polynomial_Osmult(U_744,U_745,U_746) != c_Polynomial_OpCons(U_744,U_747,U_746)
    | ~ class_Rings_Ocomm__semiring__0(U_744) ),
    inference(clausify,[status(thm)],[f_225_3]) ).

fof(f_226_1,plain,
    ! [V_p,V_b,V_a,T_a] :
      ( c_Polynomial_Osmult(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_p) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_b,V_p))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_smult__add__left]) ).

fof(f_226_2,plain,
    ! [U_751,U_750,U_749,U_748] :
      ( c_Polynomial_Osmult(U_748,c_Groups_Oplus__class_Oplus(U_748,U_749,U_750),U_751) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_748),c_Polynomial_Osmult(U_748,U_749,U_751),c_Polynomial_Osmult(U_748,U_750,U_751))
      | ~ class_Rings_Ocomm__semiring__0(U_748) ),
    inference(variable_rename,[status(thm)],[f_226_1]) ).

fof(f_226_3,plain,
    ! [U_748,U_749,U_750,U_751] :
      ( c_Polynomial_Osmult(U_748,c_Groups_Oplus__class_Oplus(U_748,U_749,U_750),U_751) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_748),c_Polynomial_Osmult(U_748,U_749,U_751),c_Polynomial_Osmult(U_748,U_750,U_751))
      | ~ class_Rings_Ocomm__semiring__0(U_748) ),
    inference(definitional_conversion,[status(esa)],[f_226_2]) ).

cnf(f_226_4,plain,
    ( c_Polynomial_Osmult(U_748,c_Groups_Oplus__class_Oplus(U_748,U_749,U_750),U_751) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_748),c_Polynomial_Osmult(U_748,U_749,U_751),c_Polynomial_Osmult(U_748,U_750,U_751))
    | ~ class_Rings_Ocomm__semiring__0(U_748) ),
    inference(clausify,[status(thm)],[f_226_3]) ).

fof(f_227_1,plain,
    ! [V_n,T_a] :
      ( c_Polynomial_Omonom(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
      | ~ class_Groups_Ozero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_monom__eq__0]) ).

fof(f_227_2,plain,
    ! [U_753,U_752] :
      ( c_Polynomial_Omonom(U_752,c_Groups_Ozero__class_Ozero(U_752),U_753) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_752))
      | ~ class_Groups_Ozero(U_752) ),
    inference(variable_rename,[status(thm)],[f_227_1]) ).

fof(f_227_3,plain,
    ! [U_753,U_752] :
      ( c_Polynomial_Omonom(U_752,c_Groups_Ozero__class_Ozero(U_752),U_753) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_752))
      | ~ class_Groups_Ozero(U_752) ),
    inference(definitional_conversion,[status(esa)],[f_227_2]) ).

cnf(f_227_4,plain,
    ( c_Polynomial_Omonom(U_752,c_Groups_Ozero__class_Ozero(U_752),U_753) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_752))
    | ~ class_Groups_Ozero(U_752) ),
    inference(clausify,[status(thm)],[f_227_3]) ).

fof(f_228_1,plain,
    ! [V_n_2,V_ab_2,T_a] :
      ( ( ( c_Polynomial_Omonom(T_a,V_ab_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
          | V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a)
          | c_Polynomial_Omonom(T_a,V_ab_2,V_n_2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
      | ~ class_Groups_Ozero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_monom__eq__0__iff]) ).

fof(f_228_2,plain,
    ! [U_756,U_755,U_754] :
      ( ( ( c_Polynomial_Omonom(U_754,U_755,U_756) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_754))
          | U_755 != c_Groups_Ozero__class_Ozero(U_754) )
        & ( U_755 = c_Groups_Ozero__class_Ozero(U_754)
          | c_Polynomial_Omonom(U_754,U_755,U_756) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_754)) ) )
      | ~ class_Groups_Ozero(U_754) ),
    inference(variable_rename,[status(thm)],[f_228_1]) ).

fof(f_228_3,plain,
    ( ! [U_754,U_755,U_756] :
        ( c_Polynomial_Omonom(U_754,U_755,U_756) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_754))
        | U_755 != c_Groups_Ozero__class_Ozero(U_754)
        | ~ sP52(U_754,U_755,U_756) )
    & ! [U_754,U_755,U_756] :
        ( U_755 = c_Groups_Ozero__class_Ozero(U_754)
        | c_Polynomial_Omonom(U_754,U_755,U_756) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_754))
        | ~ sP52(U_754,U_755,U_756) )
    & ! [U_754,U_755,U_756] :
        ( sP52(U_754,U_755,U_756)
        | ~ class_Groups_Ozero(U_754) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP52])],[f_228_2]) ).

cnf(f_228_4,plain,
    ( sP52(U_754,U_755,U_756)
    | ~ class_Groups_Ozero(U_754) ),
    inference(clausify,[status(thm)],[f_228_3]) ).

cnf(f_228_5,plain,
    ( U_755 = c_Groups_Ozero__class_Ozero(U_754)
    | c_Polynomial_Omonom(U_754,U_755,U_756) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_754))
    | ~ sP52(U_754,U_755,U_756) ),
    inference(clausify,[status(thm)],[f_228_3]) ).

cnf(f_228_6,plain,
    ( c_Polynomial_Omonom(U_754,U_755,U_756) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_754))
    | U_755 != c_Groups_Ozero__class_Ozero(U_754)
    | ~ sP52(U_754,U_755,U_756) ),
    inference(clausify,[status(thm)],[f_228_3]) ).

fof(f_229_1,plain,
    ! [V_b,V_n,V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n),c_Polynomial_Omonom(T_a,V_b,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_n)
      | ~ class_Groups_Ocomm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__monom]) ).

fof(f_229_2,plain,
    ! [U_760,U_759,U_758,U_757] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_757),c_Polynomial_Omonom(U_757,U_758,U_759),c_Polynomial_Omonom(U_757,U_760,U_759)) = c_Polynomial_Omonom(U_757,c_Groups_Oplus__class_Oplus(U_757,U_758,U_760),U_759)
      | ~ class_Groups_Ocomm__monoid__add(U_757) ),
    inference(variable_rename,[status(thm)],[f_229_1]) ).

fof(f_229_3,plain,
    ! [U_758,U_759,U_760,U_757] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_757),c_Polynomial_Omonom(U_757,U_758,U_759),c_Polynomial_Omonom(U_757,U_760,U_759)) = c_Polynomial_Omonom(U_757,c_Groups_Oplus__class_Oplus(U_757,U_758,U_760),U_759)
      | ~ class_Groups_Ocomm__monoid__add(U_757) ),
    inference(definitional_conversion,[status(esa)],[f_229_2]) ).

cnf(f_229_4,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_757),c_Polynomial_Omonom(U_757,U_758,U_759),c_Polynomial_Omonom(U_757,U_760,U_759)) = c_Polynomial_Omonom(U_757,c_Groups_Oplus__class_Oplus(U_757,U_758,U_760),U_759)
    | ~ class_Groups_Ocomm__monoid__add(U_757) ),
    inference(clausify,[status(thm)],[f_229_3]) ).

fof(f_230_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)),c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)))
      | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_norm__diff__ineq]) ).

fof(f_230_2,plain,
    ! [U_763,U_762,U_761] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_761,U_762),c_RealVector_Onorm__class_Onorm(U_761,U_763)),c_RealVector_Onorm__class_Onorm(U_761,c_Groups_Oplus__class_Oplus(U_761,U_762,U_763)))
      | ~ class_RealVector_Oreal__normed__vector(U_761) ),
    inference(variable_rename,[status(thm)],[f_230_1]) ).

fof(f_230_3,plain,
    ! [U_761,U_762,U_763] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_761,U_762),c_RealVector_Onorm__class_Onorm(U_761,U_763)),c_RealVector_Onorm__class_Onorm(U_761,c_Groups_Oplus__class_Oplus(U_761,U_762,U_763)))
      | ~ class_RealVector_Oreal__normed__vector(U_761) ),
    inference(definitional_conversion,[status(esa)],[f_230_2]) ).

cnf(f_230_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_761,U_762),c_RealVector_Onorm__class_Onorm(U_761,U_763)),c_RealVector_Onorm__class_Onorm(U_761,c_Groups_Oplus__class_Oplus(U_761,U_762,U_763)))
    | ~ class_RealVector_Oreal__normed__vector(U_761) ),
    inference(clausify,[status(thm)],[f_230_3]) ).

fof(f_231_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_a),c_RealVector_Onorm__class_Onorm(T_a,V_b)))
      | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq4]) ).

fof(f_231_2,plain,
    ! [U_766,U_765,U_764] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_764,c_Groups_Ominus__class_Ominus(U_764,U_765,U_766)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_764,U_765),c_RealVector_Onorm__class_Onorm(U_764,U_766)))
      | ~ class_RealVector_Oreal__normed__vector(U_764) ),
    inference(variable_rename,[status(thm)],[f_231_1]) ).

fof(f_231_3,plain,
    ! [U_764,U_765,U_766] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_764,c_Groups_Ominus__class_Ominus(U_764,U_765,U_766)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_764,U_765),c_RealVector_Onorm__class_Onorm(U_764,U_766)))
      | ~ class_RealVector_Oreal__normed__vector(U_764) ),
    inference(definitional_conversion,[status(esa)],[f_231_2]) ).

cnf(f_231_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_764,c_Groups_Ominus__class_Ominus(U_764,U_765,U_766)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_764,U_765),c_RealVector_Onorm__class_Onorm(U_764,U_766)))
    | ~ class_RealVector_Oreal__normed__vector(U_764) ),
    inference(clausify,[status(thm)],[f_231_3]) ).

fof(f_232_1,plain,
    ! [V_n,V_m] :
      ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) != V_m ),
    inference(fof_nnf,[status(thm)],[fact_add__eq__self__zero]) ).

fof(f_232_2,plain,
    ! [U_768,U_767] :
      ( U_768 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_767,U_768) != U_767 ),
    inference(variable_rename,[status(thm)],[f_232_1]) ).

fof(f_232_3,plain,
    ! [U_768] :
      ( ! [U_767] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_767,U_768) != U_767
      | U_768 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(miniscope,[status(thm)],[f_232_2]) ).

fof(f_232_4,plain,
    ! [U_767,U_768] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_767,U_768) != U_767
      | U_768 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_232_3]) ).

cnf(f_232_5,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_767,U_768) != U_767
    | U_768 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_232_4]) ).

fof(f_233_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_add__is__0]) ).

fof(f_233_2,plain,
    ! [U_770,U_769] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_769,U_770) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_770 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_769 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( U_770 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_769 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_769,U_770) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_233_1]) ).

fof(f_233_3,plain,
    ( ! [U_774,U_772] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_772,U_774) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_774 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_772 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_773,U_771] :
        ( ( U_773 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_771,U_773) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_233_2]) ).

fof(f_233_4,plain,
    ( ! [U_771,U_773] :
        ( U_773 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP53(U_771,U_773) )
    & ! [U_771,U_773] :
        ( U_771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP53(U_771,U_773) )
    & ! [U_774,U_772] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_772,U_774) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_774 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_772 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_771,U_773] :
        ( sP53(U_771,U_773)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_771,U_773) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP53])],[f_233_3]) ).

cnf(f_233_5,plain,
    ( sP53(U_771,U_773)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_771,U_773) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_233_4]) ).

cnf(f_233_6,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_772,U_774) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_774 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_772 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_233_4]) ).

cnf(f_233_7,plain,
    ( U_771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP53(U_771,U_773) ),
    inference(clausify,[status(thm)],[f_233_4]) ).

cnf(f_233_8,plain,
    ( U_773 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP53(U_771,U_773) ),
    inference(clausify,[status(thm)],[f_233_4]) ).

fof(f_234_1,plain,
    ! [V_n_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__0__eq]) ).

fof(f_234_2,plain,
    ! [U_775] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_775,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_775 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_775 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_775,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_234_1]) ).

fof(f_234_3,plain,
    ( ! [U_777] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_777,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_777 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_776] :
        ( U_776 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_776,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_234_2]) ).

fof(f_234_4,plain,
    ( ! [U_777] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_777,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_777 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_776] :
        ( U_776 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_776,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa)],[f_234_3]) ).

cnf(f_234_5,plain,
    ( U_776 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_776,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_234_4]) ).

cnf(f_234_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_777,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_777 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_234_4]) ).

fof(f_235_1,plain,
    ! [V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
    inference(fof_nnf,[status(thm)],[fact_Nat_Oadd__0__right]) ).

fof(f_235_2,plain,
    ! [U_778] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_778,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_778,
    inference(variable_rename,[status(thm)],[f_235_1]) ).

fof(f_235_3,plain,
    ! [U_778] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_778,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_778,
    inference(definitional_conversion,[status(esa)],[f_235_2]) ).

cnf(f_235_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_778,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_778,
    inference(clausify,[status(thm)],[f_235_3]) ).

fof(f_236_1,plain,
    ! [V_n] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) = V_n,
    inference(fof_nnf,[status(thm)],[fact_plus__nat_Oadd__0]) ).

fof(f_236_2,plain,
    ! [U_779] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_779) = U_779,
    inference(variable_rename,[status(thm)],[f_236_1]) ).

fof(f_236_3,plain,
    ! [U_779] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_779) = U_779,
    inference(definitional_conversion,[status(esa)],[f_236_2]) ).

cnf(f_236_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_779) = U_779,
    inference(clausify,[status(thm)],[f_236_3]) ).

fof(f_237_1,plain,
    ! [V_y,V_x,V_c,T_a] :
      ( V_x = c_Groups_Ozero__class_Ozero(T_a)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_RealVector_Onorm__class_Onorm(T_a,V_y)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_norm__ratiotest__lemma]) ).

fof(f_237_2,plain,
    ! [U_783,U_782,U_781,U_780] :
      ( U_782 = c_Groups_Ozero__class_Ozero(U_780)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_780,U_782),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_781),c_RealVector_Onorm__class_Onorm(U_780,U_783)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_781,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      | ~ class_RealVector_Oreal__normed__vector(U_780) ),
    inference(variable_rename,[status(thm)],[f_237_1]) ).

fof(f_237_3,plain,
    ! [U_780,U_781,U_782,U_783] :
      ( U_782 = c_Groups_Ozero__class_Ozero(U_780)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_780,U_782),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_781),c_RealVector_Onorm__class_Onorm(U_780,U_783)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_781,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      | ~ class_RealVector_Oreal__normed__vector(U_780) ),
    inference(definitional_conversion,[status(esa)],[f_237_2]) ).

cnf(f_237_4,plain,
    ( U_782 = c_Groups_Ozero__class_Ozero(U_780)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_780,U_782),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_781),c_RealVector_Onorm__class_Onorm(U_780,U_783)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_781,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ class_RealVector_Oreal__normed__vector(U_780) ),
    inference(clausify,[status(thm)],[f_237_3]) ).

fof(f_238_1,plain,
    ! [V_db_2,V_b_2,V_ca_2,V_e_2,V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2)),V_e_2),V_ca_2),V_db_2) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2)),V_e_2),V_ca_2),V_db_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2)) ) )
      | ~ class_Rings_Oordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__add__iff1]) ).

fof(f_238_2,plain,
    ! [U_789,U_788,U_787,U_786,U_785,U_784] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_784,c_Groups_Oplus__class_Oplus(U_784,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),U_785),U_786),U_787),c_Groups_Oplus__class_Oplus(U_784,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),U_788),U_786),U_789))
          | ~ c_Orderings_Oord__class_Oless__eq(U_784,c_Groups_Oplus__class_Oplus(U_784,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),c_Groups_Ominus__class_Ominus(U_784,U_785,U_788)),U_786),U_787),U_789) )
        & ( c_Orderings_Oord__class_Oless__eq(U_784,c_Groups_Oplus__class_Oplus(U_784,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),c_Groups_Ominus__class_Ominus(U_784,U_785,U_788)),U_786),U_787),U_789)
          | ~ c_Orderings_Oord__class_Oless__eq(U_784,c_Groups_Oplus__class_Oplus(U_784,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),U_785),U_786),U_787),c_Groups_Oplus__class_Oplus(U_784,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),U_788),U_786),U_789)) ) )
      | ~ class_Rings_Oordered__ring(U_784) ),
    inference(variable_rename,[status(thm)],[f_238_1]) ).

fof(f_238_3,plain,
    ( ! [U_785,U_784,U_786,U_787,U_788,U_789] :
        ( c_Orderings_Oord__class_Oless__eq(U_784,c_Groups_Oplus__class_Oplus(U_784,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),U_785),U_786),U_787),c_Groups_Oplus__class_Oplus(U_784,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),U_788),U_786),U_789))
        | ~ c_Orderings_Oord__class_Oless__eq(U_784,c_Groups_Oplus__class_Oplus(U_784,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),c_Groups_Ominus__class_Ominus(U_784,U_785,U_788)),U_786),U_787),U_789)
        | ~ sP54(U_785,U_784,U_786,U_787,U_788,U_789) )
    & ! [U_785,U_784,U_786,U_787,U_788,U_789] :
        ( c_Orderings_Oord__class_Oless__eq(U_784,c_Groups_Oplus__class_Oplus(U_784,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),c_Groups_Ominus__class_Ominus(U_784,U_785,U_788)),U_786),U_787),U_789)
        | ~ c_Orderings_Oord__class_Oless__eq(U_784,c_Groups_Oplus__class_Oplus(U_784,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),U_785),U_786),U_787),c_Groups_Oplus__class_Oplus(U_784,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),U_788),U_786),U_789))
        | ~ sP54(U_785,U_784,U_786,U_787,U_788,U_789) )
    & ! [U_785,U_784,U_786,U_787,U_788,U_789] :
        ( sP54(U_785,U_784,U_786,U_787,U_788,U_789)
        | ~ class_Rings_Oordered__ring(U_784) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP54])],[f_238_2]) ).

cnf(f_238_4,plain,
    ( sP54(U_785,U_784,U_786,U_787,U_788,U_789)
    | ~ class_Rings_Oordered__ring(U_784) ),
    inference(clausify,[status(thm)],[f_238_3]) ).

cnf(f_238_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_784,c_Groups_Oplus__class_Oplus(U_784,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),c_Groups_Ominus__class_Ominus(U_784,U_785,U_788)),U_786),U_787),U_789)
    | ~ c_Orderings_Oord__class_Oless__eq(U_784,c_Groups_Oplus__class_Oplus(U_784,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),U_785),U_786),U_787),c_Groups_Oplus__class_Oplus(U_784,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),U_788),U_786),U_789))
    | ~ sP54(U_785,U_784,U_786,U_787,U_788,U_789) ),
    inference(clausify,[status(thm)],[f_238_3]) ).

cnf(f_238_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_784,c_Groups_Oplus__class_Oplus(U_784,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),U_785),U_786),U_787),c_Groups_Oplus__class_Oplus(U_784,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),U_788),U_786),U_789))
    | ~ c_Orderings_Oord__class_Oless__eq(U_784,c_Groups_Oplus__class_Oplus(U_784,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_784),c_Groups_Ominus__class_Ominus(U_784,U_785,U_788)),U_786),U_787),U_789)
    | ~ sP54(U_785,U_784,U_786,U_787,U_788,U_789) ),
    inference(clausify,[status(thm)],[f_238_3]) ).

fof(f_239_1,plain,
    ! [V_db_2,V_b_2,V_ca_2,V_e_2,V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_ab_2)),V_e_2),V_db_2)) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_ab_2)),V_e_2),V_db_2))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2)) ) )
      | ~ class_Rings_Oordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__add__iff2]) ).

fof(f_239_2,plain,
    ! [U_795,U_794,U_793,U_792,U_791,U_790] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_790,c_Groups_Oplus__class_Oplus(U_790,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_790),U_791),U_792),U_793),c_Groups_Oplus__class_Oplus(U_790,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_790),U_794),U_792),U_795))
          | ~ c_Orderings_Oord__class_Oless__eq(U_790,U_793,c_Groups_Oplus__class_Oplus(U_790,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_790),c_Groups_Ominus__class_Ominus(U_790,U_794,U_791)),U_792),U_795)) )
        & ( c_Orderings_Oord__class_Oless__eq(U_790,U_793,c_Groups_Oplus__class_Oplus(U_790,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_790),c_Groups_Ominus__class_Ominus(U_790,U_794,U_791)),U_792),U_795))
          | ~ c_Orderings_Oord__class_Oless__eq(U_790,c_Groups_Oplus__class_Oplus(U_790,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_790),U_791),U_792),U_793),c_Groups_Oplus__class_Oplus(U_790,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_790),U_794),U_792),U_795)) ) )
      | ~ class_Rings_Oordered__ring(U_790) ),
    inference(variable_rename,[status(thm)],[f_239_1]) ).

fof(f_239_3,plain,
    ( ! [U_790,U_791,U_792,U_793,U_794,U_795] :
        ( c_Orderings_Oord__class_Oless__eq(U_790,c_Groups_Oplus__class_Oplus(U_790,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_790),U_791),U_792),U_793),c_Groups_Oplus__class_Oplus(U_790,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_790),U_794),U_792),U_795))
        | ~ c_Orderings_Oord__class_Oless__eq(U_790,U_793,c_Groups_Oplus__class_Oplus(U_790,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_790),c_Groups_Ominus__class_Ominus(U_790,U_794,U_791)),U_792),U_795))
        | ~ sP55(U_790,U_791,U_792,U_793,U_794,U_795) )
    & ! [U_790,U_791,U_792,U_793,U_794,U_795] :
        ( c_Orderings_Oord__class_Oless__eq(U_790,U_793,c_Groups_Oplus__class_Oplus(U_790,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_790),c_Groups_Ominus__class_Ominus(U_790,U_794,U_791)),U_792),U_795))
        | ~ c_Orderings_Oord__class_Oless__eq(U_790,c_Groups_Oplus__class_Oplus(U_790,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_790),U_791),U_792),U_793),c_Groups_Oplus__class_Oplus(U_790,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_790),U_794),U_792),U_795))
        | ~ sP55(U_790,U_791,U_792,U_793,U_794,U_795) )
    & ! [U_790,U_791,U_792,U_793,U_794,U_795] :
        ( sP55(U_790,U_791,U_792,U_793,U_794,U_795)
        | ~ class_Rings_Oordered__ring(U_790) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP55])],[f_239_2]) ).

cnf(f_239_4,plain,
    ( sP55(U_790,U_791,U_792,U_793,U_794,U_795)
    | ~ class_Rings_Oordered__ring(U_790) ),
    inference(clausify,[status(thm)],[f_239_3]) ).

cnf(f_239_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_790,U_793,c_Groups_Oplus__class_Oplus(U_790,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_790),c_Groups_Ominus__class_Ominus(U_790,U_794,U_791)),U_792),U_795))
    | ~ c_Orderings_Oord__class_Oless__eq(U_790,c_Groups_Oplus__class_Oplus(U_790,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_790),U_791),U_792),U_793),c_Groups_Oplus__class_Oplus(U_790,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_790),U_794),U_792),U_795))
    | ~ sP55(U_790,U_791,U_792,U_793,U_794,U_795) ),
    inference(clausify,[status(thm)],[f_239_3]) ).

cnf(f_239_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_790,c_Groups_Oplus__class_Oplus(U_790,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_790),U_791),U_792),U_793),c_Groups_Oplus__class_Oplus(U_790,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_790),U_794),U_792),U_795))
    | ~ c_Orderings_Oord__class_Oless__eq(U_790,U_793,c_Groups_Oplus__class_Oplus(U_790,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_790),c_Groups_Ominus__class_Ominus(U_790,U_794,U_791)),U_792),U_795))
    | ~ sP55(U_790,U_791,U_792,U_793,U_794,U_795) ),
    inference(clausify,[status(thm)],[f_239_3]) ).

fof(f_240_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))
          | V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
            & V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a)) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff]) ).

fof(f_240_2,plain,
    ! [U_798,U_797,U_796] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_796,c_Groups_Oplus__class_Oplus(U_796,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_796),U_797),U_797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_796),U_798),U_798)),c_Groups_Ozero__class_Ozero(U_796))
          | U_798 != c_Groups_Ozero__class_Ozero(U_796)
          | U_797 != c_Groups_Ozero__class_Ozero(U_796) )
        & ( ( U_798 = c_Groups_Ozero__class_Ozero(U_796)
            & U_797 = c_Groups_Ozero__class_Ozero(U_796) )
          | ~ c_Orderings_Oord__class_Oless__eq(U_796,c_Groups_Oplus__class_Oplus(U_796,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_796),U_797),U_797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_796),U_798),U_798)),c_Groups_Ozero__class_Ozero(U_796)) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_796) ),
    inference(variable_rename,[status(thm)],[f_240_1]) ).

fof(f_240_3,plain,
    ( ! [U_796,U_798,U_797] :
        ( U_798 = c_Groups_Ozero__class_Ozero(U_796)
        | ~ sP56(U_796,U_798,U_797) )
    & ! [U_796,U_798,U_797] :
        ( U_797 = c_Groups_Ozero__class_Ozero(U_796)
        | ~ sP56(U_796,U_798,U_797) )
    & ! [U_796,U_798,U_797] :
        ( c_Orderings_Oord__class_Oless__eq(U_796,c_Groups_Oplus__class_Oplus(U_796,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_796),U_797),U_797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_796),U_798),U_798)),c_Groups_Ozero__class_Ozero(U_796))
        | U_798 != c_Groups_Ozero__class_Ozero(U_796)
        | U_797 != c_Groups_Ozero__class_Ozero(U_796)
        | ~ sP57(U_796,U_798,U_797) )
    & ! [U_796,U_798,U_797] :
        ( sP56(U_796,U_798,U_797)
        | ~ c_Orderings_Oord__class_Oless__eq(U_796,c_Groups_Oplus__class_Oplus(U_796,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_796),U_797),U_797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_796),U_798),U_798)),c_Groups_Ozero__class_Ozero(U_796))
        | ~ sP57(U_796,U_798,U_797) )
    & ! [U_796,U_798,U_797] :
        ( sP57(U_796,U_798,U_797)
        | ~ class_Rings_Olinordered__ring__strict(U_796) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP56,sP57])],[f_240_2]) ).

cnf(f_240_4,plain,
    ( sP57(U_796,U_798,U_797)
    | ~ class_Rings_Olinordered__ring__strict(U_796) ),
    inference(clausify,[status(thm)],[f_240_3]) ).

cnf(f_240_5,plain,
    ( sP56(U_796,U_798,U_797)
    | ~ c_Orderings_Oord__class_Oless__eq(U_796,c_Groups_Oplus__class_Oplus(U_796,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_796),U_797),U_797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_796),U_798),U_798)),c_Groups_Ozero__class_Ozero(U_796))
    | ~ sP57(U_796,U_798,U_797) ),
    inference(clausify,[status(thm)],[f_240_3]) ).

cnf(f_240_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_796,c_Groups_Oplus__class_Oplus(U_796,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_796),U_797),U_797),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_796),U_798),U_798)),c_Groups_Ozero__class_Ozero(U_796))
    | U_798 != c_Groups_Ozero__class_Ozero(U_796)
    | U_797 != c_Groups_Ozero__class_Ozero(U_796)
    | ~ sP57(U_796,U_798,U_797) ),
    inference(clausify,[status(thm)],[f_240_3]) ).

cnf(f_240_7,plain,
    ( U_797 = c_Groups_Ozero__class_Ozero(U_796)
    | ~ sP56(U_796,U_798,U_797) ),
    inference(clausify,[status(thm)],[f_240_3]) ).

cnf(f_240_8,plain,
    ( U_798 = c_Groups_Ozero__class_Ozero(U_796)
    | ~ sP56(U_796,U_798,U_797) ),
    inference(clausify,[status(thm)],[f_240_3]) ).

fof(f_241_1,plain,
    ! [V_y,V_x,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))
      | ~ class_Rings_Olinordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sum__squares__ge__zero]) ).

fof(f_241_2,plain,
    ! [U_801,U_800,U_799] :
      ( c_Orderings_Oord__class_Oless__eq(U_799,c_Groups_Ozero__class_Ozero(U_799),c_Groups_Oplus__class_Oplus(U_799,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_799),U_800),U_800),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_799),U_801),U_801)))
      | ~ class_Rings_Olinordered__ring(U_799) ),
    inference(variable_rename,[status(thm)],[f_241_1]) ).

fof(f_241_3,plain,
    ! [U_801,U_800,U_799] :
      ( c_Orderings_Oord__class_Oless__eq(U_799,c_Groups_Ozero__class_Ozero(U_799),c_Groups_Oplus__class_Oplus(U_799,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_799),U_800),U_800),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_799),U_801),U_801)))
      | ~ class_Rings_Olinordered__ring(U_799) ),
    inference(definitional_conversion,[status(esa)],[f_241_2]) ).

cnf(f_241_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_799,c_Groups_Ozero__class_Ozero(U_799),c_Groups_Oplus__class_Oplus(U_799,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_799),U_800),U_800),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_799),U_801),U_801)))
    | ~ class_Rings_Olinordered__ring(U_799) ),
    inference(clausify,[status(thm)],[f_241_3]) ).

fof(f_242_1,plain,
    ! [V_a,V_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_b,V_a)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_b)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_a)),
    inference(fof_nnf,[status(thm)],[fact_complex__mod__triangle__ineq2]) ).

fof(f_242_2,plain,
    ! [U_803,U_802] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_802,U_803)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_802)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_803)),
    inference(variable_rename,[status(thm)],[f_242_1]) ).

fof(f_242_3,plain,
    ! [U_802,U_803] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_802,U_803)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_802)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_803)),
    inference(definitional_conversion,[status(esa)],[f_242_2]) ).

cnf(f_242_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_802,U_803)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_802)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_803)),
    inference(clausify,[status(thm)],[f_242_3]) ).

fof(f_243_1,plain,
    ! [V_db_2,V_b_2,V_ca_2,V_e_2,V_ab_2,T_a] :
      ( ( ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2)
          | V_ca_2 != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_ab_2)),V_e_2),V_db_2) )
        & ( V_ca_2 = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_ab_2)),V_e_2),V_db_2)
          | c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2) ) )
      | ~ class_Rings_Oring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_eq__add__iff2]) ).

fof(f_243_2,plain,
    ! [U_809,U_808,U_807,U_806,U_805,U_804] :
      ( ( ( c_Groups_Oplus__class_Oplus(U_804,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_804),U_805),U_806),U_807) = c_Groups_Oplus__class_Oplus(U_804,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_804),U_808),U_806),U_809)
          | U_807 != c_Groups_Oplus__class_Oplus(U_804,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_804),c_Groups_Ominus__class_Ominus(U_804,U_808,U_805)),U_806),U_809) )
        & ( U_807 = c_Groups_Oplus__class_Oplus(U_804,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_804),c_Groups_Ominus__class_Ominus(U_804,U_808,U_805)),U_806),U_809)
          | c_Groups_Oplus__class_Oplus(U_804,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_804),U_805),U_806),U_807) != c_Groups_Oplus__class_Oplus(U_804,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_804),U_808),U_806),U_809) ) )
      | ~ class_Rings_Oring(U_804) ),
    inference(variable_rename,[status(thm)],[f_243_1]) ).

fof(f_243_3,plain,
    ( ! [U_804,U_805,U_806,U_807,U_808,U_809] :
        ( c_Groups_Oplus__class_Oplus(U_804,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_804),U_805),U_806),U_807) = c_Groups_Oplus__class_Oplus(U_804,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_804),U_808),U_806),U_809)
        | U_807 != c_Groups_Oplus__class_Oplus(U_804,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_804),c_Groups_Ominus__class_Ominus(U_804,U_808,U_805)),U_806),U_809)
        | ~ sP58(U_804,U_805,U_806,U_807,U_808,U_809) )
    & ! [U_804,U_805,U_806,U_807,U_808,U_809] :
        ( U_807 = c_Groups_Oplus__class_Oplus(U_804,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_804),c_Groups_Ominus__class_Ominus(U_804,U_808,U_805)),U_806),U_809)
        | c_Groups_Oplus__class_Oplus(U_804,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_804),U_805),U_806),U_807) != c_Groups_Oplus__class_Oplus(U_804,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_804),U_808),U_806),U_809)
        | ~ sP58(U_804,U_805,U_806,U_807,U_808,U_809) )
    & ! [U_804,U_805,U_806,U_807,U_808,U_809] :
        ( sP58(U_804,U_805,U_806,U_807,U_808,U_809)
        | ~ class_Rings_Oring(U_804) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP58])],[f_243_2]) ).

cnf(f_243_4,plain,
    ( sP58(U_804,U_805,U_806,U_807,U_808,U_809)
    | ~ class_Rings_Oring(U_804) ),
    inference(clausify,[status(thm)],[f_243_3]) ).

cnf(f_243_5,plain,
    ( U_807 = c_Groups_Oplus__class_Oplus(U_804,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_804),c_Groups_Ominus__class_Ominus(U_804,U_808,U_805)),U_806),U_809)
    | c_Groups_Oplus__class_Oplus(U_804,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_804),U_805),U_806),U_807) != c_Groups_Oplus__class_Oplus(U_804,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_804),U_808),U_806),U_809)
    | ~ sP58(U_804,U_805,U_806,U_807,U_808,U_809) ),
    inference(clausify,[status(thm)],[f_243_3]) ).

cnf(f_243_6,plain,
    ( c_Groups_Oplus__class_Oplus(U_804,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_804),U_805),U_806),U_807) = c_Groups_Oplus__class_Oplus(U_804,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_804),U_808),U_806),U_809)
    | U_807 != c_Groups_Oplus__class_Oplus(U_804,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_804),c_Groups_Ominus__class_Ominus(U_804,U_808,U_805)),U_806),U_809)
    | ~ sP58(U_804,U_805,U_806,U_807,U_808,U_809) ),
    inference(clausify,[status(thm)],[f_243_3]) ).

fof(f_244_1,plain,
    ! [V_db_2,V_b_2,V_ca_2,V_e_2,V_ab_2,T_a] :
      ( ( ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2)
          | c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2)),V_e_2),V_ca_2) != V_db_2 )
        & ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2)),V_e_2),V_ca_2) = V_db_2
          | c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2) ) )
      | ~ class_Rings_Oring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_eq__add__iff1]) ).

fof(f_244_2,plain,
    ! [U_815,U_814,U_813,U_812,U_811,U_810] :
      ( ( ( c_Groups_Oplus__class_Oplus(U_810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_810),U_811),U_812),U_813) = c_Groups_Oplus__class_Oplus(U_810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_810),U_814),U_812),U_815)
          | c_Groups_Oplus__class_Oplus(U_810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_810),c_Groups_Ominus__class_Ominus(U_810,U_811,U_814)),U_812),U_813) != U_815 )
        & ( c_Groups_Oplus__class_Oplus(U_810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_810),c_Groups_Ominus__class_Ominus(U_810,U_811,U_814)),U_812),U_813) = U_815
          | c_Groups_Oplus__class_Oplus(U_810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_810),U_811),U_812),U_813) != c_Groups_Oplus__class_Oplus(U_810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_810),U_814),U_812),U_815) ) )
      | ~ class_Rings_Oring(U_810) ),
    inference(variable_rename,[status(thm)],[f_244_1]) ).

fof(f_244_3,plain,
    ( ! [U_810,U_811,U_812,U_814,U_813,U_815] :
        ( c_Groups_Oplus__class_Oplus(U_810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_810),U_811),U_812),U_813) = c_Groups_Oplus__class_Oplus(U_810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_810),U_814),U_812),U_815)
        | c_Groups_Oplus__class_Oplus(U_810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_810),c_Groups_Ominus__class_Ominus(U_810,U_811,U_814)),U_812),U_813) != U_815
        | ~ sP59(U_810,U_811,U_812,U_814,U_813,U_815) )
    & ! [U_810,U_811,U_812,U_814,U_813,U_815] :
        ( c_Groups_Oplus__class_Oplus(U_810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_810),c_Groups_Ominus__class_Ominus(U_810,U_811,U_814)),U_812),U_813) = U_815
        | c_Groups_Oplus__class_Oplus(U_810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_810),U_811),U_812),U_813) != c_Groups_Oplus__class_Oplus(U_810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_810),U_814),U_812),U_815)
        | ~ sP59(U_810,U_811,U_812,U_814,U_813,U_815) )
    & ! [U_810,U_811,U_812,U_814,U_813,U_815] :
        ( sP59(U_810,U_811,U_812,U_814,U_813,U_815)
        | ~ class_Rings_Oring(U_810) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP59])],[f_244_2]) ).

cnf(f_244_4,plain,
    ( sP59(U_810,U_811,U_812,U_814,U_813,U_815)
    | ~ class_Rings_Oring(U_810) ),
    inference(clausify,[status(thm)],[f_244_3]) ).

cnf(f_244_5,plain,
    ( c_Groups_Oplus__class_Oplus(U_810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_810),c_Groups_Ominus__class_Ominus(U_810,U_811,U_814)),U_812),U_813) = U_815
    | c_Groups_Oplus__class_Oplus(U_810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_810),U_811),U_812),U_813) != c_Groups_Oplus__class_Oplus(U_810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_810),U_814),U_812),U_815)
    | ~ sP59(U_810,U_811,U_812,U_814,U_813,U_815) ),
    inference(clausify,[status(thm)],[f_244_3]) ).

cnf(f_244_6,plain,
    ( c_Groups_Oplus__class_Oplus(U_810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_810),U_811),U_812),U_813) = c_Groups_Oplus__class_Oplus(U_810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_810),U_814),U_812),U_815)
    | c_Groups_Oplus__class_Oplus(U_810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_810),c_Groups_Ominus__class_Ominus(U_810,U_811,U_814)),U_812),U_813) != U_815
    | ~ sP59(U_810,U_811,U_812,U_814,U_813,U_815) ),
    inference(clausify,[status(thm)],[f_244_3]) ).

fof(f_245_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_a)
          | V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
            & V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
          | c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff]) ).

fof(f_245_2,plain,
    ! [U_818,U_817,U_816] :
      ( ( ( c_Groups_Oplus__class_Oplus(U_816,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_816),U_817),U_817),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_816),U_818),U_818)) = c_Groups_Ozero__class_Ozero(U_816)
          | U_818 != c_Groups_Ozero__class_Ozero(U_816)
          | U_817 != c_Groups_Ozero__class_Ozero(U_816) )
        & ( ( U_818 = c_Groups_Ozero__class_Ozero(U_816)
            & U_817 = c_Groups_Ozero__class_Ozero(U_816) )
          | c_Groups_Oplus__class_Oplus(U_816,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_816),U_817),U_817),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_816),U_818),U_818)) != c_Groups_Ozero__class_Ozero(U_816) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_816) ),
    inference(variable_rename,[status(thm)],[f_245_1]) ).

fof(f_245_3,plain,
    ( ! [U_816,U_817,U_818] :
        ( U_818 = c_Groups_Ozero__class_Ozero(U_816)
        | ~ sP60(U_816,U_817,U_818) )
    & ! [U_816,U_817,U_818] :
        ( U_817 = c_Groups_Ozero__class_Ozero(U_816)
        | ~ sP60(U_816,U_817,U_818) )
    & ! [U_816,U_817,U_818] :
        ( c_Groups_Oplus__class_Oplus(U_816,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_816),U_817),U_817),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_816),U_818),U_818)) = c_Groups_Ozero__class_Ozero(U_816)
        | U_818 != c_Groups_Ozero__class_Ozero(U_816)
        | U_817 != c_Groups_Ozero__class_Ozero(U_816)
        | ~ sP61(U_816,U_817,U_818) )
    & ! [U_816,U_817,U_818] :
        ( sP60(U_816,U_817,U_818)
        | c_Groups_Oplus__class_Oplus(U_816,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_816),U_817),U_817),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_816),U_818),U_818)) != c_Groups_Ozero__class_Ozero(U_816)
        | ~ sP61(U_816,U_817,U_818) )
    & ! [U_816,U_817,U_818] :
        ( sP61(U_816,U_817,U_818)
        | ~ class_Rings_Olinordered__ring__strict(U_816) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP60,sP61])],[f_245_2]) ).

cnf(f_245_4,plain,
    ( sP61(U_816,U_817,U_818)
    | ~ class_Rings_Olinordered__ring__strict(U_816) ),
    inference(clausify,[status(thm)],[f_245_3]) ).

cnf(f_245_5,plain,
    ( sP60(U_816,U_817,U_818)
    | c_Groups_Oplus__class_Oplus(U_816,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_816),U_817),U_817),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_816),U_818),U_818)) != c_Groups_Ozero__class_Ozero(U_816)
    | ~ sP61(U_816,U_817,U_818) ),
    inference(clausify,[status(thm)],[f_245_3]) ).

cnf(f_245_6,plain,
    ( c_Groups_Oplus__class_Oplus(U_816,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_816),U_817),U_817),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_816),U_818),U_818)) = c_Groups_Ozero__class_Ozero(U_816)
    | U_818 != c_Groups_Ozero__class_Ozero(U_816)
    | U_817 != c_Groups_Ozero__class_Ozero(U_816)
    | ~ sP61(U_816,U_817,U_818) ),
    inference(clausify,[status(thm)],[f_245_3]) ).

cnf(f_245_7,plain,
    ( U_817 = c_Groups_Ozero__class_Ozero(U_816)
    | ~ sP60(U_816,U_817,U_818) ),
    inference(clausify,[status(thm)],[f_245_3]) ).

cnf(f_245_8,plain,
    ( U_818 = c_Groups_Ozero__class_Ozero(U_816)
    | ~ sP60(U_816,U_817,U_818) ),
    inference(clausify,[status(thm)],[f_245_3]) ).

fof(f_246_1,plain,
    ! [V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a))
      | ~ class_Rings_Olinordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__square]) ).

fof(f_246_2,plain,
    ! [U_820,U_819] :
      ( c_Orderings_Oord__class_Oless__eq(U_819,c_Groups_Ozero__class_Ozero(U_819),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_819),U_820),U_820))
      | ~ class_Rings_Olinordered__ring(U_819) ),
    inference(variable_rename,[status(thm)],[f_246_1]) ).

fof(f_246_3,plain,
    ! [U_820,U_819] :
      ( c_Orderings_Oord__class_Oless__eq(U_819,c_Groups_Ozero__class_Ozero(U_819),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_819),U_820),U_820))
      | ~ class_Rings_Olinordered__ring(U_819) ),
    inference(definitional_conversion,[status(esa)],[f_246_2]) ).

cnf(f_246_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_819,c_Groups_Ozero__class_Ozero(U_819),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_819),U_820),U_820))
    | ~ class_Rings_Olinordered__ring(U_819) ),
    inference(clausify,[status(thm)],[f_246_3]) ).

fof(f_247_1,plain,
    ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),
    inference(fof_nnf,[status(thm)],[fact_nat__add__commute]) ).

fof(f_247_2,plain,
    ! [U_822,U_821] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_821,U_822) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_822,U_821),
    inference(variable_rename,[status(thm)],[f_247_1]) ).

fof(f_247_3,plain,
    ! [U_821,U_822] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_821,U_822) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_822,U_821),
    inference(definitional_conversion,[status(esa)],[f_247_2]) ).

cnf(f_247_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_821,U_822) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_822,U_821),
    inference(clausify,[status(thm)],[f_247_3]) ).

fof(f_248_1,plain,
    ! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z)),
    inference(fof_nnf,[status(thm)],[fact_nat__add__left__commute]) ).

fof(f_248_2,plain,
    ! [U_825,U_824,U_823] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_823,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_824,U_825)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_824,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_823,U_825)),
    inference(variable_rename,[status(thm)],[f_248_1]) ).

fof(f_248_3,plain,
    ! [U_824,U_825,U_823] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_823,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_824,U_825)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_824,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_823,U_825)),
    inference(definitional_conversion,[status(esa)],[f_248_2]) ).

cnf(f_248_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_823,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_824,U_825)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_824,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_823,U_825)),
    inference(clausify,[status(thm)],[f_248_3]) ).

fof(f_249_1,plain,
    ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
    inference(fof_nnf,[status(thm)],[fact_add__mult__distrib2]) ).

fof(f_249_2,plain,
    ! [U_828,U_827,U_826] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_826),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_827,U_828)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_826),U_827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_826),U_828)),
    inference(variable_rename,[status(thm)],[f_249_1]) ).

fof(f_249_3,plain,
    ! [U_826,U_827,U_828] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_826),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_827,U_828)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_826),U_827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_826),U_828)),
    inference(definitional_conversion,[status(esa)],[f_249_2]) ).

cnf(f_249_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_826),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_827,U_828)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_826),U_827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_826),U_828)),
    inference(clausify,[status(thm)],[f_249_3]) ).

fof(f_250_1,plain,
    ! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n) = V_m,
    inference(fof_nnf,[status(thm)],[fact_diff__add__inverse2]) ).

fof(f_250_2,plain,
    ! [U_830,U_829] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_829,U_830),U_830) = U_829,
    inference(variable_rename,[status(thm)],[f_250_1]) ).

fof(f_250_3,plain,
    ! [U_829,U_830] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_829,U_830),U_830) = U_829,
    inference(definitional_conversion,[status(esa)],[f_250_2]) ).

cnf(f_250_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_829,U_830),U_830) = U_829,
    inference(clausify,[status(thm)],[f_250_3]) ).

fof(f_251_1,plain,
    ! [V_m,V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_n) = V_m,
    inference(fof_nnf,[status(thm)],[fact_diff__add__inverse]) ).

fof(f_251_2,plain,
    ! [U_832,U_831] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_831,U_832),U_831) = U_832,
    inference(variable_rename,[status(thm)],[f_251_1]) ).

fof(f_251_3,plain,
    ! [U_832,U_831] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_831,U_832),U_831) = U_832,
    inference(definitional_conversion,[status(esa)],[f_251_2]) ).

cnf(f_251_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_831,U_832),U_831) = U_832,
    inference(clausify,[status(thm)],[f_251_3]) ).

fof(f_252_1,plain,
    ! [V_k,V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)),
    inference(fof_nnf,[status(thm)],[fact_nat__add__assoc]) ).

fof(f_252_2,plain,
    ! [U_835,U_834,U_833] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_833,U_834),U_835) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_833,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_834,U_835)),
    inference(variable_rename,[status(thm)],[f_252_1]) ).

fof(f_252_3,plain,
    ! [U_834,U_833,U_835] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_833,U_834),U_835) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_833,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_834,U_835)),
    inference(definitional_conversion,[status(esa)],[f_252_2]) ).

cnf(f_252_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_833,U_834),U_835) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_833,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_834,U_835)),
    inference(clausify,[status(thm)],[f_252_3]) ).

fof(f_253_1,plain,
    ! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)),
    inference(fof_nnf,[status(thm)],[fact_diff__diff__left]) ).

fof(f_253_2,plain,
    ! [U_838,U_837,U_836] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_836,U_837),U_838) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_836,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_837,U_838)),
    inference(variable_rename,[status(thm)],[f_253_1]) ).

fof(f_253_3,plain,
    ! [U_837,U_836,U_838] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_836,U_837),U_838) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_836,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_837,U_838)),
    inference(definitional_conversion,[status(esa)],[f_253_2]) ).

cnf(f_253_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_836,U_837),U_838) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_836,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_837,U_838)),
    inference(clausify,[status(thm)],[f_253_3]) ).

fof(f_254_1,plain,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),V_k) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
    inference(fof_nnf,[status(thm)],[fact_add__mult__distrib]) ).

fof(f_254_2,plain,
    ! [U_841,U_840,U_839] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_839,U_840)),U_841) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_839),U_841),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_840),U_841)),
    inference(variable_rename,[status(thm)],[f_254_1]) ).

fof(f_254_3,plain,
    ! [U_839,U_840,U_841] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_839,U_840)),U_841) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_839),U_841),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_840),U_841)),
    inference(definitional_conversion,[status(esa)],[f_254_2]) ).

cnf(f_254_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_839,U_840)),U_841) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_839),U_841),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_840),U_841)),
    inference(clausify,[status(thm)],[f_254_3]) ).

fof(f_255_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)
        | V_m_2 != V_n_2 )
      & ( V_m_2 = V_n_2
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel]) ).

fof(f_255_2,plain,
    ! [U_844,U_843,U_842] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_842,U_843) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_842,U_844)
        | U_843 != U_844 )
      & ( U_843 = U_844
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_842,U_843) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_842,U_844) ) ),
    inference(variable_rename,[status(thm)],[f_255_1]) ).

fof(f_255_3,plain,
    ( ! [U_850,U_848] :
        ( ! [U_846] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_846,U_848) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_846,U_850)
        | U_848 != U_850 )
    & ! [U_849,U_847] :
        ( ! [U_845] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_845,U_847) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_845,U_849)
        | U_847 = U_849 ) ),
    inference(miniscope,[status(thm)],[f_255_2]) ).

fof(f_255_4,plain,
    ( ! [U_848,U_846,U_850] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_846,U_848) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_846,U_850)
        | U_848 != U_850 )
    & ! [U_845,U_847,U_849] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_845,U_847) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_845,U_849)
        | U_847 = U_849 ) ),
    inference(definitional_conversion,[status(esa)],[f_255_3]) ).

cnf(f_255_5,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_845,U_847) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_845,U_849)
    | U_847 = U_849 ),
    inference(clausify,[status(thm)],[f_255_4]) ).

cnf(f_255_6,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_846,U_848) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_846,U_850)
    | U_848 != U_850 ),
    inference(clausify,[status(thm)],[f_255_4]) ).

fof(f_256_1,plain,
    ! [V_n_2,V_k_2,V_m_2] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)
        | V_m_2 != V_n_2 )
      & ( V_m_2 = V_n_2
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel]) ).

fof(f_256_2,plain,
    ! [U_853,U_852,U_851] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_851,U_852) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_853,U_852)
        | U_851 != U_853 )
      & ( U_851 = U_853
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_851,U_852) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_853,U_852) ) ),
    inference(variable_rename,[status(thm)],[f_256_1]) ).

fof(f_256_3,plain,
    ( ! [U_859,U_857,U_855] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_855,U_857) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_859,U_857)
        | U_855 != U_859 )
    & ! [U_858,U_856,U_854] :
        ( U_854 = U_858
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_854,U_856) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_858,U_856) ) ),
    inference(miniscope,[status(thm)],[f_256_2]) ).

fof(f_256_4,plain,
    ( ! [U_857,U_859,U_855] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_855,U_857) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_859,U_857)
        | U_855 != U_859 )
    & ! [U_854,U_856,U_858] :
        ( U_854 = U_858
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_854,U_856) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_858,U_856) ) ),
    inference(definitional_conversion,[status(esa)],[f_256_3]) ).

cnf(f_256_5,plain,
    ( U_854 = U_858
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_854,U_856) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_858,U_856) ),
    inference(clausify,[status(thm)],[f_256_4]) ).

cnf(f_256_6,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_855,U_857) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_859,U_857)
    | U_855 != U_859 ),
    inference(clausify,[status(thm)],[f_256_4]) ).

fof(f_257_1,plain,
    ! [V_n,V_m,V_k] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),
    inference(fof_nnf,[status(thm)],[fact_diff__cancel]) ).

fof(f_257_2,plain,
    ! [U_862,U_861,U_860] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_860,U_861),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_860,U_862)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_861,U_862),
    inference(variable_rename,[status(thm)],[f_257_1]) ).

fof(f_257_3,plain,
    ! [U_862,U_860,U_861] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_860,U_861),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_860,U_862)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_861,U_862),
    inference(definitional_conversion,[status(esa)],[f_257_2]) ).

cnf(f_257_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_860,U_861),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_860,U_862)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_861,U_862),
    inference(clausify,[status(thm)],[f_257_3]) ).

fof(f_258_1,plain,
    ! [V_n,V_k,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),
    inference(fof_nnf,[status(thm)],[fact_diff__cancel2]) ).

fof(f_258_2,plain,
    ! [U_865,U_864,U_863] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_863,U_864),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_865,U_864)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_863,U_865),
    inference(variable_rename,[status(thm)],[f_258_1]) ).

fof(f_258_3,plain,
    ! [U_864,U_863,U_865] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_863,U_864),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_865,U_864)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_863,U_865),
    inference(definitional_conversion,[status(esa)],[f_258_2]) ).

cnf(f_258_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_863,U_864),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_865,U_864)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_863,U_865),
    inference(clausify,[status(thm)],[f_258_3]) ).

fof(f_259_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__commute]) ).

fof(f_259_2,plain,
    ! [U_867,U_866] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_866),U_867) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_867),U_866),
    inference(variable_rename,[status(thm)],[f_259_1]) ).

fof(f_259_3,plain,
    ! [U_866,U_867] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_866),U_867) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_867),U_866),
    inference(definitional_conversion,[status(esa)],[f_259_2]) ).

cnf(f_259_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_866),U_867) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_867),U_866),
    inference(clausify,[status(thm)],[f_259_3]) ).

fof(f_260_1,plain,
    ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
    inference(fof_nnf,[status(thm)],[fact_diff__mult__distrib2]) ).

fof(f_260_2,plain,
    ! [U_870,U_869,U_868] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_868),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_869,U_870)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_868),U_869),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_868),U_870)),
    inference(variable_rename,[status(thm)],[f_260_1]) ).

fof(f_260_3,plain,
    ! [U_868,U_869,U_870] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_868),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_869,U_870)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_868),U_869),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_868),U_870)),
    inference(definitional_conversion,[status(esa)],[f_260_2]) ).

cnf(f_260_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_868),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_869,U_870)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_868),U_869),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_868),U_870)),
    inference(clausify,[status(thm)],[f_260_3]) ).

fof(f_261_1,plain,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__assoc]) ).

fof(f_261_2,plain,
    ! [U_873,U_872,U_871] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_871),U_872)),U_873) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_871),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_872),U_873)),
    inference(variable_rename,[status(thm)],[f_261_1]) ).

fof(f_261_3,plain,
    ! [U_871,U_872,U_873] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_871),U_872)),U_873) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_871),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_872),U_873)),
    inference(definitional_conversion,[status(esa)],[f_261_2]) ).

cnf(f_261_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_871),U_872)),U_873) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_871),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_872),U_873)),
    inference(clausify,[status(thm)],[f_261_3]) ).

fof(f_262_1,plain,
    ! [V_k,V_j,V_i] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j),
    inference(fof_nnf,[status(thm)],[fact_diff__commute]) ).

fof(f_262_2,plain,
    ! [U_876,U_875,U_874] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_874,U_875),U_876) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_874,U_876),U_875),
    inference(variable_rename,[status(thm)],[f_262_1]) ).

fof(f_262_3,plain,
    ! [U_875,U_874,U_876] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_874,U_875),U_876) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_874,U_876),U_875),
    inference(definitional_conversion,[status(esa)],[f_262_2]) ).

cnf(f_262_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_874,U_875),U_876) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_874,U_876),U_875),
    inference(clausify,[status(thm)],[f_262_3]) ).

fof(f_263_1,plain,
    ! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
    inference(fof_nnf,[status(thm)],[fact_diff__mult__distrib]) ).

fof(f_263_2,plain,
    ! [U_879,U_878,U_877] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_877,U_878)),U_879) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_877),U_879),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_878),U_879)),
    inference(variable_rename,[status(thm)],[f_263_1]) ).

fof(f_263_3,plain,
    ! [U_877,U_878,U_879] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_877,U_878)),U_879) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_877),U_879),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_878),U_879)),
    inference(definitional_conversion,[status(esa)],[f_263_2]) ).

cnf(f_263_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_877,U_878)),U_879) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_877),U_879),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_878),U_879)),
    inference(clausify,[status(thm)],[f_263_3]) ).

fof(f_264_1,plain,
    ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_z3)),
    inference(fof_nnf,[status(thm)],[fact_real__mult__assoc]) ).

fof(f_264_2,plain,
    ! [U_882,U_881,U_880] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_880),U_881)),U_882) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_880),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_881),U_882)),
    inference(variable_rename,[status(thm)],[f_264_1]) ).

fof(f_264_3,plain,
    ! [U_880,U_881,U_882] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_880),U_881)),U_882) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_880),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_881),U_882)),
    inference(definitional_conversion,[status(esa)],[f_264_2]) ).

cnf(f_264_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_880),U_881)),U_882) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_880),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_881),U_882)),
    inference(clausify,[status(thm)],[f_264_3]) ).

fof(f_265_1,plain,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z),
    inference(fof_nnf,[status(thm)],[fact_real__mult__commute]) ).

fof(f_265_2,plain,
    ! [U_884,U_883] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_883),U_884) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_884),U_883),
    inference(variable_rename,[status(thm)],[f_265_1]) ).

fof(f_265_3,plain,
    ! [U_883,U_884] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_883),U_884) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_884),U_883),
    inference(definitional_conversion,[status(esa)],[f_265_2]) ).

cnf(f_265_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_883),U_884) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_884),U_883),
    inference(clausify,[status(thm)],[f_265_3]) ).

fof(f_266_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2)
        | ! [B_n] : V_l_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n) )
      & ( ? [B_n] : V_l_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_l_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__Suc__ex__iff]) ).

fof(f_266_2,plain,
    ! [U_888,U_887] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_887,U_888)
        | ! [U_886] : U_888 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_887,U_886) )
      & ( ? [U_885] : U_888 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_887,U_885)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_887,U_888) ) ),
    inference(variable_rename,[status(thm)],[f_266_1]) ).

fof(f_266_3,plain,
    ( ! [U_892,U_890] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_890,U_892)
        | ! [U_886] : U_892 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_890,U_886) )
    & ! [U_891,U_889] :
        ( ? [U_885] : U_891 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_889,U_885)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_889,U_891) ) ),
    inference(miniscope,[status(thm)],[f_266_2]) ).

fof(f_266_4,plain,
    ( ! [U_892,U_890] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_890,U_892)
        | ! [U_886] : U_892 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_890,U_886) )
    & ! [U_891,U_889] :
        ( U_891 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_889,sK6(U_891,U_889))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_889,U_891) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_885,sK6(U_891,U_889))],[f_266_3]) ).

fof(f_266_5,plain,
    ( ! [U_892,U_886,U_890] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_890,U_892)
        | U_892 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_890,U_886) )
    & ! [U_889,U_891] :
        ( U_891 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_889,sK6(U_891,U_889))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_889,U_891) ) ),
    inference(definitional_conversion,[status(esa)],[f_266_4]) ).

cnf(f_266_6,plain,
    ( U_891 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_889,sK6(U_891,U_889))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_889,U_891) ),
    inference(clausify,[status(thm)],[f_266_5]) ).

cnf(f_266_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_890,U_892)
    | U_892 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_890,U_886) ),
    inference(clausify,[status(thm)],[f_266_5]) ).

fof(f_267_1,plain,
    ! [V_b,V_a,T_a] :
      ( V_b = c_Groups_Ozero__class_Ozero(T_a)
      | V_a = c_Groups_Ozero__class_Ozero(T_a)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Ono__zero__divisors(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_divisors__zero]) ).

fof(f_267_2,plain,
    ! [U_895,U_894,U_893] :
      ( U_895 = c_Groups_Ozero__class_Ozero(U_893)
      | U_894 = c_Groups_Ozero__class_Ozero(U_893)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_893),U_894),U_895) != c_Groups_Ozero__class_Ozero(U_893)
      | ~ class_Rings_Ono__zero__divisors(U_893) ),
    inference(variable_rename,[status(thm)],[f_267_1]) ).

fof(f_267_3,plain,
    ! [U_894,U_893,U_895] :
      ( U_895 = c_Groups_Ozero__class_Ozero(U_893)
      | U_894 = c_Groups_Ozero__class_Ozero(U_893)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_893),U_894),U_895) != c_Groups_Ozero__class_Ozero(U_893)
      | ~ class_Rings_Ono__zero__divisors(U_893) ),
    inference(definitional_conversion,[status(esa)],[f_267_2]) ).

cnf(f_267_4,plain,
    ( U_895 = c_Groups_Ozero__class_Ozero(U_893)
    | U_894 = c_Groups_Ozero__class_Ozero(U_893)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_893),U_894),U_895) != c_Groups_Ozero__class_Ozero(U_893)
    | ~ class_Rings_Ono__zero__divisors(U_893) ),
    inference(clausify,[status(thm)],[f_267_3]) ).

fof(f_268_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a)
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | V_a = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Ono__zero__divisors(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_no__zero__divisors]) ).

fof(f_268_2,plain,
    ! [U_898,U_897,U_896] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_896),U_897),U_898) != c_Groups_Ozero__class_Ozero(U_896)
      | U_898 = c_Groups_Ozero__class_Ozero(U_896)
      | U_897 = c_Groups_Ozero__class_Ozero(U_896)
      | ~ class_Rings_Ono__zero__divisors(U_896) ),
    inference(variable_rename,[status(thm)],[f_268_1]) ).

fof(f_268_3,plain,
    ! [U_898,U_896,U_897] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_896),U_897),U_898) != c_Groups_Ozero__class_Ozero(U_896)
      | U_898 = c_Groups_Ozero__class_Ozero(U_896)
      | U_897 = c_Groups_Ozero__class_Ozero(U_896)
      | ~ class_Rings_Ono__zero__divisors(U_896) ),
    inference(definitional_conversion,[status(esa)],[f_268_2]) ).

cnf(f_268_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_896),U_897),U_898) != c_Groups_Ozero__class_Ozero(U_896)
    | U_898 = c_Groups_Ozero__class_Ozero(U_896)
    | U_897 = c_Groups_Ozero__class_Ozero(U_896)
    | ~ class_Rings_Ono__zero__divisors(U_896) ),
    inference(clausify,[status(thm)],[f_268_3]) ).

fof(f_269_1,plain,
    ! [V_b_2,V_ab_2,T_a] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
          | ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a)
            & V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
        & ( V_b_2 = c_Groups_Ozero__class_Ozero(T_a)
          | V_ab_2 = c_Groups_Ozero__class_Ozero(T_a)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_b_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Rings_Oring__no__zero__divisors(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff]) ).

fof(f_269_2,plain,
    ! [U_901,U_900,U_899] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_899),U_900),U_901) = c_Groups_Ozero__class_Ozero(U_899)
          | ( U_901 != c_Groups_Ozero__class_Ozero(U_899)
            & U_900 != c_Groups_Ozero__class_Ozero(U_899) ) )
        & ( U_901 = c_Groups_Ozero__class_Ozero(U_899)
          | U_900 = c_Groups_Ozero__class_Ozero(U_899)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_899),U_900),U_901) != c_Groups_Ozero__class_Ozero(U_899) ) )
      | ~ class_Rings_Oring__no__zero__divisors(U_899) ),
    inference(variable_rename,[status(thm)],[f_269_1]) ).

fof(f_269_3,plain,
    ( ! [U_899,U_900,U_901] :
        ( U_901 != c_Groups_Ozero__class_Ozero(U_899)
        | ~ sP62(U_899,U_900,U_901) )
    & ! [U_899,U_900,U_901] :
        ( U_900 != c_Groups_Ozero__class_Ozero(U_899)
        | ~ sP62(U_899,U_900,U_901) )
    & ! [U_899,U_900,U_901] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_899),U_900),U_901) = c_Groups_Ozero__class_Ozero(U_899)
        | sP62(U_899,U_900,U_901)
        | ~ sP63(U_899,U_900,U_901) )
    & ! [U_899,U_900,U_901] :
        ( U_901 = c_Groups_Ozero__class_Ozero(U_899)
        | U_900 = c_Groups_Ozero__class_Ozero(U_899)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_899),U_900),U_901) != c_Groups_Ozero__class_Ozero(U_899)
        | ~ sP63(U_899,U_900,U_901) )
    & ! [U_899,U_900,U_901] :
        ( sP63(U_899,U_900,U_901)
        | ~ class_Rings_Oring__no__zero__divisors(U_899) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP62,sP63])],[f_269_2]) ).

cnf(f_269_4,plain,
    ( sP63(U_899,U_900,U_901)
    | ~ class_Rings_Oring__no__zero__divisors(U_899) ),
    inference(clausify,[status(thm)],[f_269_3]) ).

cnf(f_269_5,plain,
    ( U_901 = c_Groups_Ozero__class_Ozero(U_899)
    | U_900 = c_Groups_Ozero__class_Ozero(U_899)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_899),U_900),U_901) != c_Groups_Ozero__class_Ozero(U_899)
    | ~ sP63(U_899,U_900,U_901) ),
    inference(clausify,[status(thm)],[f_269_3]) ).

cnf(f_269_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_899),U_900),U_901) = c_Groups_Ozero__class_Ozero(U_899)
    | sP62(U_899,U_900,U_901)
    | ~ sP63(U_899,U_900,U_901) ),
    inference(clausify,[status(thm)],[f_269_3]) ).

cnf(f_269_7,plain,
    ( U_900 != c_Groups_Ozero__class_Ozero(U_899)
    | ~ sP62(U_899,U_900,U_901) ),
    inference(clausify,[status(thm)],[f_269_3]) ).

cnf(f_269_8,plain,
    ( U_901 != c_Groups_Ozero__class_Ozero(U_899)
    | ~ sP62(U_899,U_900,U_901) ),
    inference(clausify,[status(thm)],[f_269_3]) ).

fof(f_270_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Omult__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__zero__right]) ).

fof(f_270_2,plain,
    ! [U_903,U_902] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_902),U_903),c_Groups_Ozero__class_Ozero(U_902)) = c_Groups_Ozero__class_Ozero(U_902)
      | ~ class_Rings_Omult__zero(U_902) ),
    inference(variable_rename,[status(thm)],[f_270_1]) ).

fof(f_270_3,plain,
    ! [U_902,U_903] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_902),U_903),c_Groups_Ozero__class_Ozero(U_902)) = c_Groups_Ozero__class_Ozero(U_902)
      | ~ class_Rings_Omult__zero(U_902) ),
    inference(definitional_conversion,[status(esa)],[f_270_2]) ).

cnf(f_270_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_902),U_903),c_Groups_Ozero__class_Ozero(U_902)) = c_Groups_Ozero__class_Ozero(U_902)
    | ~ class_Rings_Omult__zero(U_902) ),
    inference(clausify,[status(thm)],[f_270_3]) ).

fof(f_271_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Omult__zero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__zero__left]) ).

fof(f_271_2,plain,
    ! [U_905,U_904] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_904),c_Groups_Ozero__class_Ozero(U_904)),U_905) = c_Groups_Ozero__class_Ozero(U_904)
      | ~ class_Rings_Omult__zero(U_904) ),
    inference(variable_rename,[status(thm)],[f_271_1]) ).

fof(f_271_3,plain,
    ! [U_904,U_905] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_904),c_Groups_Ozero__class_Ozero(U_904)),U_905) = c_Groups_Ozero__class_Ozero(U_904)
      | ~ class_Rings_Omult__zero(U_904) ),
    inference(definitional_conversion,[status(esa)],[f_271_2]) ).

cnf(f_271_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_904),c_Groups_Ozero__class_Ozero(U_904)),U_905) = c_Groups_Ozero__class_Ozero(U_904)
    | ~ class_Rings_Omult__zero(U_904) ),
    inference(clausify,[status(thm)],[f_271_3]) ).

fof(f_272_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_c) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
      | ~ class_Rings_Ocomm__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib]) ).

fof(f_272_2,plain,
    ! [U_909,U_908,U_907,U_906] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_906),c_Groups_Oplus__class_Oplus(U_906,U_907,U_908)),U_909) = c_Groups_Oplus__class_Oplus(U_906,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_906),U_907),U_909),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_906),U_908),U_909))
      | ~ class_Rings_Ocomm__semiring(U_906) ),
    inference(variable_rename,[status(thm)],[f_272_1]) ).

fof(f_272_3,plain,
    ! [U_906,U_907,U_908,U_909] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_906),c_Groups_Oplus__class_Oplus(U_906,U_907,U_908)),U_909) = c_Groups_Oplus__class_Oplus(U_906,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_906),U_907),U_909),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_906),U_908),U_909))
      | ~ class_Rings_Ocomm__semiring(U_906) ),
    inference(definitional_conversion,[status(esa)],[f_272_2]) ).

cnf(f_272_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_906),c_Groups_Oplus__class_Oplus(U_906,U_907,U_908)),U_909) = c_Groups_Oplus__class_Oplus(U_906,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_906),U_907),U_909),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_906),U_908),U_909))
    | ~ class_Rings_Ocomm__semiring(U_906) ),
    inference(clausify,[status(thm)],[f_272_3]) ).

fof(f_273_1,plain,
    ! [V_c,V_b,V_e,V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e),V_c)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_e),V_c)
      | ~ class_Rings_Osemiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_combine__common__factor]) ).

fof(f_273_2,plain,
    ! [U_914,U_913,U_912,U_911,U_910] :
      ( c_Groups_Oplus__class_Oplus(U_910,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),U_911),U_912),c_Groups_Oplus__class_Oplus(U_910,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),U_913),U_912),U_914)) = c_Groups_Oplus__class_Oplus(U_910,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),c_Groups_Oplus__class_Oplus(U_910,U_911,U_913)),U_912),U_914)
      | ~ class_Rings_Osemiring(U_910) ),
    inference(variable_rename,[status(thm)],[f_273_1]) ).

fof(f_273_3,plain,
    ! [U_910,U_911,U_912,U_913,U_914] :
      ( c_Groups_Oplus__class_Oplus(U_910,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),U_911),U_912),c_Groups_Oplus__class_Oplus(U_910,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),U_913),U_912),U_914)) = c_Groups_Oplus__class_Oplus(U_910,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),c_Groups_Oplus__class_Oplus(U_910,U_911,U_913)),U_912),U_914)
      | ~ class_Rings_Osemiring(U_910) ),
    inference(definitional_conversion,[status(esa)],[f_273_2]) ).

cnf(f_273_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_910,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),U_911),U_912),c_Groups_Oplus__class_Oplus(U_910,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),U_913),U_912),U_914)) = c_Groups_Oplus__class_Oplus(U_910,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),c_Groups_Oplus__class_Oplus(U_910,U_911,U_913)),U_912),U_914)
    | ~ class_Rings_Osemiring(U_910) ),
    inference(clausify,[status(thm)],[f_273_3]) ).

fof(f_274_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))
      | ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
        & ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )
      | ~ class_Rings_Oordered__cancel__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le]) ).

fof(f_274_2,plain,
    ! [U_917,U_916,U_915] :
      ( c_Orderings_Oord__class_Oless__eq(U_915,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_915),U_916),U_917),c_Groups_Ozero__class_Ozero(U_915))
      | ( ( ~ c_Orderings_Oord__class_Oless__eq(U_915,c_Groups_Ozero__class_Ozero(U_915),U_917)
          | ~ c_Orderings_Oord__class_Oless__eq(U_915,U_916,c_Groups_Ozero__class_Ozero(U_915)) )
        & ( ~ c_Orderings_Oord__class_Oless__eq(U_915,U_917,c_Groups_Ozero__class_Ozero(U_915))
          | ~ c_Orderings_Oord__class_Oless__eq(U_915,c_Groups_Ozero__class_Ozero(U_915),U_916) ) )
      | ~ class_Rings_Oordered__cancel__semiring(U_915) ),
    inference(variable_rename,[status(thm)],[f_274_1]) ).

fof(f_274_3,plain,
    ( ! [U_917,U_916,U_915] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_915,c_Groups_Ozero__class_Ozero(U_915),U_917)
        | ~ c_Orderings_Oord__class_Oless__eq(U_915,U_916,c_Groups_Ozero__class_Ozero(U_915))
        | ~ sP64(U_917,U_916,U_915) )
    & ! [U_917,U_916,U_915] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_915,U_917,c_Groups_Ozero__class_Ozero(U_915))
        | ~ c_Orderings_Oord__class_Oless__eq(U_915,c_Groups_Ozero__class_Ozero(U_915),U_916)
        | ~ sP64(U_917,U_916,U_915) )
    & ! [U_917,U_916,U_915] :
        ( c_Orderings_Oord__class_Oless__eq(U_915,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_915),U_916),U_917),c_Groups_Ozero__class_Ozero(U_915))
        | sP64(U_917,U_916,U_915)
        | ~ class_Rings_Oordered__cancel__semiring(U_915) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP64])],[f_274_2]) ).

cnf(f_274_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_915,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_915),U_916),U_917),c_Groups_Ozero__class_Ozero(U_915))
    | sP64(U_917,U_916,U_915)
    | ~ class_Rings_Oordered__cancel__semiring(U_915) ),
    inference(clausify,[status(thm)],[f_274_3]) ).

cnf(f_274_5,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_915,U_917,c_Groups_Ozero__class_Ozero(U_915))
    | ~ c_Orderings_Oord__class_Oless__eq(U_915,c_Groups_Ozero__class_Ozero(U_915),U_916)
    | ~ sP64(U_917,U_916,U_915) ),
    inference(clausify,[status(thm)],[f_274_3]) ).

cnf(f_274_6,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_915,c_Groups_Ozero__class_Ozero(U_915),U_917)
    | ~ c_Orderings_Oord__class_Oless__eq(U_915,U_916,c_Groups_Ozero__class_Ozero(U_915))
    | ~ sP64(U_917,U_916,U_915) ),
    inference(clausify,[status(thm)],[f_274_3]) ).

fof(f_275_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
      | ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
        & ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )
      | ~ class_Rings_Oordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_split__mult__pos__le]) ).

fof(f_275_2,plain,
    ! [U_920,U_919,U_918] :
      ( c_Orderings_Oord__class_Oless__eq(U_918,c_Groups_Ozero__class_Ozero(U_918),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_918),U_919),U_920))
      | ( ( ~ c_Orderings_Oord__class_Oless__eq(U_918,U_920,c_Groups_Ozero__class_Ozero(U_918))
          | ~ c_Orderings_Oord__class_Oless__eq(U_918,U_919,c_Groups_Ozero__class_Ozero(U_918)) )
        & ( ~ c_Orderings_Oord__class_Oless__eq(U_918,c_Groups_Ozero__class_Ozero(U_918),U_920)
          | ~ c_Orderings_Oord__class_Oless__eq(U_918,c_Groups_Ozero__class_Ozero(U_918),U_919) ) )
      | ~ class_Rings_Oordered__ring(U_918) ),
    inference(variable_rename,[status(thm)],[f_275_1]) ).

fof(f_275_3,plain,
    ( ! [U_920,U_919,U_918] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_918,U_920,c_Groups_Ozero__class_Ozero(U_918))
        | ~ c_Orderings_Oord__class_Oless__eq(U_918,U_919,c_Groups_Ozero__class_Ozero(U_918))
        | ~ sP65(U_920,U_919,U_918) )
    & ! [U_920,U_919,U_918] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_918,c_Groups_Ozero__class_Ozero(U_918),U_920)
        | ~ c_Orderings_Oord__class_Oless__eq(U_918,c_Groups_Ozero__class_Ozero(U_918),U_919)
        | ~ sP65(U_920,U_919,U_918) )
    & ! [U_920,U_919,U_918] :
        ( c_Orderings_Oord__class_Oless__eq(U_918,c_Groups_Ozero__class_Ozero(U_918),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_918),U_919),U_920))
        | sP65(U_920,U_919,U_918)
        | ~ class_Rings_Oordered__ring(U_918) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP65])],[f_275_2]) ).

cnf(f_275_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_918,c_Groups_Ozero__class_Ozero(U_918),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_918),U_919),U_920))
    | sP65(U_920,U_919,U_918)
    | ~ class_Rings_Oordered__ring(U_918) ),
    inference(clausify,[status(thm)],[f_275_3]) ).

cnf(f_275_5,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_918,c_Groups_Ozero__class_Ozero(U_918),U_920)
    | ~ c_Orderings_Oord__class_Oless__eq(U_918,c_Groups_Ozero__class_Ozero(U_918),U_919)
    | ~ sP65(U_920,U_919,U_918) ),
    inference(clausify,[status(thm)],[f_275_3]) ).

cnf(f_275_6,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_918,U_920,c_Groups_Ozero__class_Ozero(U_918))
    | ~ c_Orderings_Oord__class_Oless__eq(U_918,U_919,c_Groups_Ozero__class_Ozero(U_918))
    | ~ sP65(U_920,U_919,U_918) ),
    inference(clausify,[status(thm)],[f_275_3]) ).

fof(f_276_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
      | ~ class_Rings_Oordered__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__mono]) ).

fof(f_276_2,plain,
    ! [U_925,U_924,U_923,U_922,U_921] :
      ( c_Orderings_Oord__class_Oless__eq(U_921,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_921),U_922),U_924),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_921),U_923),U_925))
      | ~ c_Orderings_Oord__class_Oless__eq(U_921,c_Groups_Ozero__class_Ozero(U_921),U_924)
      | ~ c_Orderings_Oord__class_Oless__eq(U_921,c_Groups_Ozero__class_Ozero(U_921),U_923)
      | ~ c_Orderings_Oord__class_Oless__eq(U_921,U_924,U_925)
      | ~ c_Orderings_Oord__class_Oless__eq(U_921,U_922,U_923)
      | ~ class_Rings_Oordered__semiring(U_921) ),
    inference(variable_rename,[status(thm)],[f_276_1]) ).

fof(f_276_3,plain,
    ! [U_925,U_922,U_923,U_921,U_924] :
      ( c_Orderings_Oord__class_Oless__eq(U_921,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_921),U_922),U_924),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_921),U_923),U_925))
      | ~ c_Orderings_Oord__class_Oless__eq(U_921,c_Groups_Ozero__class_Ozero(U_921),U_924)
      | ~ c_Orderings_Oord__class_Oless__eq(U_921,c_Groups_Ozero__class_Ozero(U_921),U_923)
      | ~ c_Orderings_Oord__class_Oless__eq(U_921,U_924,U_925)
      | ~ c_Orderings_Oord__class_Oless__eq(U_921,U_922,U_923)
      | ~ class_Rings_Oordered__semiring(U_921) ),
    inference(definitional_conversion,[status(esa)],[f_276_2]) ).

cnf(f_276_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_921,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_921),U_922),U_924),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_921),U_923),U_925))
    | ~ c_Orderings_Oord__class_Oless__eq(U_921,c_Groups_Ozero__class_Ozero(U_921),U_924)
    | ~ c_Orderings_Oord__class_Oless__eq(U_921,c_Groups_Ozero__class_Ozero(U_921),U_923)
    | ~ c_Orderings_Oord__class_Oless__eq(U_921,U_924,U_925)
    | ~ c_Orderings_Oord__class_Oless__eq(U_921,U_922,U_923)
    | ~ class_Rings_Oordered__semiring(U_921) ),
    inference(clausify,[status(thm)],[f_276_3]) ).

fof(f_277_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
      | ~ class_Rings_Oordered__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__mono_H]) ).

fof(f_277_2,plain,
    ! [U_930,U_929,U_928,U_927,U_926] :
      ( c_Orderings_Oord__class_Oless__eq(U_926,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_926),U_927),U_929),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_926),U_928),U_930))
      | ~ c_Orderings_Oord__class_Oless__eq(U_926,c_Groups_Ozero__class_Ozero(U_926),U_929)
      | ~ c_Orderings_Oord__class_Oless__eq(U_926,c_Groups_Ozero__class_Ozero(U_926),U_927)
      | ~ c_Orderings_Oord__class_Oless__eq(U_926,U_929,U_930)
      | ~ c_Orderings_Oord__class_Oless__eq(U_926,U_927,U_928)
      | ~ class_Rings_Oordered__semiring(U_926) ),
    inference(variable_rename,[status(thm)],[f_277_1]) ).

fof(f_277_3,plain,
    ! [U_928,U_927,U_930,U_926,U_929] :
      ( c_Orderings_Oord__class_Oless__eq(U_926,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_926),U_927),U_929),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_926),U_928),U_930))
      | ~ c_Orderings_Oord__class_Oless__eq(U_926,c_Groups_Ozero__class_Ozero(U_926),U_929)
      | ~ c_Orderings_Oord__class_Oless__eq(U_926,c_Groups_Ozero__class_Ozero(U_926),U_927)
      | ~ c_Orderings_Oord__class_Oless__eq(U_926,U_929,U_930)
      | ~ c_Orderings_Oord__class_Oless__eq(U_926,U_927,U_928)
      | ~ class_Rings_Oordered__semiring(U_926) ),
    inference(definitional_conversion,[status(esa)],[f_277_2]) ).

cnf(f_277_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_926,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_926),U_927),U_929),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_926),U_928),U_930))
    | ~ c_Orderings_Oord__class_Oless__eq(U_926,c_Groups_Ozero__class_Ozero(U_926),U_929)
    | ~ c_Orderings_Oord__class_Oless__eq(U_926,c_Groups_Ozero__class_Ozero(U_926),U_927)
    | ~ c_Orderings_Oord__class_Oless__eq(U_926,U_929,U_930)
    | ~ c_Orderings_Oord__class_Oless__eq(U_926,U_927,U_928)
    | ~ class_Rings_Oordered__semiring(U_926) ),
    inference(clausify,[status(thm)],[f_277_3]) ).

fof(f_278_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
      | ~ class_Rings_Oordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__left__mono__neg]) ).

fof(f_278_2,plain,
    ! [U_934,U_933,U_932,U_931] :
      ( c_Orderings_Oord__class_Oless__eq(U_931,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_931),U_934),U_933),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_931),U_934),U_932))
      | ~ c_Orderings_Oord__class_Oless__eq(U_931,U_934,c_Groups_Ozero__class_Ozero(U_931))
      | ~ c_Orderings_Oord__class_Oless__eq(U_931,U_932,U_933)
      | ~ class_Rings_Oordered__ring(U_931) ),
    inference(variable_rename,[status(thm)],[f_278_1]) ).

fof(f_278_3,plain,
    ! [U_931,U_932,U_934,U_933] :
      ( c_Orderings_Oord__class_Oless__eq(U_931,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_931),U_934),U_933),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_931),U_934),U_932))
      | ~ c_Orderings_Oord__class_Oless__eq(U_931,U_934,c_Groups_Ozero__class_Ozero(U_931))
      | ~ c_Orderings_Oord__class_Oless__eq(U_931,U_932,U_933)
      | ~ class_Rings_Oordered__ring(U_931) ),
    inference(definitional_conversion,[status(esa)],[f_278_2]) ).

cnf(f_278_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_931,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_931),U_934),U_933),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_931),U_934),U_932))
    | ~ c_Orderings_Oord__class_Oless__eq(U_931,U_934,c_Groups_Ozero__class_Ozero(U_931))
    | ~ c_Orderings_Oord__class_Oless__eq(U_931,U_932,U_933)
    | ~ class_Rings_Oordered__ring(U_931) ),
    inference(clausify,[status(thm)],[f_278_3]) ).

fof(f_279_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
      | ~ class_Rings_Oordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__right__mono__neg]) ).

fof(f_279_2,plain,
    ! [U_938,U_937,U_936,U_935] :
      ( c_Orderings_Oord__class_Oless__eq(U_935,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_935),U_937),U_938),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_935),U_936),U_938))
      | ~ c_Orderings_Oord__class_Oless__eq(U_935,U_938,c_Groups_Ozero__class_Ozero(U_935))
      | ~ c_Orderings_Oord__class_Oless__eq(U_935,U_936,U_937)
      | ~ class_Rings_Oordered__ring(U_935) ),
    inference(variable_rename,[status(thm)],[f_279_1]) ).

fof(f_279_3,plain,
    ! [U_936,U_938,U_935,U_937] :
      ( c_Orderings_Oord__class_Oless__eq(U_935,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_935),U_937),U_938),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_935),U_936),U_938))
      | ~ c_Orderings_Oord__class_Oless__eq(U_935,U_938,c_Groups_Ozero__class_Ozero(U_935))
      | ~ c_Orderings_Oord__class_Oless__eq(U_935,U_936,U_937)
      | ~ class_Rings_Oordered__ring(U_935) ),
    inference(definitional_conversion,[status(esa)],[f_279_2]) ).

cnf(f_279_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_935,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_935),U_937),U_938),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_935),U_936),U_938))
    | ~ c_Orderings_Oord__class_Oless__eq(U_935,U_938,c_Groups_Ozero__class_Ozero(U_935))
    | ~ c_Orderings_Oord__class_Oless__eq(U_935,U_936,U_937)
    | ~ class_Rings_Oordered__ring(U_935) ),
    inference(clausify,[status(thm)],[f_279_3]) ).

fof(f_280_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
      | ~ class_Rings_Oordered__comm__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__mult__left__mono]) ).

fof(f_280_2,plain,
    ! [U_942,U_941,U_940,U_939] :
      ( c_Orderings_Oord__class_Oless__eq(U_939,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_939),U_942),U_940),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_939),U_942),U_941))
      | ~ c_Orderings_Oord__class_Oless__eq(U_939,c_Groups_Ozero__class_Ozero(U_939),U_942)
      | ~ c_Orderings_Oord__class_Oless__eq(U_939,U_940,U_941)
      | ~ class_Rings_Oordered__comm__semiring(U_939) ),
    inference(variable_rename,[status(thm)],[f_280_1]) ).

fof(f_280_3,plain,
    ! [U_939,U_940,U_941,U_942] :
      ( c_Orderings_Oord__class_Oless__eq(U_939,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_939),U_942),U_940),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_939),U_942),U_941))
      | ~ c_Orderings_Oord__class_Oless__eq(U_939,c_Groups_Ozero__class_Ozero(U_939),U_942)
      | ~ c_Orderings_Oord__class_Oless__eq(U_939,U_940,U_941)
      | ~ class_Rings_Oordered__comm__semiring(U_939) ),
    inference(definitional_conversion,[status(esa)],[f_280_2]) ).

cnf(f_280_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_939,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_939),U_942),U_940),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_939),U_942),U_941))
    | ~ c_Orderings_Oord__class_Oless__eq(U_939,c_Groups_Ozero__class_Ozero(U_939),U_942)
    | ~ c_Orderings_Oord__class_Oless__eq(U_939,U_940,U_941)
    | ~ class_Rings_Oordered__comm__semiring(U_939) ),
    inference(clausify,[status(thm)],[f_280_3]) ).

fof(f_281_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
      | ~ class_Rings_Oordered__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__left__mono]) ).

fof(f_281_2,plain,
    ! [U_946,U_945,U_944,U_943] :
      ( c_Orderings_Oord__class_Oless__eq(U_943,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_943),U_946),U_944),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_943),U_946),U_945))
      | ~ c_Orderings_Oord__class_Oless__eq(U_943,c_Groups_Ozero__class_Ozero(U_943),U_946)
      | ~ c_Orderings_Oord__class_Oless__eq(U_943,U_944,U_945)
      | ~ class_Rings_Oordered__semiring(U_943) ),
    inference(variable_rename,[status(thm)],[f_281_1]) ).

fof(f_281_3,plain,
    ! [U_943,U_944,U_945,U_946] :
      ( c_Orderings_Oord__class_Oless__eq(U_943,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_943),U_946),U_944),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_943),U_946),U_945))
      | ~ c_Orderings_Oord__class_Oless__eq(U_943,c_Groups_Ozero__class_Ozero(U_943),U_946)
      | ~ c_Orderings_Oord__class_Oless__eq(U_943,U_944,U_945)
      | ~ class_Rings_Oordered__semiring(U_943) ),
    inference(definitional_conversion,[status(esa)],[f_281_2]) ).

cnf(f_281_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_943,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_943),U_946),U_944),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_943),U_946),U_945))
    | ~ c_Orderings_Oord__class_Oless__eq(U_943,c_Groups_Ozero__class_Ozero(U_943),U_946)
    | ~ c_Orderings_Oord__class_Oless__eq(U_943,U_944,U_945)
    | ~ class_Rings_Oordered__semiring(U_943) ),
    inference(clausify,[status(thm)],[f_281_3]) ).

fof(f_282_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
      | ~ class_Rings_Oordered__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__right__mono]) ).

fof(f_282_2,plain,
    ! [U_950,U_949,U_948,U_947] :
      ( c_Orderings_Oord__class_Oless__eq(U_947,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_947),U_948),U_950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_947),U_949),U_950))
      | ~ c_Orderings_Oord__class_Oless__eq(U_947,c_Groups_Ozero__class_Ozero(U_947),U_950)
      | ~ c_Orderings_Oord__class_Oless__eq(U_947,U_948,U_949)
      | ~ class_Rings_Oordered__semiring(U_947) ),
    inference(variable_rename,[status(thm)],[f_282_1]) ).

fof(f_282_3,plain,
    ! [U_947,U_950,U_949,U_948] :
      ( c_Orderings_Oord__class_Oless__eq(U_947,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_947),U_948),U_950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_947),U_949),U_950))
      | ~ c_Orderings_Oord__class_Oless__eq(U_947,c_Groups_Ozero__class_Ozero(U_947),U_950)
      | ~ c_Orderings_Oord__class_Oless__eq(U_947,U_948,U_949)
      | ~ class_Rings_Oordered__semiring(U_947) ),
    inference(definitional_conversion,[status(esa)],[f_282_2]) ).

cnf(f_282_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_947,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_947),U_948),U_950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_947),U_949),U_950))
    | ~ c_Orderings_Oord__class_Oless__eq(U_947,c_Groups_Ozero__class_Ozero(U_947),U_950)
    | ~ c_Orderings_Oord__class_Oless__eq(U_947,U_948,U_949)
    | ~ class_Rings_Oordered__semiring(U_947) ),
    inference(clausify,[status(thm)],[f_282_3]) ).

fof(f_283_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
      | ~ class_Rings_Oordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonpos]) ).

fof(f_283_2,plain,
    ! [U_953,U_952,U_951] :
      ( c_Orderings_Oord__class_Oless__eq(U_951,c_Groups_Ozero__class_Ozero(U_951),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_951),U_952),U_953))
      | ~ c_Orderings_Oord__class_Oless__eq(U_951,U_953,c_Groups_Ozero__class_Ozero(U_951))
      | ~ c_Orderings_Oord__class_Oless__eq(U_951,U_952,c_Groups_Ozero__class_Ozero(U_951))
      | ~ class_Rings_Oordered__ring(U_951) ),
    inference(variable_rename,[status(thm)],[f_283_1]) ).

fof(f_283_3,plain,
    ! [U_951,U_952,U_953] :
      ( c_Orderings_Oord__class_Oless__eq(U_951,c_Groups_Ozero__class_Ozero(U_951),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_951),U_952),U_953))
      | ~ c_Orderings_Oord__class_Oless__eq(U_951,U_953,c_Groups_Ozero__class_Ozero(U_951))
      | ~ c_Orderings_Oord__class_Oless__eq(U_951,U_952,c_Groups_Ozero__class_Ozero(U_951))
      | ~ class_Rings_Oordered__ring(U_951) ),
    inference(definitional_conversion,[status(esa)],[f_283_2]) ).

cnf(f_283_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_951,c_Groups_Ozero__class_Ozero(U_951),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_951),U_952),U_953))
    | ~ c_Orderings_Oord__class_Oless__eq(U_951,U_953,c_Groups_Ozero__class_Ozero(U_951))
    | ~ c_Orderings_Oord__class_Oless__eq(U_951,U_952,c_Groups_Ozero__class_Ozero(U_951))
    | ~ class_Rings_Oordered__ring(U_951) ),
    inference(clausify,[status(thm)],[f_283_3]) ).

fof(f_284_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
      | ~ class_Rings_Oordered__cancel__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonneg]) ).

fof(f_284_2,plain,
    ! [U_956,U_955,U_954] :
      ( c_Orderings_Oord__class_Oless__eq(U_954,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_954),U_955),U_956),c_Groups_Ozero__class_Ozero(U_954))
      | ~ c_Orderings_Oord__class_Oless__eq(U_954,c_Groups_Ozero__class_Ozero(U_954),U_956)
      | ~ c_Orderings_Oord__class_Oless__eq(U_954,U_955,c_Groups_Ozero__class_Ozero(U_954))
      | ~ class_Rings_Oordered__cancel__semiring(U_954) ),
    inference(variable_rename,[status(thm)],[f_284_1]) ).

fof(f_284_3,plain,
    ! [U_954,U_955,U_956] :
      ( c_Orderings_Oord__class_Oless__eq(U_954,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_954),U_955),U_956),c_Groups_Ozero__class_Ozero(U_954))
      | ~ c_Orderings_Oord__class_Oless__eq(U_954,c_Groups_Ozero__class_Ozero(U_954),U_956)
      | ~ c_Orderings_Oord__class_Oless__eq(U_954,U_955,c_Groups_Ozero__class_Ozero(U_954))
      | ~ class_Rings_Oordered__cancel__semiring(U_954) ),
    inference(definitional_conversion,[status(esa)],[f_284_2]) ).

cnf(f_284_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_954,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_954),U_955),U_956),c_Groups_Ozero__class_Ozero(U_954))
    | ~ c_Orderings_Oord__class_Oless__eq(U_954,c_Groups_Ozero__class_Ozero(U_954),U_956)
    | ~ c_Orderings_Oord__class_Oless__eq(U_954,U_955,c_Groups_Ozero__class_Ozero(U_954))
    | ~ class_Rings_Oordered__cancel__semiring(U_954) ),
    inference(clausify,[status(thm)],[f_284_3]) ).

fof(f_285_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ class_Rings_Oordered__cancel__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos2]) ).

fof(f_285_2,plain,
    ! [U_959,U_958,U_957] :
      ( c_Orderings_Oord__class_Oless__eq(U_957,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_957),U_959),U_958),c_Groups_Ozero__class_Ozero(U_957))
      | ~ c_Orderings_Oord__class_Oless__eq(U_957,U_959,c_Groups_Ozero__class_Ozero(U_957))
      | ~ c_Orderings_Oord__class_Oless__eq(U_957,c_Groups_Ozero__class_Ozero(U_957),U_958)
      | ~ class_Rings_Oordered__cancel__semiring(U_957) ),
    inference(variable_rename,[status(thm)],[f_285_1]) ).

fof(f_285_3,plain,
    ! [U_958,U_959,U_957] :
      ( c_Orderings_Oord__class_Oless__eq(U_957,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_957),U_959),U_958),c_Groups_Ozero__class_Ozero(U_957))
      | ~ c_Orderings_Oord__class_Oless__eq(U_957,U_959,c_Groups_Ozero__class_Ozero(U_957))
      | ~ c_Orderings_Oord__class_Oless__eq(U_957,c_Groups_Ozero__class_Ozero(U_957),U_958)
      | ~ class_Rings_Oordered__cancel__semiring(U_957) ),
    inference(definitional_conversion,[status(esa)],[f_285_2]) ).

cnf(f_285_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_957,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_957),U_959),U_958),c_Groups_Ozero__class_Ozero(U_957))
    | ~ c_Orderings_Oord__class_Oless__eq(U_957,U_959,c_Groups_Ozero__class_Ozero(U_957))
    | ~ c_Orderings_Oord__class_Oless__eq(U_957,c_Groups_Ozero__class_Ozero(U_957),U_958)
    | ~ class_Rings_Oordered__cancel__semiring(U_957) ),
    inference(clausify,[status(thm)],[f_285_3]) ).

fof(f_286_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ class_Rings_Oordered__cancel__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos]) ).

fof(f_286_2,plain,
    ! [U_962,U_961,U_960] :
      ( c_Orderings_Oord__class_Oless__eq(U_960,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_960),U_961),U_962),c_Groups_Ozero__class_Ozero(U_960))
      | ~ c_Orderings_Oord__class_Oless__eq(U_960,U_962,c_Groups_Ozero__class_Ozero(U_960))
      | ~ c_Orderings_Oord__class_Oless__eq(U_960,c_Groups_Ozero__class_Ozero(U_960),U_961)
      | ~ class_Rings_Oordered__cancel__semiring(U_960) ),
    inference(variable_rename,[status(thm)],[f_286_1]) ).

fof(f_286_3,plain,
    ! [U_960,U_962,U_961] :
      ( c_Orderings_Oord__class_Oless__eq(U_960,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_960),U_961),U_962),c_Groups_Ozero__class_Ozero(U_960))
      | ~ c_Orderings_Oord__class_Oless__eq(U_960,U_962,c_Groups_Ozero__class_Ozero(U_960))
      | ~ c_Orderings_Oord__class_Oless__eq(U_960,c_Groups_Ozero__class_Ozero(U_960),U_961)
      | ~ class_Rings_Oordered__cancel__semiring(U_960) ),
    inference(definitional_conversion,[status(esa)],[f_286_2]) ).

cnf(f_286_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_960,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_960),U_961),U_962),c_Groups_Ozero__class_Ozero(U_960))
    | ~ c_Orderings_Oord__class_Oless__eq(U_960,U_962,c_Groups_Ozero__class_Ozero(U_960))
    | ~ c_Orderings_Oord__class_Oless__eq(U_960,c_Groups_Ozero__class_Ozero(U_960),U_961)
    | ~ class_Rings_Oordered__cancel__semiring(U_960) ),
    inference(clausify,[status(thm)],[f_286_3]) ).

fof(f_287_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ class_Rings_Oordered__cancel__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonneg]) ).

fof(f_287_2,plain,
    ! [U_965,U_964,U_963] :
      ( c_Orderings_Oord__class_Oless__eq(U_963,c_Groups_Ozero__class_Ozero(U_963),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_963),U_964),U_965))
      | ~ c_Orderings_Oord__class_Oless__eq(U_963,c_Groups_Ozero__class_Ozero(U_963),U_965)
      | ~ c_Orderings_Oord__class_Oless__eq(U_963,c_Groups_Ozero__class_Ozero(U_963),U_964)
      | ~ class_Rings_Oordered__cancel__semiring(U_963) ),
    inference(variable_rename,[status(thm)],[f_287_1]) ).

fof(f_287_3,plain,
    ! [U_963,U_965,U_964] :
      ( c_Orderings_Oord__class_Oless__eq(U_963,c_Groups_Ozero__class_Ozero(U_963),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_963),U_964),U_965))
      | ~ c_Orderings_Oord__class_Oless__eq(U_963,c_Groups_Ozero__class_Ozero(U_963),U_965)
      | ~ c_Orderings_Oord__class_Oless__eq(U_963,c_Groups_Ozero__class_Ozero(U_963),U_964)
      | ~ class_Rings_Oordered__cancel__semiring(U_963) ),
    inference(definitional_conversion,[status(esa)],[f_287_2]) ).

cnf(f_287_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_963,c_Groups_Ozero__class_Ozero(U_963),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_963),U_964),U_965))
    | ~ c_Orderings_Oord__class_Oless__eq(U_963,c_Groups_Ozero__class_Ozero(U_963),U_965)
    | ~ c_Orderings_Oord__class_Oless__eq(U_963,c_Groups_Ozero__class_Ozero(U_963),U_964)
    | ~ class_Rings_Oordered__cancel__semiring(U_963) ),
    inference(clausify,[status(thm)],[f_287_3]) ).

fof(f_288_1,plain,
    ! [V_b_2,V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a))
          | ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
              | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) )
            & ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
              | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) ) ) )
        & ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
            & c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) )
          | ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
            & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) )
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_b_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff]) ).

fof(f_288_2,plain,
    ! [U_968,U_967,U_966] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_967),U_968),c_Groups_Ozero__class_Ozero(U_966))
          | ( ( ~ c_Orderings_Oord__class_Oless__eq(U_966,c_Groups_Ozero__class_Ozero(U_966),U_968)
              | ~ c_Orderings_Oord__class_Oless__eq(U_966,U_967,c_Groups_Ozero__class_Ozero(U_966)) )
            & ( ~ c_Orderings_Oord__class_Oless__eq(U_966,U_968,c_Groups_Ozero__class_Ozero(U_966))
              | ~ c_Orderings_Oord__class_Oless__eq(U_966,c_Groups_Ozero__class_Ozero(U_966),U_967) ) ) )
        & ( ( c_Orderings_Oord__class_Oless__eq(U_966,c_Groups_Ozero__class_Ozero(U_966),U_968)
            & c_Orderings_Oord__class_Oless__eq(U_966,U_967,c_Groups_Ozero__class_Ozero(U_966)) )
          | ( c_Orderings_Oord__class_Oless__eq(U_966,U_968,c_Groups_Ozero__class_Ozero(U_966))
            & c_Orderings_Oord__class_Oless__eq(U_966,c_Groups_Ozero__class_Ozero(U_966),U_967) )
          | ~ c_Orderings_Oord__class_Oless__eq(U_966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_967),U_968),c_Groups_Ozero__class_Ozero(U_966)) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_966) ),
    inference(variable_rename,[status(thm)],[f_288_1]) ).

fof(f_288_3,plain,
    ( ! [U_967,U_966,U_968] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_966,c_Groups_Ozero__class_Ozero(U_966),U_968)
        | ~ c_Orderings_Oord__class_Oless__eq(U_966,U_967,c_Groups_Ozero__class_Ozero(U_966))
        | ~ sP68(U_967,U_966,U_968) )
    & ! [U_967,U_966,U_968] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_966,U_968,c_Groups_Ozero__class_Ozero(U_966))
        | ~ c_Orderings_Oord__class_Oless__eq(U_966,c_Groups_Ozero__class_Ozero(U_966),U_967)
        | ~ sP68(U_967,U_966,U_968) )
    & ! [U_967,U_966,U_968] :
        ( c_Orderings_Oord__class_Oless__eq(U_966,c_Groups_Ozero__class_Ozero(U_966),U_968)
        | ~ sP67(U_967,U_966,U_968) )
    & ! [U_967,U_966,U_968] :
        ( c_Orderings_Oord__class_Oless__eq(U_966,U_967,c_Groups_Ozero__class_Ozero(U_966))
        | ~ sP67(U_967,U_966,U_968) )
    & ! [U_967,U_966,U_968] :
        ( c_Orderings_Oord__class_Oless__eq(U_966,U_968,c_Groups_Ozero__class_Ozero(U_966))
        | ~ sP66(U_967,U_966,U_968) )
    & ! [U_967,U_966,U_968] :
        ( c_Orderings_Oord__class_Oless__eq(U_966,c_Groups_Ozero__class_Ozero(U_966),U_967)
        | ~ sP66(U_967,U_966,U_968) )
    & ! [U_967,U_966,U_968] :
        ( c_Orderings_Oord__class_Oless__eq(U_966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_967),U_968),c_Groups_Ozero__class_Ozero(U_966))
        | sP68(U_967,U_966,U_968)
        | ~ sP69(U_967,U_966,U_968) )
    & ! [U_967,U_966,U_968] :
        ( sP67(U_967,U_966,U_968)
        | sP66(U_967,U_966,U_968)
        | ~ c_Orderings_Oord__class_Oless__eq(U_966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_967),U_968),c_Groups_Ozero__class_Ozero(U_966))
        | ~ sP69(U_967,U_966,U_968) )
    & ! [U_967,U_966,U_968] :
        ( sP69(U_967,U_966,U_968)
        | ~ class_Rings_Olinordered__ring__strict(U_966) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP66,sP67,sP68,sP69])],[f_288_2]) ).

cnf(f_288_4,plain,
    ( sP69(U_967,U_966,U_968)
    | ~ class_Rings_Olinordered__ring__strict(U_966) ),
    inference(clausify,[status(thm)],[f_288_3]) ).

cnf(f_288_5,plain,
    ( sP67(U_967,U_966,U_968)
    | sP66(U_967,U_966,U_968)
    | ~ c_Orderings_Oord__class_Oless__eq(U_966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_967),U_968),c_Groups_Ozero__class_Ozero(U_966))
    | ~ sP69(U_967,U_966,U_968) ),
    inference(clausify,[status(thm)],[f_288_3]) ).

cnf(f_288_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_967),U_968),c_Groups_Ozero__class_Ozero(U_966))
    | sP68(U_967,U_966,U_968)
    | ~ sP69(U_967,U_966,U_968) ),
    inference(clausify,[status(thm)],[f_288_3]) ).

cnf(f_288_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_966,c_Groups_Ozero__class_Ozero(U_966),U_967)
    | ~ sP66(U_967,U_966,U_968) ),
    inference(clausify,[status(thm)],[f_288_3]) ).

cnf(f_288_8,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_966,U_968,c_Groups_Ozero__class_Ozero(U_966))
    | ~ sP66(U_967,U_966,U_968) ),
    inference(clausify,[status(thm)],[f_288_3]) ).

cnf(f_288_9,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_966,U_967,c_Groups_Ozero__class_Ozero(U_966))
    | ~ sP67(U_967,U_966,U_968) ),
    inference(clausify,[status(thm)],[f_288_3]) ).

cnf(f_288_10,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_966,c_Groups_Ozero__class_Ozero(U_966),U_968)
    | ~ sP67(U_967,U_966,U_968) ),
    inference(clausify,[status(thm)],[f_288_3]) ).

cnf(f_288_11,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_966,U_968,c_Groups_Ozero__class_Ozero(U_966))
    | ~ c_Orderings_Oord__class_Oless__eq(U_966,c_Groups_Ozero__class_Ozero(U_966),U_967)
    | ~ sP68(U_967,U_966,U_968) ),
    inference(clausify,[status(thm)],[f_288_3]) ).

cnf(f_288_12,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_966,c_Groups_Ozero__class_Ozero(U_966),U_968)
    | ~ c_Orderings_Oord__class_Oless__eq(U_966,U_967,c_Groups_Ozero__class_Ozero(U_966))
    | ~ sP68(U_967,U_966,U_968) ),
    inference(clausify,[status(thm)],[f_288_3]) ).

fof(f_289_1,plain,
    ! [V_b_2,V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_b_2))
          | ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
              | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) )
            & ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
              | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) ) ) )
        & ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))
            & c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) )
          | ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)
            & c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) )
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_b_2)) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff]) ).

fof(f_289_2,plain,
    ! [U_971,U_970,U_969] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_969,c_Groups_Ozero__class_Ozero(U_969),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_969),U_970),U_971))
          | ( ( ~ c_Orderings_Oord__class_Oless__eq(U_969,U_971,c_Groups_Ozero__class_Ozero(U_969))
              | ~ c_Orderings_Oord__class_Oless__eq(U_969,U_970,c_Groups_Ozero__class_Ozero(U_969)) )
            & ( ~ c_Orderings_Oord__class_Oless__eq(U_969,c_Groups_Ozero__class_Ozero(U_969),U_971)
              | ~ c_Orderings_Oord__class_Oless__eq(U_969,c_Groups_Ozero__class_Ozero(U_969),U_970) ) ) )
        & ( ( c_Orderings_Oord__class_Oless__eq(U_969,U_971,c_Groups_Ozero__class_Ozero(U_969))
            & c_Orderings_Oord__class_Oless__eq(U_969,U_970,c_Groups_Ozero__class_Ozero(U_969)) )
          | ( c_Orderings_Oord__class_Oless__eq(U_969,c_Groups_Ozero__class_Ozero(U_969),U_971)
            & c_Orderings_Oord__class_Oless__eq(U_969,c_Groups_Ozero__class_Ozero(U_969),U_970) )
          | ~ c_Orderings_Oord__class_Oless__eq(U_969,c_Groups_Ozero__class_Ozero(U_969),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_969),U_970),U_971)) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_969) ),
    inference(variable_rename,[status(thm)],[f_289_1]) ).

fof(f_289_3,plain,
    ( ! [U_970,U_969,U_971] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_969,U_971,c_Groups_Ozero__class_Ozero(U_969))
        | ~ c_Orderings_Oord__class_Oless__eq(U_969,U_970,c_Groups_Ozero__class_Ozero(U_969))
        | ~ sP72(U_970,U_969,U_971) )
    & ! [U_970,U_969,U_971] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_969,c_Groups_Ozero__class_Ozero(U_969),U_971)
        | ~ c_Orderings_Oord__class_Oless__eq(U_969,c_Groups_Ozero__class_Ozero(U_969),U_970)
        | ~ sP72(U_970,U_969,U_971) )
    & ! [U_970,U_969,U_971] :
        ( c_Orderings_Oord__class_Oless__eq(U_969,U_971,c_Groups_Ozero__class_Ozero(U_969))
        | ~ sP71(U_970,U_969,U_971) )
    & ! [U_970,U_969,U_971] :
        ( c_Orderings_Oord__class_Oless__eq(U_969,U_970,c_Groups_Ozero__class_Ozero(U_969))
        | ~ sP71(U_970,U_969,U_971) )
    & ! [U_970,U_969,U_971] :
        ( c_Orderings_Oord__class_Oless__eq(U_969,c_Groups_Ozero__class_Ozero(U_969),U_971)
        | ~ sP70(U_970,U_969,U_971) )
    & ! [U_970,U_969,U_971] :
        ( c_Orderings_Oord__class_Oless__eq(U_969,c_Groups_Ozero__class_Ozero(U_969),U_970)
        | ~ sP70(U_970,U_969,U_971) )
    & ! [U_970,U_969,U_971] :
        ( c_Orderings_Oord__class_Oless__eq(U_969,c_Groups_Ozero__class_Ozero(U_969),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_969),U_970),U_971))
        | sP72(U_970,U_969,U_971)
        | ~ sP73(U_970,U_969,U_971) )
    & ! [U_970,U_969,U_971] :
        ( sP71(U_970,U_969,U_971)
        | sP70(U_970,U_969,U_971)
        | ~ c_Orderings_Oord__class_Oless__eq(U_969,c_Groups_Ozero__class_Ozero(U_969),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_969),U_970),U_971))
        | ~ sP73(U_970,U_969,U_971) )
    & ! [U_970,U_969,U_971] :
        ( sP73(U_970,U_969,U_971)
        | ~ class_Rings_Olinordered__ring__strict(U_969) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP70,sP71,sP72,sP73])],[f_289_2]) ).

cnf(f_289_4,plain,
    ( sP73(U_970,U_969,U_971)
    | ~ class_Rings_Olinordered__ring__strict(U_969) ),
    inference(clausify,[status(thm)],[f_289_3]) ).

cnf(f_289_5,plain,
    ( sP71(U_970,U_969,U_971)
    | sP70(U_970,U_969,U_971)
    | ~ c_Orderings_Oord__class_Oless__eq(U_969,c_Groups_Ozero__class_Ozero(U_969),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_969),U_970),U_971))
    | ~ sP73(U_970,U_969,U_971) ),
    inference(clausify,[status(thm)],[f_289_3]) ).

cnf(f_289_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_969,c_Groups_Ozero__class_Ozero(U_969),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_969),U_970),U_971))
    | sP72(U_970,U_969,U_971)
    | ~ sP73(U_970,U_969,U_971) ),
    inference(clausify,[status(thm)],[f_289_3]) ).

cnf(f_289_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_969,c_Groups_Ozero__class_Ozero(U_969),U_970)
    | ~ sP70(U_970,U_969,U_971) ),
    inference(clausify,[status(thm)],[f_289_3]) ).

cnf(f_289_8,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_969,c_Groups_Ozero__class_Ozero(U_969),U_971)
    | ~ sP70(U_970,U_969,U_971) ),
    inference(clausify,[status(thm)],[f_289_3]) ).

cnf(f_289_9,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_969,U_970,c_Groups_Ozero__class_Ozero(U_969))
    | ~ sP71(U_970,U_969,U_971) ),
    inference(clausify,[status(thm)],[f_289_3]) ).

cnf(f_289_10,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_969,U_971,c_Groups_Ozero__class_Ozero(U_969))
    | ~ sP71(U_970,U_969,U_971) ),
    inference(clausify,[status(thm)],[f_289_3]) ).

cnf(f_289_11,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_969,c_Groups_Ozero__class_Ozero(U_969),U_971)
    | ~ c_Orderings_Oord__class_Oless__eq(U_969,c_Groups_Ozero__class_Ozero(U_969),U_970)
    | ~ sP72(U_970,U_969,U_971) ),
    inference(clausify,[status(thm)],[f_289_3]) ).

cnf(f_289_12,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_969,U_971,c_Groups_Ozero__class_Ozero(U_969))
    | ~ c_Orderings_Oord__class_Oless__eq(U_969,U_970,c_Groups_Ozero__class_Ozero(U_969))
    | ~ sP72(U_970,U_969,U_971) ),
    inference(clausify,[status(thm)],[f_289_3]) ).

fof(f_290_1,plain,
    ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2),V_n_2) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2),V_n_2)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2) ),
    inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff1]) ).

fof(f_290_2,plain,
    ! [U_976,U_975,U_974,U_973,U_972] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_973),U_974),U_975),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_972),U_974),U_976))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_973,U_972)),U_974),U_975),U_976) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_973,U_972)),U_974),U_975),U_976)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_973),U_974),U_975),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_972),U_974),U_976)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_972,U_973) ),
    inference(variable_rename,[status(thm)],[f_290_1]) ).

fof(f_290_3,plain,
    ( ! [U_975,U_976,U_973,U_974,U_972] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_973),U_974),U_975),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_972),U_974),U_976))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_973,U_972)),U_974),U_975),U_976)
        | ~ sP74(U_975,U_976,U_973,U_974,U_972) )
    & ! [U_975,U_976,U_973,U_974,U_972] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_973,U_972)),U_974),U_975),U_976)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_973),U_974),U_975),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_972),U_974),U_976))
        | ~ sP74(U_975,U_976,U_973,U_974,U_972) )
    & ! [U_975,U_976,U_973,U_974,U_972] :
        ( sP74(U_975,U_976,U_973,U_974,U_972)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_972,U_973) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP74])],[f_290_2]) ).

cnf(f_290_4,plain,
    ( sP74(U_975,U_976,U_973,U_974,U_972)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_972,U_973) ),
    inference(clausify,[status(thm)],[f_290_3]) ).

cnf(f_290_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_973,U_972)),U_974),U_975),U_976)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_973),U_974),U_975),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_972),U_974),U_976))
    | ~ sP74(U_975,U_976,U_973,U_974,U_972) ),
    inference(clausify,[status(thm)],[f_290_3]) ).

cnf(f_290_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_973),U_974),U_975),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_972),U_974),U_976))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_973,U_972)),U_974),U_975),U_976)
    | ~ sP74(U_975,U_976,U_973,U_974,U_972) ),
    inference(clausify,[status(thm)],[f_290_3]) ).

fof(f_291_1,plain,
    ! [V_n,V_m,V_u,V_i,V_j] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j)),V_u),V_m),V_n)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_i) ),
    inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq1]) ).

fof(f_291_2,plain,
    ! [U_981,U_980,U_979,U_978,U_977] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_978),U_979),U_980),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_977),U_979),U_981)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_978,U_977)),U_979),U_980),U_981)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_977,U_978) ),
    inference(variable_rename,[status(thm)],[f_291_1]) ).

fof(f_291_3,plain,
    ! [U_979,U_977,U_978,U_981,U_980] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_978),U_979),U_980),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_977),U_979),U_981)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_978,U_977)),U_979),U_980),U_981)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_977,U_978) ),
    inference(definitional_conversion,[status(esa)],[f_291_2]) ).

cnf(f_291_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_978),U_979),U_980),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_977),U_979),U_981)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_978,U_977)),U_979),U_980),U_981)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_977,U_978) ),
    inference(clausify,[status(thm)],[f_291_3]) ).

fof(f_292_1,plain,
    ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
      ( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)
          | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2) != V_n_2 )
        & ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2) = V_n_2
          | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2) ),
    inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff1]) ).

fof(f_292_2,plain,
    ! [U_986,U_985,U_984,U_983,U_982] :
      ( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_983),U_984),U_985) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_982),U_984),U_986)
          | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_983,U_982)),U_984),U_985) != U_986 )
        & ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_983,U_982)),U_984),U_985) = U_986
          | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_983),U_984),U_985) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_982),U_984),U_986) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_982,U_983) ),
    inference(variable_rename,[status(thm)],[f_292_1]) ).

fof(f_292_3,plain,
    ( ! [U_982,U_983,U_984,U_985,U_986] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_983),U_984),U_985) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_982),U_984),U_986)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_983,U_982)),U_984),U_985) != U_986
        | ~ sP75(U_982,U_983,U_984,U_985,U_986) )
    & ! [U_982,U_983,U_984,U_985,U_986] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_983,U_982)),U_984),U_985) = U_986
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_983),U_984),U_985) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_982),U_984),U_986)
        | ~ sP75(U_982,U_983,U_984,U_985,U_986) )
    & ! [U_982,U_983,U_984,U_985,U_986] :
        ( sP75(U_982,U_983,U_984,U_985,U_986)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_982,U_983) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP75])],[f_292_2]) ).

cnf(f_292_4,plain,
    ( sP75(U_982,U_983,U_984,U_985,U_986)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_982,U_983) ),
    inference(clausify,[status(thm)],[f_292_3]) ).

cnf(f_292_5,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_983,U_982)),U_984),U_985) = U_986
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_983),U_984),U_985) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_982),U_984),U_986)
    | ~ sP75(U_982,U_983,U_984,U_985,U_986) ),
    inference(clausify,[status(thm)],[f_292_3]) ).

cnf(f_292_6,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_983),U_984),U_985) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_982),U_984),U_986)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_983,U_982)),U_984),U_985) != U_986
    | ~ sP75(U_982,U_983,U_984,U_985,U_986) ),
    inference(clausify,[status(thm)],[f_292_3]) ).

fof(f_293_1,plain,
    ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2)) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) ),
    inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff2]) ).

fof(f_293_2,plain,
    ! [U_991,U_990,U_989,U_988,U_987] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_987),U_989),U_990),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_988),U_989),U_991))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_990,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_988,U_987)),U_989),U_991)) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_990,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_988,U_987)),U_989),U_991))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_987),U_989),U_990),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_988),U_989),U_991)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_987,U_988) ),
    inference(variable_rename,[status(thm)],[f_293_1]) ).

fof(f_293_3,plain,
    ( ! [U_989,U_991,U_988,U_987,U_990] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_987),U_989),U_990),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_988),U_989),U_991))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_990,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_988,U_987)),U_989),U_991))
        | ~ sP76(U_989,U_991,U_988,U_987,U_990) )
    & ! [U_989,U_991,U_988,U_987,U_990] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_990,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_988,U_987)),U_989),U_991))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_987),U_989),U_990),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_988),U_989),U_991))
        | ~ sP76(U_989,U_991,U_988,U_987,U_990) )
    & ! [U_989,U_991,U_988,U_987,U_990] :
        ( sP76(U_989,U_991,U_988,U_987,U_990)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_987,U_988) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP76])],[f_293_2]) ).

cnf(f_293_4,plain,
    ( sP76(U_989,U_991,U_988,U_987,U_990)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_987,U_988) ),
    inference(clausify,[status(thm)],[f_293_3]) ).

cnf(f_293_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_990,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_988,U_987)),U_989),U_991))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_987),U_989),U_990),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_988),U_989),U_991))
    | ~ sP76(U_989,U_991,U_988,U_987,U_990) ),
    inference(clausify,[status(thm)],[f_293_3]) ).

cnf(f_293_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_987),U_989),U_990),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_988),U_989),U_991))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_990,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_988,U_987)),U_989),U_991))
    | ~ sP76(U_989,U_991,U_988,U_987,U_990) ),
    inference(clausify,[status(thm)],[f_293_3]) ).

fof(f_294_1,plain,
    ! [V_n,V_m,V_u,V_j,V_i] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u),V_n))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq2]) ).

fof(f_294_2,plain,
    ! [U_996,U_995,U_994,U_993,U_992] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_992),U_994),U_995),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_993),U_994),U_996)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_995,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_993,U_992)),U_994),U_996))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_992,U_993) ),
    inference(variable_rename,[status(thm)],[f_294_1]) ).

fof(f_294_3,plain,
    ! [U_993,U_995,U_994,U_996,U_992] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_992),U_994),U_995),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_993),U_994),U_996)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_995,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_993,U_992)),U_994),U_996))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_992,U_993) ),
    inference(definitional_conversion,[status(esa)],[f_294_2]) ).

cnf(f_294_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_992),U_994),U_995),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_993),U_994),U_996)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_995,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_993,U_992)),U_994),U_996))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_992,U_993) ),
    inference(clausify,[status(thm)],[f_294_3]) ).

fof(f_295_1,plain,
    ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
      ( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)
          | V_m_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2) )
        & ( V_m_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2)
          | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) ),
    inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff2]) ).

fof(f_295_2,plain,
    ! [U_1001,U_1000,U_999,U_998,U_997] :
      ( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_997),U_999),U_1000) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_998),U_999),U_1001)
          | U_1000 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_998,U_997)),U_999),U_1001) )
        & ( U_1000 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_998,U_997)),U_999),U_1001)
          | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_997),U_999),U_1000) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_998),U_999),U_1001) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_997,U_998) ),
    inference(variable_rename,[status(thm)],[f_295_1]) ).

fof(f_295_3,plain,
    ( ! [U_997,U_998,U_999,U_1000,U_1001] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_997),U_999),U_1000) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_998),U_999),U_1001)
        | U_1000 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_998,U_997)),U_999),U_1001)
        | ~ sP77(U_997,U_998,U_999,U_1000,U_1001) )
    & ! [U_997,U_998,U_999,U_1000,U_1001] :
        ( U_1000 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_998,U_997)),U_999),U_1001)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_997),U_999),U_1000) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_998),U_999),U_1001)
        | ~ sP77(U_997,U_998,U_999,U_1000,U_1001) )
    & ! [U_997,U_998,U_999,U_1000,U_1001] :
        ( sP77(U_997,U_998,U_999,U_1000,U_1001)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_997,U_998) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP77])],[f_295_2]) ).

cnf(f_295_4,plain,
    ( sP77(U_997,U_998,U_999,U_1000,U_1001)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_997,U_998) ),
    inference(clausify,[status(thm)],[f_295_3]) ).

cnf(f_295_5,plain,
    ( U_1000 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_998,U_997)),U_999),U_1001)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_997),U_999),U_1000) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_998),U_999),U_1001)
    | ~ sP77(U_997,U_998,U_999,U_1000,U_1001) ),
    inference(clausify,[status(thm)],[f_295_3]) ).

cnf(f_295_6,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_997),U_999),U_1000) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_998),U_999),U_1001)
    | U_1000 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_998,U_997)),U_999),U_1001)
    | ~ sP77(U_997,U_998,U_999,U_1000,U_1001) ),
    inference(clausify,[status(thm)],[f_295_3]) ).

fof(f_296_1,plain,
    ! [V_q,V_p,V_a,T_a] :
      ( c_Polynomial_Opcompose(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),c_Polynomial_Opcompose(T_a,V_p,V_q)))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_pcompose__pCons]) ).

fof(f_296_2,plain,
    ! [U_1005,U_1004,U_1003,U_1002] :
      ( c_Polynomial_Opcompose(U_1002,c_Polynomial_OpCons(U_1002,U_1003,U_1004),U_1005) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1002),c_Polynomial_OpCons(U_1002,U_1003,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1002))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1002)),U_1005),c_Polynomial_Opcompose(U_1002,U_1004,U_1005)))
      | ~ class_Rings_Ocomm__semiring__0(U_1002) ),
    inference(variable_rename,[status(thm)],[f_296_1]) ).

fof(f_296_3,plain,
    ! [U_1004,U_1003,U_1002,U_1005] :
      ( c_Polynomial_Opcompose(U_1002,c_Polynomial_OpCons(U_1002,U_1003,U_1004),U_1005) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1002),c_Polynomial_OpCons(U_1002,U_1003,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1002))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1002)),U_1005),c_Polynomial_Opcompose(U_1002,U_1004,U_1005)))
      | ~ class_Rings_Ocomm__semiring__0(U_1002) ),
    inference(definitional_conversion,[status(esa)],[f_296_2]) ).

cnf(f_296_4,plain,
    ( c_Polynomial_Opcompose(U_1002,c_Polynomial_OpCons(U_1002,U_1003,U_1004),U_1005) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1002),c_Polynomial_OpCons(U_1002,U_1003,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1002))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1002)),U_1005),c_Polynomial_Opcompose(U_1002,U_1004,U_1005)))
    | ~ class_Rings_Ocomm__semiring__0(U_1002) ),
    inference(clausify,[status(thm)],[f_296_3]) ).

fof(f_297_1,plain,
    ! [V_q,T_a] :
      ( c_Polynomial_Opcompose(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_pcompose__0]) ).

fof(f_297_2,plain,
    ! [U_1007,U_1006] :
      ( c_Polynomial_Opcompose(U_1006,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1006)),U_1007) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1006))
      | ~ class_Rings_Ocomm__semiring__0(U_1006) ),
    inference(variable_rename,[status(thm)],[f_297_1]) ).

fof(f_297_3,plain,
    ! [U_1006,U_1007] :
      ( c_Polynomial_Opcompose(U_1006,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1006)),U_1007) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1006))
      | ~ class_Rings_Ocomm__semiring__0(U_1006) ),
    inference(definitional_conversion,[status(esa)],[f_297_2]) ).

cnf(f_297_4,plain,
    ( c_Polynomial_Opcompose(U_1006,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1006)),U_1007) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1006))
    | ~ class_Rings_Ocomm__semiring__0(U_1006) ),
    inference(clausify,[status(thm)],[f_297_3]) ).

fof(f_298_1,plain,
    ! [V_x,V_q,V_p,T_a] :
      ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Opcompose(T_a,V_p,V_q)),V_x) = hAPP(c_Polynomial_Opoly(T_a,V_p),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))
      | ~ class_Rings_Ocomm__semiring__0(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_poly__pcompose]) ).

fof(f_298_2,plain,
    ! [U_1011,U_1010,U_1009,U_1008] :
      ( hAPP(c_Polynomial_Opoly(U_1008,c_Polynomial_Opcompose(U_1008,U_1009,U_1010)),U_1011) = hAPP(c_Polynomial_Opoly(U_1008,U_1009),hAPP(c_Polynomial_Opoly(U_1008,U_1010),U_1011))
      | ~ class_Rings_Ocomm__semiring__0(U_1008) ),
    inference(variable_rename,[status(thm)],[f_298_1]) ).

fof(f_298_3,plain,
    ! [U_1008,U_1009,U_1010,U_1011] :
      ( hAPP(c_Polynomial_Opoly(U_1008,c_Polynomial_Opcompose(U_1008,U_1009,U_1010)),U_1011) = hAPP(c_Polynomial_Opoly(U_1008,U_1009),hAPP(c_Polynomial_Opoly(U_1008,U_1010),U_1011))
      | ~ class_Rings_Ocomm__semiring__0(U_1008) ),
    inference(definitional_conversion,[status(esa)],[f_298_2]) ).

cnf(f_298_4,plain,
    ( hAPP(c_Polynomial_Opoly(U_1008,c_Polynomial_Opcompose(U_1008,U_1009,U_1010)),U_1011) = hAPP(c_Polynomial_Opoly(U_1008,U_1009),hAPP(c_Polynomial_Opoly(U_1008,U_1010),U_1011))
    | ~ class_Rings_Ocomm__semiring__0(U_1008) ),
    inference(clausify,[status(thm)],[f_298_3]) ).

fof(f_299_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
        | ( V_m_2 != V_n_2
          & V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( V_m_2 = V_n_2
        | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj]) ).

fof(f_299_2,plain,
    ! [U_1014,U_1013,U_1012] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1012),U_1013) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1012),U_1014)
        | ( U_1013 != U_1014
          & U_1012 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_1013 = U_1014
        | U_1012 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1012),U_1013) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1012),U_1014) ) ),
    inference(variable_rename,[status(thm)],[f_299_1]) ).

fof(f_299_3,plain,
    ( ! [U_1020,U_1018,U_1016] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1016),U_1018) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1016),U_1020)
        | ( U_1018 != U_1020
          & U_1016 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_1019,U_1017,U_1015] :
        ( U_1017 = U_1019
        | U_1015 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1015),U_1017) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1015),U_1019) ) ),
    inference(miniscope,[status(thm)],[f_299_2]) ).

fof(f_299_4,plain,
    ( ! [U_1020,U_1018,U_1016] :
        ( U_1018 != U_1020
        | ~ sP78(U_1020,U_1018,U_1016) )
    & ! [U_1020,U_1018,U_1016] :
        ( U_1016 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP78(U_1020,U_1018,U_1016) )
    & ! [U_1020,U_1018,U_1016] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1016),U_1018) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1016),U_1020)
        | sP78(U_1020,U_1018,U_1016) )
    & ! [U_1017,U_1015,U_1019] :
        ( U_1017 = U_1019
        | U_1015 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1015),U_1017) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1015),U_1019) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP78])],[f_299_3]) ).

cnf(f_299_5,plain,
    ( U_1017 = U_1019
    | U_1015 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1015),U_1017) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1015),U_1019) ),
    inference(clausify,[status(thm)],[f_299_4]) ).

cnf(f_299_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1016),U_1018) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1016),U_1020)
    | sP78(U_1020,U_1018,U_1016) ),
    inference(clausify,[status(thm)],[f_299_4]) ).

cnf(f_299_7,plain,
    ( U_1016 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP78(U_1020,U_1018,U_1016) ),
    inference(clausify,[status(thm)],[f_299_4]) ).

cnf(f_299_8,plain,
    ( U_1018 != U_1020
    | ~ sP78(U_1020,U_1018,U_1016) ),
    inference(clausify,[status(thm)],[f_299_4]) ).

fof(f_300_1,plain,
    ! [V_k,V_j,V_u,V_i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j)),V_u),V_k),
    inference(fof_nnf,[status(thm)],[fact_left__add__mult__distrib]) ).

fof(f_300_2,plain,
    ! [U_1024,U_1023,U_1022,U_1021] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1021),U_1022),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1023),U_1022),U_1024)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1021,U_1023)),U_1022),U_1024),
    inference(variable_rename,[status(thm)],[f_300_1]) ).

fof(f_300_3,plain,
    ! [U_1024,U_1021,U_1023,U_1022] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1021),U_1022),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1023),U_1022),U_1024)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1021,U_1023)),U_1022),U_1024),
    inference(definitional_conversion,[status(esa)],[f_300_2]) ).

cnf(f_300_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1021),U_1022),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1023),U_1022),U_1024)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1021,U_1023)),U_1022),U_1024),
    inference(clausify,[status(thm)],[f_300_3]) ).

fof(f_301_1,plain,
    ! [V_z,V_y,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y) ),
    inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J]) ).

fof(f_301_2,plain,
    ! [U_1027,U_1026,U_1025] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1025,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1026,U_1027))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1025,U_1026) ),
    inference(variable_rename,[status(thm)],[f_301_1]) ).

fof(f_301_3,plain,
    ! [U_1027,U_1025,U_1026] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1025,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1026,U_1027))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1025,U_1026) ),
    inference(definitional_conversion,[status(esa)],[f_301_2]) ).

cnf(f_301_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1025,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1026,U_1027))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1025,U_1026) ),
    inference(clausify,[status(thm)],[f_301_3]) ).

fof(f_302_1,plain,
    ! [V_y,V_z,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_z) ),
    inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J]) ).

fof(f_302_2,plain,
    ! [U_1030,U_1029,U_1028] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1028,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1030,U_1029))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1028,U_1029) ),
    inference(variable_rename,[status(thm)],[f_302_1]) ).

fof(f_302_3,plain,
    ! [U_1030,U_1029,U_1028] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1028,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1030,U_1029))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1028,U_1029) ),
    inference(definitional_conversion,[status(esa)],[f_302_2]) ).

cnf(f_302_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1028,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1030,U_1029))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1028,U_1029) ),
    inference(clausify,[status(thm)],[f_302_3]) ).

fof(f_303_1,plain,
    ! [V_d,V_b,V_c,V_a,T_a] :
      ( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d))
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Deriv_Oadd__diff__add]) ).

fof(f_303_2,plain,
    ! [U_1035,U_1034,U_1033,U_1032,U_1031] :
      ( c_Groups_Ominus__class_Ominus(U_1031,c_Groups_Oplus__class_Oplus(U_1031,U_1032,U_1033),c_Groups_Oplus__class_Oplus(U_1031,U_1034,U_1035)) = c_Groups_Oplus__class_Oplus(U_1031,c_Groups_Ominus__class_Ominus(U_1031,U_1032,U_1034),c_Groups_Ominus__class_Ominus(U_1031,U_1033,U_1035))
      | ~ class_Groups_Oab__group__add(U_1031) ),
    inference(variable_rename,[status(thm)],[f_303_1]) ).

fof(f_303_3,plain,
    ! [U_1031,U_1032,U_1033,U_1034,U_1035] :
      ( c_Groups_Ominus__class_Ominus(U_1031,c_Groups_Oplus__class_Oplus(U_1031,U_1032,U_1033),c_Groups_Oplus__class_Oplus(U_1031,U_1034,U_1035)) = c_Groups_Oplus__class_Oplus(U_1031,c_Groups_Ominus__class_Ominus(U_1031,U_1032,U_1034),c_Groups_Ominus__class_Ominus(U_1031,U_1033,U_1035))
      | ~ class_Groups_Oab__group__add(U_1031) ),
    inference(definitional_conversion,[status(esa)],[f_303_2]) ).

cnf(f_303_4,plain,
    ( c_Groups_Ominus__class_Ominus(U_1031,c_Groups_Oplus__class_Oplus(U_1031,U_1032,U_1033),c_Groups_Oplus__class_Oplus(U_1031,U_1034,U_1035)) = c_Groups_Oplus__class_Oplus(U_1031,c_Groups_Ominus__class_Ominus(U_1031,U_1032,U_1034),c_Groups_Ominus__class_Ominus(U_1031,U_1033,U_1035))
    | ~ class_Groups_Oab__group__add(U_1031) ),
    inference(clausify,[status(thm)],[f_303_3]) ).

fof(f_304_1,plain,
    ! [T_a] :
      ( ? [B_K] :
          ( ! [B_a,B_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult_Ononneg__bounded]) ).

fof(f_304_2,plain,
    ! [U_1039] :
      ( ? [U_1038] :
          ( ! [U_1037,U_1036] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1039,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1039),U_1037),U_1036)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1039,U_1037)),c_RealVector_Onorm__class_Onorm(U_1039,U_1036))),U_1038))
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1038) )
      | ~ class_RealVector_Oreal__normed__algebra(U_1039) ),
    inference(variable_rename,[status(thm)],[f_304_1]) ).

fof(f_304_3,plain,
    ! [U_1039] :
      ( ( ! [U_1037,U_1036] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1039,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1039),U_1037),U_1036)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1039,U_1037)),c_RealVector_Onorm__class_Onorm(U_1039,U_1036))),sK7(U_1039)))
        & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK7(U_1039)) )
      | ~ class_RealVector_Oreal__normed__algebra(U_1039) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_1038,sK7(U_1039))],[f_304_2]) ).

fof(f_304_4,plain,
    ( ! [U_1037,U_1036,U_1039] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1039,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1039),U_1037),U_1036)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1039,U_1037)),c_RealVector_Onorm__class_Onorm(U_1039,U_1036))),sK7(U_1039)))
        | ~ sP79(U_1037,U_1036,U_1039) )
    & ! [U_1037,U_1036,U_1039] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK7(U_1039))
        | ~ sP79(U_1037,U_1036,U_1039) )
    & ! [U_1037,U_1036,U_1039] :
        ( sP79(U_1037,U_1036,U_1039)
        | ~ class_RealVector_Oreal__normed__algebra(U_1039) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP79])],[f_304_3]) ).

cnf(f_304_5,plain,
    ( sP79(U_1037,U_1036,U_1039)
    | ~ class_RealVector_Oreal__normed__algebra(U_1039) ),
    inference(clausify,[status(thm)],[f_304_4]) ).

cnf(f_304_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK7(U_1039))
    | ~ sP79(U_1037,U_1036,U_1039) ),
    inference(clausify,[status(thm)],[f_304_4]) ).

cnf(f_304_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1039,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1039),U_1037),U_1036)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1039,U_1037)),c_RealVector_Onorm__class_Onorm(U_1039,U_1036))),sK7(U_1039)))
    | ~ sP79(U_1037,U_1036,U_1039) ),
    inference(clausify,[status(thm)],[f_304_4]) ).

fof(f_305_1,plain,
    ! [V_x,T_a] :
      ( ? [B_K] :
          ( ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__right_Ononneg__bounded]) ).

fof(f_305_2,plain,
    ! [U_1043,U_1042] :
      ( ? [U_1041] :
          ( ! [U_1040] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1042),U_1043),U_1040)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1042,U_1040)),U_1041))
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1041) )
      | ~ class_RealVector_Oreal__normed__algebra(U_1042) ),
    inference(variable_rename,[status(thm)],[f_305_1]) ).

fof(f_305_3,plain,
    ! [U_1043,U_1042] :
      ( ( ! [U_1040] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1042),U_1043),U_1040)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1042,U_1040)),sK8(U_1043,U_1042)))
        & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK8(U_1043,U_1042)) )
      | ~ class_RealVector_Oreal__normed__algebra(U_1042) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_1041,sK8(U_1043,U_1042))],[f_305_2]) ).

fof(f_305_4,plain,
    ( ! [U_1040,U_1042,U_1043] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1042),U_1043),U_1040)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1042,U_1040)),sK8(U_1043,U_1042)))
        | ~ sP80(U_1040,U_1042,U_1043) )
    & ! [U_1040,U_1042,U_1043] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK8(U_1043,U_1042))
        | ~ sP80(U_1040,U_1042,U_1043) )
    & ! [U_1040,U_1042,U_1043] :
        ( sP80(U_1040,U_1042,U_1043)
        | ~ class_RealVector_Oreal__normed__algebra(U_1042) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP80])],[f_305_3]) ).

cnf(f_305_5,plain,
    ( sP80(U_1040,U_1042,U_1043)
    | ~ class_RealVector_Oreal__normed__algebra(U_1042) ),
    inference(clausify,[status(thm)],[f_305_4]) ).

cnf(f_305_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK8(U_1043,U_1042))
    | ~ sP80(U_1040,U_1042,U_1043) ),
    inference(clausify,[status(thm)],[f_305_4]) ).

cnf(f_305_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1042),U_1043),U_1040)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1042,U_1040)),sK8(U_1043,U_1042)))
    | ~ sP80(U_1040,U_1042,U_1043) ),
    inference(clausify,[status(thm)],[f_305_4]) ).

fof(f_306_1,plain,
    ! [V_y,T_a] :
      ( ? [B_K] :
          ( ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__left_Ononneg__bounded]) ).

fof(f_306_2,plain,
    ! [U_1047,U_1046] :
      ( ? [U_1045] :
          ( ! [U_1044] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1046,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1046),U_1044),U_1047)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1046,U_1044)),U_1045))
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1045) )
      | ~ class_RealVector_Oreal__normed__algebra(U_1046) ),
    inference(variable_rename,[status(thm)],[f_306_1]) ).

fof(f_306_3,plain,
    ! [U_1047,U_1046] :
      ( ( ! [U_1044] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1046,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1046),U_1044),U_1047)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1046,U_1044)),sK9(U_1047,U_1046)))
        & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK9(U_1047,U_1046)) )
      | ~ class_RealVector_Oreal__normed__algebra(U_1046) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_1045,sK9(U_1047,U_1046))],[f_306_2]) ).

fof(f_306_4,plain,
    ( ! [U_1044,U_1046,U_1047] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1046,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1046),U_1044),U_1047)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1046,U_1044)),sK9(U_1047,U_1046)))
        | ~ sP81(U_1044,U_1046,U_1047) )
    & ! [U_1044,U_1046,U_1047] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK9(U_1047,U_1046))
        | ~ sP81(U_1044,U_1046,U_1047) )
    & ! [U_1044,U_1046,U_1047] :
        ( sP81(U_1044,U_1046,U_1047)
        | ~ class_RealVector_Oreal__normed__algebra(U_1046) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP81])],[f_306_3]) ).

cnf(f_306_5,plain,
    ( sP81(U_1044,U_1046,U_1047)
    | ~ class_RealVector_Oreal__normed__algebra(U_1046) ),
    inference(clausify,[status(thm)],[f_306_4]) ).

cnf(f_306_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK9(U_1047,U_1046))
    | ~ sP81(U_1044,U_1046,U_1047) ),
    inference(clausify,[status(thm)],[f_306_4]) ).

cnf(f_306_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1046,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1046),U_1044),U_1047)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1046,U_1044)),sK9(U_1047,U_1046)))
    | ~ sP81(U_1044,U_1046,U_1047) ),
    inference(clausify,[status(thm)],[f_306_4]) ).

fof(f_307_1,plain,
    ! [T_a] :
      ( ? [B_K] :
        ! [B_a,B_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult_Obounded]) ).

fof(f_307_2,plain,
    ! [U_1051] :
      ( ? [U_1050] :
        ! [U_1049,U_1048] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1051,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1051),U_1049),U_1048)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1051,U_1049)),c_RealVector_Onorm__class_Onorm(U_1051,U_1048))),U_1050))
      | ~ class_RealVector_Oreal__normed__algebra(U_1051) ),
    inference(variable_rename,[status(thm)],[f_307_1]) ).

fof(f_307_3,plain,
    ! [U_1051] :
      ( ! [U_1049,U_1048] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1051,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1051),U_1049),U_1048)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1051,U_1049)),c_RealVector_Onorm__class_Onorm(U_1051,U_1048))),sK10(U_1051)))
      | ~ class_RealVector_Oreal__normed__algebra(U_1051) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_1050,sK10(U_1051))],[f_307_2]) ).

fof(f_307_4,plain,
    ! [U_1048,U_1049,U_1051] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1051,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1051),U_1049),U_1048)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1051,U_1049)),c_RealVector_Onorm__class_Onorm(U_1051,U_1048))),sK10(U_1051)))
      | ~ class_RealVector_Oreal__normed__algebra(U_1051) ),
    inference(definitional_conversion,[status(esa)],[f_307_3]) ).

cnf(f_307_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1051,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1051),U_1049),U_1048)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1051,U_1049)),c_RealVector_Onorm__class_Onorm(U_1051,U_1048))),sK10(U_1051)))
    | ~ class_RealVector_Oreal__normed__algebra(U_1051) ),
    inference(clausify,[status(thm)],[f_307_4]) ).

fof(f_308_1,plain,
    ! [V_x,T_a] :
      ( ? [B_K] :
        ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__right_Obounded]) ).

fof(f_308_2,plain,
    ! [U_1055,U_1054] :
      ( ? [U_1053] :
        ! [U_1052] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1054,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1054),U_1055),U_1052)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1054,U_1052)),U_1053))
      | ~ class_RealVector_Oreal__normed__algebra(U_1054) ),
    inference(variable_rename,[status(thm)],[f_308_1]) ).

fof(f_308_3,plain,
    ! [U_1055,U_1054] :
      ( ! [U_1052] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1054,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1054),U_1055),U_1052)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1054,U_1052)),sK11(U_1055,U_1054)))
      | ~ class_RealVector_Oreal__normed__algebra(U_1054) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_1053,sK11(U_1055,U_1054))],[f_308_2]) ).

fof(f_308_4,plain,
    ! [U_1052,U_1054,U_1055] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1054,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1054),U_1055),U_1052)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1054,U_1052)),sK11(U_1055,U_1054)))
      | ~ class_RealVector_Oreal__normed__algebra(U_1054) ),
    inference(definitional_conversion,[status(esa)],[f_308_3]) ).

cnf(f_308_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1054,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1054),U_1055),U_1052)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1054,U_1052)),sK11(U_1055,U_1054)))
    | ~ class_RealVector_Oreal__normed__algebra(U_1054) ),
    inference(clausify,[status(thm)],[f_308_4]) ).

fof(f_309_1,plain,
    ! [V_y,T_a] :
      ( ? [B_K] :
        ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__left_Obounded]) ).

fof(f_309_2,plain,
    ! [U_1059,U_1058] :
      ( ? [U_1057] :
        ! [U_1056] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1058,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1058),U_1056),U_1059)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1058,U_1056)),U_1057))
      | ~ class_RealVector_Oreal__normed__algebra(U_1058) ),
    inference(variable_rename,[status(thm)],[f_309_1]) ).

fof(f_309_3,plain,
    ! [U_1059,U_1058] :
      ( ! [U_1056] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1058,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1058),U_1056),U_1059)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1058,U_1056)),sK12(U_1059,U_1058)))
      | ~ class_RealVector_Oreal__normed__algebra(U_1058) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_1057,sK12(U_1059,U_1058))],[f_309_2]) ).

fof(f_309_4,plain,
    ! [U_1056,U_1058,U_1059] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1058,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1058),U_1056),U_1059)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1058,U_1056)),sK12(U_1059,U_1058)))
      | ~ class_RealVector_Oreal__normed__algebra(U_1058) ),
    inference(definitional_conversion,[status(esa)],[f_309_3]) ).

cnf(f_309_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1058,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1058),U_1056),U_1059)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1058,U_1056)),sK12(U_1059,U_1058)))
    | ~ class_RealVector_Oreal__normed__algebra(U_1058) ),
    inference(clausify,[status(thm)],[f_309_4]) ).

fof(f_310_1,plain,
    ! [V_n,V_m] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n))
        | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__eq__if]) ).

fof(f_310_2,plain,
    ! [U_1061,U_1060] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1060),U_1061) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1061,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1060,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_1061))
        | U_1060 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1060),U_1061) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1060 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_310_1]) ).

fof(f_310_3,plain,
    ( ! [U_1065,U_1063] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1063),U_1065) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1065,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1063,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_1065))
        | U_1063 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1064,U_1062] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1062),U_1064) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1062 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_310_2]) ).

fof(f_310_4,plain,
    ( ! [U_1063,U_1065] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1063),U_1065) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1065,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1063,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_1065))
        | U_1063 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1062,U_1064] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1062),U_1064) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1062 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_310_3]) ).

cnf(f_310_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1062),U_1064) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_1062 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_310_4]) ).

cnf(f_310_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1063),U_1065) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1065,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1063,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_1065))
    | U_1063 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_310_4]) ).

fof(f_311_1,plain,
    ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2),V_n_2) )
        & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2),V_n_2)
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2) ),
    inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff1]) ).

fof(f_311_2,plain,
    ! [U_1070,U_1069,U_1068,U_1067,U_1066] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1067),U_1068),U_1069),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1066),U_1068),U_1070))
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1067,U_1066)),U_1068),U_1069),U_1070) )
        & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1067,U_1066)),U_1068),U_1069),U_1070)
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1067),U_1068),U_1069),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1066),U_1068),U_1070)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1066,U_1067) ),
    inference(variable_rename,[status(thm)],[f_311_1]) ).

fof(f_311_3,plain,
    ( ! [U_1066,U_1067,U_1068,U_1069,U_1070] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1067),U_1068),U_1069),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1066),U_1068),U_1070))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1067,U_1066)),U_1068),U_1069),U_1070)
        | ~ sP82(U_1066,U_1067,U_1068,U_1069,U_1070) )
    & ! [U_1066,U_1067,U_1068,U_1069,U_1070] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1067,U_1066)),U_1068),U_1069),U_1070)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1067),U_1068),U_1069),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1066),U_1068),U_1070))
        | ~ sP82(U_1066,U_1067,U_1068,U_1069,U_1070) )
    & ! [U_1066,U_1067,U_1068,U_1069,U_1070] :
        ( sP82(U_1066,U_1067,U_1068,U_1069,U_1070)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1066,U_1067) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP82])],[f_311_2]) ).

cnf(f_311_4,plain,
    ( sP82(U_1066,U_1067,U_1068,U_1069,U_1070)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1066,U_1067) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1067,U_1066)),U_1068),U_1069),U_1070)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1067),U_1068),U_1069),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1066),U_1068),U_1070))
    | ~ sP82(U_1066,U_1067,U_1068,U_1069,U_1070) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

cnf(f_311_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1067),U_1068),U_1069),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1066),U_1068),U_1070))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1067,U_1066)),U_1068),U_1069),U_1070)
    | ~ sP82(U_1066,U_1067,U_1068,U_1069,U_1070) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

fof(f_312_1,plain,
    ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2)) )
        & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2))
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) ),
    inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff2]) ).

fof(f_312_2,plain,
    ! [U_1075,U_1074,U_1073,U_1072,U_1071] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1071),U_1073),U_1074),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1072),U_1073),U_1075))
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1074,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1072,U_1071)),U_1073),U_1075)) )
        & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1074,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1072,U_1071)),U_1073),U_1075))
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1071),U_1073),U_1074),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1072),U_1073),U_1075)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1071,U_1072) ),
    inference(variable_rename,[status(thm)],[f_312_1]) ).

fof(f_312_3,plain,
    ( ! [U_1072,U_1075,U_1074,U_1071,U_1073] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1071),U_1073),U_1074),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1072),U_1073),U_1075))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1074,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1072,U_1071)),U_1073),U_1075))
        | ~ sP83(U_1072,U_1075,U_1074,U_1071,U_1073) )
    & ! [U_1072,U_1075,U_1074,U_1071,U_1073] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1074,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1072,U_1071)),U_1073),U_1075))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1071),U_1073),U_1074),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1072),U_1073),U_1075))
        | ~ sP83(U_1072,U_1075,U_1074,U_1071,U_1073) )
    & ! [U_1072,U_1075,U_1074,U_1071,U_1073] :
        ( sP83(U_1072,U_1075,U_1074,U_1071,U_1073)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1071,U_1072) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP83])],[f_312_2]) ).

cnf(f_312_4,plain,
    ( sP83(U_1072,U_1075,U_1074,U_1071,U_1073)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1071,U_1072) ),
    inference(clausify,[status(thm)],[f_312_3]) ).

cnf(f_312_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1074,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1072,U_1071)),U_1073),U_1075))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1071),U_1073),U_1074),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1072),U_1073),U_1075))
    | ~ sP83(U_1072,U_1075,U_1074,U_1071,U_1073) ),
    inference(clausify,[status(thm)],[f_312_3]) ).

cnf(f_312_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1071),U_1073),U_1074),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1072),U_1073),U_1075))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1074,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1072,U_1071)),U_1073),U_1075))
    | ~ sP83(U_1072,U_1075,U_1074,U_1071,U_1073) ),
    inference(clausify,[status(thm)],[f_312_3]) ).

fof(f_313_1,plain,
    ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_less__zeroE]) ).

fof(f_313_2,plain,
    ! [U_1076] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1076,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_313_1]) ).

fof(f_313_3,plain,
    ! [U_1076] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1076,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_313_2]) ).

cnf(f_313_4,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1076,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_313_3]) ).

fof(f_314_1,plain,
    ! [V_n,V_m,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n))
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__1__mult]) ).

fof(f_314_2,plain,
    ! [U_1079,U_1078,U_1077] :
      ( c_Orderings_Oord__class_Oless(U_1077,c_Groups_Oone__class_Oone(U_1077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1077),U_1078),U_1079))
      | ~ c_Orderings_Oord__class_Oless(U_1077,c_Groups_Oone__class_Oone(U_1077),U_1079)
      | ~ c_Orderings_Oord__class_Oless(U_1077,c_Groups_Oone__class_Oone(U_1077),U_1078)
      | ~ class_Rings_Olinordered__semidom(U_1077) ),
    inference(variable_rename,[status(thm)],[f_314_1]) ).

fof(f_314_3,plain,
    ! [U_1079,U_1077,U_1078] :
      ( c_Orderings_Oord__class_Oless(U_1077,c_Groups_Oone__class_Oone(U_1077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1077),U_1078),U_1079))
      | ~ c_Orderings_Oord__class_Oless(U_1077,c_Groups_Oone__class_Oone(U_1077),U_1079)
      | ~ c_Orderings_Oord__class_Oless(U_1077,c_Groups_Oone__class_Oone(U_1077),U_1078)
      | ~ class_Rings_Olinordered__semidom(U_1077) ),
    inference(definitional_conversion,[status(esa)],[f_314_2]) ).

cnf(f_314_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1077,c_Groups_Oone__class_Oone(U_1077),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1077),U_1078),U_1079))
    | ~ c_Orderings_Oord__class_Oless(U_1077,c_Groups_Oone__class_Oone(U_1077),U_1079)
    | ~ c_Orderings_Oord__class_Oless(U_1077,c_Groups_Oone__class_Oone(U_1077),U_1078)
    | ~ class_Rings_Olinordered__semidom(U_1077) ),
    inference(clausify,[status(thm)],[f_314_3]) ).

fof(f_315_1,plain,
    ! [V_y,V_x,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
      | c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
      | V_x = V_y
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).

fof(f_315_2,plain,
    ! [U_1082,U_1081,U_1080] :
      ( c_Orderings_Oord__class_Oless(U_1080,U_1082,U_1081)
      | c_Orderings_Oord__class_Oless(U_1080,U_1081,U_1082)
      | U_1081 = U_1082
      | ~ class_Rings_Olinordered__idom(U_1080) ),
    inference(variable_rename,[status(thm)],[f_315_1]) ).

fof(f_315_3,plain,
    ! [U_1081,U_1082,U_1080] :
      ( c_Orderings_Oord__class_Oless(U_1080,U_1082,U_1081)
      | c_Orderings_Oord__class_Oless(U_1080,U_1081,U_1082)
      | U_1081 = U_1082
      | ~ class_Rings_Olinordered__idom(U_1080) ),
    inference(definitional_conversion,[status(esa)],[f_315_2]) ).

cnf(f_315_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1080,U_1082,U_1081)
    | c_Orderings_Oord__class_Oless(U_1080,U_1081,U_1082)
    | U_1081 = U_1082
    | ~ class_Rings_Olinordered__idom(U_1080) ),
    inference(clausify,[status(thm)],[f_315_3]) ).

fof(f_316_1,plain,
    ! [V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a)))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__add__one]) ).

fof(f_316_2,plain,
    ! [U_1084,U_1083] :
      ( c_Orderings_Oord__class_Oless(U_1083,U_1084,c_Groups_Oplus__class_Oplus(U_1083,U_1084,c_Groups_Oone__class_Oone(U_1083)))
      | ~ class_Rings_Olinordered__semidom(U_1083) ),
    inference(variable_rename,[status(thm)],[f_316_1]) ).

fof(f_316_3,plain,
    ! [U_1084,U_1083] :
      ( c_Orderings_Oord__class_Oless(U_1083,U_1084,c_Groups_Oplus__class_Oplus(U_1083,U_1084,c_Groups_Oone__class_Oone(U_1083)))
      | ~ class_Rings_Olinordered__semidom(U_1083) ),
    inference(definitional_conversion,[status(esa)],[f_316_2]) ).

cnf(f_316_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1083,U_1084,c_Groups_Oplus__class_Oplus(U_1083,U_1084,c_Groups_Oone__class_Oone(U_1083)))
    | ~ class_Rings_Olinordered__semidom(U_1083) ),
    inference(clausify,[status(thm)],[f_316_3]) ).

fof(f_317_1,plain,
    ! [T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__one]) ).

fof(f_317_2,plain,
    ! [U_1085] :
      ( c_Orderings_Oord__class_Oless(U_1085,c_Groups_Ozero__class_Ozero(U_1085),c_Groups_Oone__class_Oone(U_1085))
      | ~ class_Rings_Olinordered__semidom(U_1085) ),
    inference(variable_rename,[status(thm)],[f_317_1]) ).

fof(f_317_3,plain,
    ! [U_1085] :
      ( c_Orderings_Oord__class_Oless(U_1085,c_Groups_Ozero__class_Ozero(U_1085),c_Groups_Oone__class_Oone(U_1085))
      | ~ class_Rings_Olinordered__semidom(U_1085) ),
    inference(definitional_conversion,[status(esa)],[f_317_2]) ).

cnf(f_317_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1085,c_Groups_Ozero__class_Ozero(U_1085),c_Groups_Oone__class_Oone(U_1085))
    | ~ class_Rings_Olinordered__semidom(U_1085) ),
    inference(clausify,[status(thm)],[f_317_3]) ).

fof(f_318_1,plain,
    ! [T_a] :
      ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_not__one__less__zero]) ).

fof(f_318_2,plain,
    ! [U_1086] :
      ( ~ c_Orderings_Oord__class_Oless(U_1086,c_Groups_Oone__class_Oone(U_1086),c_Groups_Ozero__class_Ozero(U_1086))
      | ~ class_Rings_Olinordered__semidom(U_1086) ),
    inference(variable_rename,[status(thm)],[f_318_1]) ).

fof(f_318_3,plain,
    ! [U_1086] :
      ( ~ c_Orderings_Oord__class_Oless(U_1086,c_Groups_Oone__class_Oone(U_1086),c_Groups_Ozero__class_Ozero(U_1086))
      | ~ class_Rings_Olinordered__semidom(U_1086) ),
    inference(definitional_conversion,[status(esa)],[f_318_2]) ).

cnf(f_318_4,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1086,c_Groups_Oone__class_Oone(U_1086),c_Groups_Ozero__class_Ozero(U_1086))
    | ~ class_Rings_Olinordered__semidom(U_1086) ),
    inference(clausify,[status(thm)],[f_318_3]) ).

fof(f_319_1,plain,
    ! [V_x,T_a] :
      ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_poly__1]) ).

fof(f_319_2,plain,
    ! [U_1088,U_1087] :
      ( hAPP(c_Polynomial_Opoly(U_1087,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1087))),U_1088) = c_Groups_Oone__class_Oone(U_1087)
      | ~ class_Rings_Ocomm__semiring__1(U_1087) ),
    inference(variable_rename,[status(thm)],[f_319_1]) ).

fof(f_319_3,plain,
    ! [U_1087,U_1088] :
      ( hAPP(c_Polynomial_Opoly(U_1087,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1087))),U_1088) = c_Groups_Oone__class_Oone(U_1087)
      | ~ class_Rings_Ocomm__semiring__1(U_1087) ),
    inference(definitional_conversion,[status(esa)],[f_319_2]) ).

cnf(f_319_4,plain,
    ( hAPP(c_Polynomial_Opoly(U_1087,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1087))),U_1088) = c_Groups_Oone__class_Oone(U_1087)
    | ~ class_Rings_Ocomm__semiring__1(U_1087) ),
    inference(clausify,[status(thm)],[f_319_3]) ).

fof(f_320_1,plain,
    ! [V_y,V_x,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
      | V_x = V_y
      | c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__cases]) ).

fof(f_320_2,plain,
    ! [U_1091,U_1090,U_1089] :
      ( c_Orderings_Oord__class_Oless(U_1089,U_1091,U_1090)
      | U_1090 = U_1091
      | c_Orderings_Oord__class_Oless(U_1089,U_1090,U_1091)
      | ~ class_Orderings_Olinorder(U_1089) ),
    inference(variable_rename,[status(thm)],[f_320_1]) ).

fof(f_320_3,plain,
    ! [U_1090,U_1089,U_1091] :
      ( c_Orderings_Oord__class_Oless(U_1089,U_1091,U_1090)
      | U_1090 = U_1091
      | c_Orderings_Oord__class_Oless(U_1089,U_1090,U_1091)
      | ~ class_Orderings_Olinorder(U_1089) ),
    inference(definitional_conversion,[status(esa)],[f_320_2]) ).

cnf(f_320_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1089,U_1091,U_1090)
    | U_1090 = U_1091
    | c_Orderings_Oord__class_Oless(U_1089,U_1090,U_1091)
    | ~ class_Orderings_Olinorder(U_1089) ),
    inference(clausify,[status(thm)],[f_320_3]) ).

fof(f_321_1,plain,
    ! [V_y,V_x,T_a] :
      ( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__asym]) ).

fof(f_321_2,plain,
    ! [U_1094,U_1093,U_1092] :
      ( ~ c_Orderings_Oord__class_Oless(U_1092,U_1094,U_1093)
      | ~ c_Orderings_Oord__class_Oless(U_1092,U_1093,U_1094)
      | ~ class_Orderings_Opreorder(U_1092) ),
    inference(variable_rename,[status(thm)],[f_321_1]) ).

fof(f_321_3,plain,
    ! [U_1092,U_1093,U_1094] :
      ( ~ c_Orderings_Oord__class_Oless(U_1092,U_1094,U_1093)
      | ~ c_Orderings_Oord__class_Oless(U_1092,U_1093,U_1094)
      | ~ class_Orderings_Opreorder(U_1092) ),
    inference(definitional_conversion,[status(esa)],[f_321_2]) ).

cnf(f_321_4,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1092,U_1094,U_1093)
    | ~ c_Orderings_Oord__class_Oless(U_1092,U_1093,U_1094)
    | ~ class_Orderings_Opreorder(U_1092) ),
    inference(clausify,[status(thm)],[f_321_3]) ).

fof(f_322_1,plain,
    ! [V_z,V_x,V_y,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I10_J]) ).

fof(f_322_2,plain,
    ! [U_1098,U_1097,U_1096,U_1095] :
      ( c_Orderings_Oord__class_Oless(U_1095,U_1098,U_1097)
      | ~ c_Orderings_Oord__class_Oless(U_1095,U_1098,U_1096)
      | ~ c_Orderings_Oord__class_Oless(U_1095,U_1096,U_1097)
      | ~ class_Orderings_Oorder(U_1095) ),
    inference(variable_rename,[status(thm)],[f_322_1]) ).

fof(f_322_3,plain,
    ! [U_1096,U_1095,U_1097,U_1098] :
      ( c_Orderings_Oord__class_Oless(U_1095,U_1098,U_1097)
      | ~ c_Orderings_Oord__class_Oless(U_1095,U_1098,U_1096)
      | ~ c_Orderings_Oord__class_Oless(U_1095,U_1096,U_1097)
      | ~ class_Orderings_Oorder(U_1095) ),
    inference(definitional_conversion,[status(esa)],[f_322_2]) ).

cnf(f_322_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1095,U_1098,U_1097)
    | ~ c_Orderings_Oord__class_Oless(U_1095,U_1098,U_1096)
    | ~ c_Orderings_Oord__class_Oless(U_1095,U_1096,U_1097)
    | ~ class_Orderings_Oorder(U_1095) ),
    inference(clausify,[status(thm)],[f_322_3]) ).

fof(f_323_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_x,V_z)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__trans]) ).

fof(f_323_2,plain,
    ! [U_1102,U_1101,U_1100,U_1099] :
      ( c_Orderings_Oord__class_Oless(U_1099,U_1100,U_1102)
      | ~ c_Orderings_Oord__class_Oless(U_1099,U_1101,U_1102)
      | ~ c_Orderings_Oord__class_Oless(U_1099,U_1100,U_1101)
      | ~ class_Orderings_Opreorder(U_1099) ),
    inference(variable_rename,[status(thm)],[f_323_1]) ).

fof(f_323_3,plain,
    ! [U_1102,U_1101,U_1100,U_1099] :
      ( c_Orderings_Oord__class_Oless(U_1099,U_1100,U_1102)
      | ~ c_Orderings_Oord__class_Oless(U_1099,U_1101,U_1102)
      | ~ c_Orderings_Oord__class_Oless(U_1099,U_1100,U_1101)
      | ~ class_Orderings_Opreorder(U_1099) ),
    inference(definitional_conversion,[status(esa)],[f_323_2]) ).

cnf(f_323_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1099,U_1100,U_1102)
    | ~ c_Orderings_Oord__class_Oless(U_1099,U_1101,U_1102)
    | ~ c_Orderings_Oord__class_Oless(U_1099,U_1100,U_1101)
    | ~ class_Orderings_Opreorder(U_1099) ),
    inference(clausify,[status(thm)],[f_323_3]) ).

fof(f_324_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
      | V_b != V_c
      | ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I2_J]) ).

fof(f_324_2,plain,
    ! [U_1106,U_1105,U_1104,U_1103] :
      ( c_Orderings_Oord__class_Oless(U_1103,U_1106,U_1105)
      | U_1104 != U_1106
      | ~ c_Orderings_Oord__class_Oless(U_1103,U_1104,U_1105)
      | ~ class_Orderings_Oorder(U_1103) ),
    inference(variable_rename,[status(thm)],[f_324_1]) ).

fof(f_324_3,plain,
    ! [U_1103,U_1105,U_1106,U_1104] :
      ( c_Orderings_Oord__class_Oless(U_1103,U_1106,U_1105)
      | U_1104 != U_1106
      | ~ c_Orderings_Oord__class_Oless(U_1103,U_1104,U_1105)
      | ~ class_Orderings_Oorder(U_1103) ),
    inference(definitional_conversion,[status(esa)],[f_324_2]) ).

cnf(f_324_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1103,U_1106,U_1105)
    | U_1104 != U_1106
    | ~ c_Orderings_Oord__class_Oless(U_1103,U_1104,U_1105)
    | ~ class_Orderings_Oorder(U_1103) ),
    inference(clausify,[status(thm)],[f_324_3]) ).

fof(f_325_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_a,V_c)
      | V_b != V_c
      | ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
      | ~ class_Orderings_Oord(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ord__less__eq__trans]) ).

fof(f_325_2,plain,
    ! [U_1110,U_1109,U_1108,U_1107] :
      ( c_Orderings_Oord__class_Oless(U_1107,U_1108,U_1110)
      | U_1109 != U_1110
      | ~ c_Orderings_Oord__class_Oless(U_1107,U_1108,U_1109)
      | ~ class_Orderings_Oord(U_1107) ),
    inference(variable_rename,[status(thm)],[f_325_1]) ).

fof(f_325_3,plain,
    ! [U_1108,U_1110,U_1109,U_1107] :
      ( c_Orderings_Oord__class_Oless(U_1107,U_1108,U_1110)
      | U_1109 != U_1110
      | ~ c_Orderings_Oord__class_Oless(U_1107,U_1108,U_1109)
      | ~ class_Orderings_Oord(U_1107) ),
    inference(definitional_conversion,[status(esa)],[f_325_2]) ).

cnf(f_325_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1107,U_1108,U_1110)
    | U_1109 != U_1110
    | ~ c_Orderings_Oord__class_Oless(U_1107,U_1108,U_1109)
    | ~ class_Orderings_Oord(U_1107) ),
    inference(clausify,[status(thm)],[f_325_3]) ).

fof(f_326_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_c,V_a)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_c,V_b)
      | V_a != V_b
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I1_J]) ).

fof(f_326_2,plain,
    ! [U_1114,U_1113,U_1112,U_1111] :
      ( c_Orderings_Oord__class_Oless(U_1111,U_1114,U_1112)
      | ~ c_Orderings_Oord__class_Oless(U_1111,U_1114,U_1113)
      | U_1112 != U_1113
      | ~ class_Orderings_Oorder(U_1111) ),
    inference(variable_rename,[status(thm)],[f_326_1]) ).

fof(f_326_3,plain,
    ! [U_1114,U_1113,U_1111,U_1112] :
      ( c_Orderings_Oord__class_Oless(U_1111,U_1114,U_1112)
      | ~ c_Orderings_Oord__class_Oless(U_1111,U_1114,U_1113)
      | U_1112 != U_1113
      | ~ class_Orderings_Oorder(U_1111) ),
    inference(definitional_conversion,[status(esa)],[f_326_2]) ).

cnf(f_326_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1111,U_1114,U_1112)
    | ~ c_Orderings_Oord__class_Oless(U_1111,U_1114,U_1113)
    | U_1112 != U_1113
    | ~ class_Orderings_Oorder(U_1111) ),
    inference(clausify,[status(thm)],[f_326_3]) ).

fof(f_327_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_a,V_c)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
      | V_a != V_b
      | ~ class_Orderings_Oord(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ord__eq__less__trans]) ).

fof(f_327_2,plain,
    ! [U_1118,U_1117,U_1116,U_1115] :
      ( c_Orderings_Oord__class_Oless(U_1115,U_1116,U_1118)
      | ~ c_Orderings_Oord__class_Oless(U_1115,U_1117,U_1118)
      | U_1116 != U_1117
      | ~ class_Orderings_Oord(U_1115) ),
    inference(variable_rename,[status(thm)],[f_327_1]) ).

fof(f_327_3,plain,
    ! [U_1116,U_1118,U_1117,U_1115] :
      ( c_Orderings_Oord__class_Oless(U_1115,U_1116,U_1118)
      | ~ c_Orderings_Oord__class_Oless(U_1115,U_1117,U_1118)
      | U_1116 != U_1117
      | ~ class_Orderings_Oord(U_1115) ),
    inference(definitional_conversion,[status(esa)],[f_327_2]) ).

cnf(f_327_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1115,U_1116,U_1118)
    | ~ c_Orderings_Oord__class_Oless(U_1115,U_1117,U_1118)
    | U_1116 != U_1117
    | ~ class_Orderings_Oord(U_1115) ),
    inference(clausify,[status(thm)],[f_327_3]) ).

fof(f_328_1,plain,
    ! [V_a,V_b,T_a] :
      ( ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I9_J]) ).

fof(f_328_2,plain,
    ! [U_1121,U_1120,U_1119] :
      ( ~ c_Orderings_Oord__class_Oless(U_1119,U_1121,U_1120)
      | ~ c_Orderings_Oord__class_Oless(U_1119,U_1120,U_1121)
      | ~ class_Orderings_Oorder(U_1119) ),
    inference(variable_rename,[status(thm)],[f_328_1]) ).

fof(f_328_3,plain,
    ! [U_1121,U_1119,U_1120] :
      ( ~ c_Orderings_Oord__class_Oless(U_1119,U_1121,U_1120)
      | ~ c_Orderings_Oord__class_Oless(U_1119,U_1120,U_1121)
      | ~ class_Orderings_Oorder(U_1119) ),
    inference(definitional_conversion,[status(esa)],[f_328_2]) ).

cnf(f_328_4,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1119,U_1121,U_1120)
    | ~ c_Orderings_Oord__class_Oless(U_1119,U_1120,U_1121)
    | ~ class_Orderings_Oorder(U_1119) ),
    inference(clausify,[status(thm)],[f_328_3]) ).

fof(f_329_1,plain,
    ! [V_b,V_a,T_a] :
      ( ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__asym_H]) ).

fof(f_329_2,plain,
    ! [U_1124,U_1123,U_1122] :
      ( ~ c_Orderings_Oord__class_Oless(U_1122,U_1124,U_1123)
      | ~ c_Orderings_Oord__class_Oless(U_1122,U_1123,U_1124)
      | ~ class_Orderings_Opreorder(U_1122) ),
    inference(variable_rename,[status(thm)],[f_329_1]) ).

fof(f_329_3,plain,
    ! [U_1124,U_1122,U_1123] :
      ( ~ c_Orderings_Oord__class_Oless(U_1122,U_1124,U_1123)
      | ~ c_Orderings_Oord__class_Oless(U_1122,U_1123,U_1124)
      | ~ class_Orderings_Opreorder(U_1122) ),
    inference(definitional_conversion,[status(esa)],[f_329_2]) ).

cnf(f_329_4,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1122,U_1124,U_1123)
    | ~ c_Orderings_Oord__class_Oless(U_1122,U_1123,U_1124)
    | ~ class_Orderings_Opreorder(U_1122) ),
    inference(clausify,[status(thm)],[f_329_3]) ).

fof(f_330_1,plain,
    ! [V_y,V_x,T_a] :
      ( V_y != V_x
      | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2]) ).

fof(f_330_2,plain,
    ! [U_1127,U_1126,U_1125] :
      ( U_1127 != U_1126
      | ~ c_Orderings_Oord__class_Oless(U_1125,U_1126,U_1127)
      | ~ class_Orderings_Oorder(U_1125) ),
    inference(variable_rename,[status(thm)],[f_330_1]) ).

fof(f_330_3,plain,
    ! [U_1126,U_1125,U_1127] :
      ( U_1127 != U_1126
      | ~ c_Orderings_Oord__class_Oless(U_1125,U_1126,U_1127)
      | ~ class_Orderings_Oorder(U_1125) ),
    inference(definitional_conversion,[status(esa)],[f_330_2]) ).

cnf(f_330_4,plain,
    ( U_1127 != U_1126
    | ~ c_Orderings_Oord__class_Oless(U_1125,U_1126,U_1127)
    | ~ class_Orderings_Oorder(U_1125) ),
    inference(clausify,[status(thm)],[f_330_3]) ).

fof(f_331_1,plain,
    ! [V_y,V_x,T_a] :
      ( V_x != V_y
      | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq]) ).

fof(f_331_2,plain,
    ! [U_1130,U_1129,U_1128] :
      ( U_1129 != U_1130
      | ~ c_Orderings_Oord__class_Oless(U_1128,U_1129,U_1130)
      | ~ class_Orderings_Oorder(U_1128) ),
    inference(variable_rename,[status(thm)],[f_331_1]) ).

fof(f_331_3,plain,
    ! [U_1128,U_1129,U_1130] :
      ( U_1129 != U_1130
      | ~ c_Orderings_Oord__class_Oless(U_1128,U_1129,U_1130)
      | ~ class_Orderings_Oorder(U_1128) ),
    inference(definitional_conversion,[status(esa)],[f_331_2]) ).

cnf(f_331_4,plain,
    ( U_1129 != U_1130
    | ~ c_Orderings_Oord__class_Oless(U_1128,U_1129,U_1130)
    | ~ class_Orderings_Oorder(U_1128) ),
    inference(clausify,[status(thm)],[f_331_3]) ).

fof(f_332_1,plain,
    ! [V_y,V_x,T_a] :
      ( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__less]) ).

fof(f_332_2,plain,
    ! [U_1133,U_1132,U_1131] :
      ( ~ c_Orderings_Oord__class_Oless(U_1131,U_1133,U_1132)
      | ~ c_Orderings_Oord__class_Oless(U_1131,U_1132,U_1133)
      | ~ class_Orderings_Opreorder(U_1131) ),
    inference(variable_rename,[status(thm)],[f_332_1]) ).

fof(f_332_3,plain,
    ! [U_1133,U_1132,U_1131] :
      ( ~ c_Orderings_Oord__class_Oless(U_1131,U_1133,U_1132)
      | ~ c_Orderings_Oord__class_Oless(U_1131,U_1132,U_1133)
      | ~ class_Orderings_Opreorder(U_1131) ),
    inference(definitional_conversion,[status(esa)],[f_332_2]) ).

cnf(f_332_4,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1131,U_1133,U_1132)
    | ~ c_Orderings_Oord__class_Oless(U_1131,U_1132,U_1133)
    | ~ class_Orderings_Opreorder(U_1131) ),
    inference(clausify,[status(thm)],[f_332_3]) ).

fof(f_333_1,plain,
    ! [V_y,V_x,T_a] :
      ( ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__not__sym]) ).

fof(f_333_2,plain,
    ! [U_1136,U_1135,U_1134] :
      ( ~ c_Orderings_Oord__class_Oless(U_1134,U_1136,U_1135)
      | ~ c_Orderings_Oord__class_Oless(U_1134,U_1135,U_1136)
      | ~ class_Orderings_Opreorder(U_1134) ),
    inference(variable_rename,[status(thm)],[f_333_1]) ).

fof(f_333_3,plain,
    ! [U_1136,U_1134,U_1135] :
      ( ~ c_Orderings_Oord__class_Oless(U_1134,U_1136,U_1135)
      | ~ c_Orderings_Oord__class_Oless(U_1134,U_1135,U_1136)
      | ~ class_Orderings_Opreorder(U_1134) ),
    inference(definitional_conversion,[status(esa)],[f_333_2]) ).

cnf(f_333_4,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1134,U_1136,U_1135)
    | ~ c_Orderings_Oord__class_Oless(U_1134,U_1135,U_1136)
    | ~ class_Orderings_Opreorder(U_1134) ),
    inference(clausify,[status(thm)],[f_333_3]) ).

fof(f_334_1,plain,
    ! [V_y,V_x,T_a] :
      ( V_x != V_y
      | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__imp__neq]) ).

fof(f_334_2,plain,
    ! [U_1139,U_1138,U_1137] :
      ( U_1138 != U_1139
      | ~ c_Orderings_Oord__class_Oless(U_1137,U_1138,U_1139)
      | ~ class_Orderings_Oorder(U_1137) ),
    inference(variable_rename,[status(thm)],[f_334_1]) ).

fof(f_334_3,plain,
    ! [U_1137,U_1138,U_1139] :
      ( U_1138 != U_1139
      | ~ c_Orderings_Oord__class_Oless(U_1137,U_1138,U_1139)
      | ~ class_Orderings_Oorder(U_1137) ),
    inference(definitional_conversion,[status(esa)],[f_334_2]) ).

cnf(f_334_4,plain,
    ( U_1138 != U_1139
    | ~ c_Orderings_Oord__class_Oless(U_1137,U_1138,U_1139)
    | ~ class_Orderings_Oorder(U_1137) ),
    inference(clausify,[status(thm)],[f_334_3]) ).

fof(f_335_1,plain,
    ! [V_y,V_x,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
      | c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
      | V_x = V_y
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__neqE]) ).

fof(f_335_2,plain,
    ! [U_1142,U_1141,U_1140] :
      ( c_Orderings_Oord__class_Oless(U_1140,U_1142,U_1141)
      | c_Orderings_Oord__class_Oless(U_1140,U_1141,U_1142)
      | U_1141 = U_1142
      | ~ class_Orderings_Olinorder(U_1140) ),
    inference(variable_rename,[status(thm)],[f_335_1]) ).

fof(f_335_3,plain,
    ! [U_1142,U_1141,U_1140] :
      ( c_Orderings_Oord__class_Oless(U_1140,U_1142,U_1141)
      | c_Orderings_Oord__class_Oless(U_1140,U_1141,U_1142)
      | U_1141 = U_1142
      | ~ class_Orderings_Olinorder(U_1140) ),
    inference(definitional_conversion,[status(esa)],[f_335_2]) ).

cnf(f_335_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1140,U_1142,U_1141)
    | c_Orderings_Oord__class_Oless(U_1140,U_1141,U_1142)
    | U_1141 = U_1142
    | ~ class_Orderings_Olinorder(U_1140) ),
    inference(clausify,[status(thm)],[f_335_3]) ).

fof(f_336_1,plain,
    ! [V_x_2,V_y_2,T_a] :
      ( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
      | c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv3]) ).

fof(f_336_2,plain,
    ! [U_1145,U_1144,U_1143] :
      ( ( ( ~ c_Orderings_Oord__class_Oless(U_1143,U_1145,U_1144)
          | U_1145 != U_1144 )
        & ( U_1145 = U_1144
          | c_Orderings_Oord__class_Oless(U_1143,U_1145,U_1144) ) )
      | c_Orderings_Oord__class_Oless(U_1143,U_1144,U_1145)
      | ~ class_Orderings_Olinorder(U_1143) ),
    inference(variable_rename,[status(thm)],[f_336_1]) ).

fof(f_336_3,plain,
    ( ! [U_1144,U_1143,U_1145] :
        ( ~ c_Orderings_Oord__class_Oless(U_1143,U_1145,U_1144)
        | U_1145 != U_1144
        | ~ sP84(U_1144,U_1143,U_1145) )
    & ! [U_1144,U_1143,U_1145] :
        ( U_1145 = U_1144
        | c_Orderings_Oord__class_Oless(U_1143,U_1145,U_1144)
        | ~ sP84(U_1144,U_1143,U_1145) )
    & ! [U_1144,U_1143,U_1145] :
        ( sP84(U_1144,U_1143,U_1145)
        | c_Orderings_Oord__class_Oless(U_1143,U_1144,U_1145)
        | ~ class_Orderings_Olinorder(U_1143) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP84])],[f_336_2]) ).

cnf(f_336_4,plain,
    ( sP84(U_1144,U_1143,U_1145)
    | c_Orderings_Oord__class_Oless(U_1143,U_1144,U_1145)
    | ~ class_Orderings_Olinorder(U_1143) ),
    inference(clausify,[status(thm)],[f_336_3]) ).

cnf(f_336_5,plain,
    ( U_1145 = U_1144
    | c_Orderings_Oord__class_Oless(U_1143,U_1145,U_1144)
    | ~ sP84(U_1144,U_1143,U_1145) ),
    inference(clausify,[status(thm)],[f_336_3]) ).

cnf(f_336_6,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1143,U_1145,U_1144)
    | U_1145 != U_1144
    | ~ sP84(U_1144,U_1143,U_1145) ),
    inference(clausify,[status(thm)],[f_336_3]) ).

fof(f_337_1,plain,
    ! [V_y,V_x,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
      | V_x = V_y
      | c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__less__linear]) ).

fof(f_337_2,plain,
    ! [U_1148,U_1147,U_1146] :
      ( c_Orderings_Oord__class_Oless(U_1146,U_1148,U_1147)
      | U_1147 = U_1148
      | c_Orderings_Oord__class_Oless(U_1146,U_1147,U_1148)
      | ~ class_Orderings_Olinorder(U_1146) ),
    inference(variable_rename,[status(thm)],[f_337_1]) ).

fof(f_337_3,plain,
    ! [U_1148,U_1146,U_1147] :
      ( c_Orderings_Oord__class_Oless(U_1146,U_1148,U_1147)
      | U_1147 = U_1148
      | c_Orderings_Oord__class_Oless(U_1146,U_1147,U_1148)
      | ~ class_Orderings_Olinorder(U_1146) ),
    inference(definitional_conversion,[status(esa)],[f_337_2]) ).

cnf(f_337_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1146,U_1148,U_1147)
    | U_1147 = U_1148
    | c_Orderings_Oord__class_Oless(U_1146,U_1147,U_1148)
    | ~ class_Orderings_Olinorder(U_1146) ),
    inference(clausify,[status(thm)],[f_337_3]) ).

fof(f_338_1,plain,
    ! [V_x_2,T_a] :
      ( ( ( c_Groups_Oone__class_Oone(T_a) = V_x_2
          | V_x_2 != c_Groups_Oone__class_Oone(T_a) )
        & ( V_x_2 = c_Groups_Oone__class_Oone(T_a)
          | c_Groups_Oone__class_Oone(T_a) != V_x_2 ) )
      | ~ class_Groups_Oone(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_one__reorient]) ).

fof(f_338_2,plain,
    ! [U_1150,U_1149] :
      ( ( ( c_Groups_Oone__class_Oone(U_1149) = U_1150
          | U_1150 != c_Groups_Oone__class_Oone(U_1149) )
        & ( U_1150 = c_Groups_Oone__class_Oone(U_1149)
          | c_Groups_Oone__class_Oone(U_1149) != U_1150 ) )
      | ~ class_Groups_Oone(U_1149) ),
    inference(variable_rename,[status(thm)],[f_338_1]) ).

fof(f_338_3,plain,
    ( ! [U_1150,U_1149] :
        ( c_Groups_Oone__class_Oone(U_1149) = U_1150
        | U_1150 != c_Groups_Oone__class_Oone(U_1149)
        | ~ sP85(U_1150,U_1149) )
    & ! [U_1150,U_1149] :
        ( U_1150 = c_Groups_Oone__class_Oone(U_1149)
        | c_Groups_Oone__class_Oone(U_1149) != U_1150
        | ~ sP85(U_1150,U_1149) )
    & ! [U_1150,U_1149] :
        ( sP85(U_1150,U_1149)
        | ~ class_Groups_Oone(U_1149) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP85])],[f_338_2]) ).

cnf(f_338_4,plain,
    ( sP85(U_1150,U_1149)
    | ~ class_Groups_Oone(U_1149) ),
    inference(clausify,[status(thm)],[f_338_3]) ).

cnf(f_338_5,plain,
    ( U_1150 = c_Groups_Oone__class_Oone(U_1149)
    | c_Groups_Oone__class_Oone(U_1149) != U_1150
    | ~ sP85(U_1150,U_1149) ),
    inference(clausify,[status(thm)],[f_338_3]) ).

cnf(f_338_6,plain,
    ( c_Groups_Oone__class_Oone(U_1149) = U_1150
    | U_1150 != c_Groups_Oone__class_Oone(U_1149)
    | ~ sP85(U_1150,U_1149) ),
    inference(clausify,[status(thm)],[f_338_3]) ).

fof(f_339_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
          | ( V_x_2 != V_y_2
            & ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) )
        & ( V_x_2 = V_y_2
          | c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
          | c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).

fof(f_339_2,plain,
    ! [U_1153,U_1152,U_1151] :
      ( ( ( ~ c_Orderings_Oord__class_Oless(U_1151,U_1152,U_1153)
          | ( U_1152 != U_1153
            & ~ c_Orderings_Oord__class_Oless(U_1151,U_1153,U_1152) ) )
        & ( U_1152 = U_1153
          | c_Orderings_Oord__class_Oless(U_1151,U_1153,U_1152)
          | c_Orderings_Oord__class_Oless(U_1151,U_1152,U_1153) ) )
      | ~ class_Orderings_Olinorder(U_1151) ),
    inference(variable_rename,[status(thm)],[f_339_1]) ).

fof(f_339_3,plain,
    ( ! [U_1153,U_1151,U_1152] :
        ( U_1152 != U_1153
        | ~ sP86(U_1153,U_1151,U_1152) )
    & ! [U_1153,U_1151,U_1152] :
        ( ~ c_Orderings_Oord__class_Oless(U_1151,U_1153,U_1152)
        | ~ sP86(U_1153,U_1151,U_1152) )
    & ! [U_1153,U_1151,U_1152] :
        ( ~ c_Orderings_Oord__class_Oless(U_1151,U_1152,U_1153)
        | sP86(U_1153,U_1151,U_1152)
        | ~ sP87(U_1153,U_1151,U_1152) )
    & ! [U_1153,U_1151,U_1152] :
        ( U_1152 = U_1153
        | c_Orderings_Oord__class_Oless(U_1151,U_1153,U_1152)
        | c_Orderings_Oord__class_Oless(U_1151,U_1152,U_1153)
        | ~ sP87(U_1153,U_1151,U_1152) )
    & ! [U_1153,U_1151,U_1152] :
        ( sP87(U_1153,U_1151,U_1152)
        | ~ class_Orderings_Olinorder(U_1151) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP86,sP87])],[f_339_2]) ).

cnf(f_339_4,plain,
    ( sP87(U_1153,U_1151,U_1152)
    | ~ class_Orderings_Olinorder(U_1151) ),
    inference(clausify,[status(thm)],[f_339_3]) ).

cnf(f_339_5,plain,
    ( U_1152 = U_1153
    | c_Orderings_Oord__class_Oless(U_1151,U_1153,U_1152)
    | c_Orderings_Oord__class_Oless(U_1151,U_1152,U_1153)
    | ~ sP87(U_1153,U_1151,U_1152) ),
    inference(clausify,[status(thm)],[f_339_3]) ).

cnf(f_339_6,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1151,U_1152,U_1153)
    | sP86(U_1153,U_1151,U_1152)
    | ~ sP87(U_1153,U_1151,U_1152) ),
    inference(clausify,[status(thm)],[f_339_3]) ).

cnf(f_339_7,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1151,U_1153,U_1152)
    | ~ sP86(U_1153,U_1151,U_1152) ),
    inference(clausify,[status(thm)],[f_339_3]) ).

cnf(f_339_8,plain,
    ( U_1152 != U_1153
    | ~ sP86(U_1153,U_1151,U_1152) ),
    inference(clausify,[status(thm)],[f_339_3]) ).

fof(f_340_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( V_x_2 != V_y_2
          | ( ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
            & ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
        & ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
          | c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
          | V_x_2 = V_y_2 ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff]) ).

fof(f_340_2,plain,
    ! [U_1156,U_1155,U_1154] :
      ( ( ( U_1155 != U_1156
          | ( ~ c_Orderings_Oord__class_Oless(U_1154,U_1156,U_1155)
            & ~ c_Orderings_Oord__class_Oless(U_1154,U_1155,U_1156) ) )
        & ( c_Orderings_Oord__class_Oless(U_1154,U_1156,U_1155)
          | c_Orderings_Oord__class_Oless(U_1154,U_1155,U_1156)
          | U_1155 = U_1156 ) )
      | ~ class_Orderings_Olinorder(U_1154) ),
    inference(variable_rename,[status(thm)],[f_340_1]) ).

fof(f_340_3,plain,
    ( ! [U_1154,U_1155,U_1156] :
        ( ~ c_Orderings_Oord__class_Oless(U_1154,U_1156,U_1155)
        | ~ sP88(U_1154,U_1155,U_1156) )
    & ! [U_1154,U_1155,U_1156] :
        ( ~ c_Orderings_Oord__class_Oless(U_1154,U_1155,U_1156)
        | ~ sP88(U_1154,U_1155,U_1156) )
    & ! [U_1154,U_1155,U_1156] :
        ( U_1155 != U_1156
        | sP88(U_1154,U_1155,U_1156)
        | ~ sP89(U_1154,U_1155,U_1156) )
    & ! [U_1154,U_1155,U_1156] :
        ( c_Orderings_Oord__class_Oless(U_1154,U_1156,U_1155)
        | c_Orderings_Oord__class_Oless(U_1154,U_1155,U_1156)
        | U_1155 = U_1156
        | ~ sP89(U_1154,U_1155,U_1156) )
    & ! [U_1154,U_1155,U_1156] :
        ( sP89(U_1154,U_1155,U_1156)
        | ~ class_Orderings_Olinorder(U_1154) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP88,sP89])],[f_340_2]) ).

cnf(f_340_4,plain,
    ( sP89(U_1154,U_1155,U_1156)
    | ~ class_Orderings_Olinorder(U_1154) ),
    inference(clausify,[status(thm)],[f_340_3]) ).

cnf(f_340_5,plain,
    ( c_Orderings_Oord__class_Oless(U_1154,U_1156,U_1155)
    | c_Orderings_Oord__class_Oless(U_1154,U_1155,U_1156)
    | U_1155 = U_1156
    | ~ sP89(U_1154,U_1155,U_1156) ),
    inference(clausify,[status(thm)],[f_340_3]) ).

cnf(f_340_6,plain,
    ( U_1155 != U_1156
    | sP88(U_1154,U_1155,U_1156)
    | ~ sP89(U_1154,U_1155,U_1156) ),
    inference(clausify,[status(thm)],[f_340_3]) ).

cnf(f_340_7,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1154,U_1155,U_1156)
    | ~ sP88(U_1154,U_1155,U_1156) ),
    inference(clausify,[status(thm)],[f_340_3]) ).

cnf(f_340_8,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1154,U_1156,U_1155)
    | ~ sP88(U_1154,U_1155,U_1156) ),
    inference(clausify,[status(thm)],[f_340_3]) ).

fof(f_341_1,plain,
    ! [V_x,T_a] :
      ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_x)
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__irrefl]) ).

fof(f_341_2,plain,
    ! [U_1158,U_1157] :
      ( ~ c_Orderings_Oord__class_Oless(U_1157,U_1158,U_1158)
      | ~ class_Orderings_Opreorder(U_1157) ),
    inference(variable_rename,[status(thm)],[f_341_1]) ).

fof(f_341_3,plain,
    ! [U_1157,U_1158] :
      ( ~ c_Orderings_Oord__class_Oless(U_1157,U_1158,U_1158)
      | ~ class_Orderings_Opreorder(U_1157) ),
    inference(definitional_conversion,[status(esa)],[f_341_2]) ).

cnf(f_341_4,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1157,U_1158,U_1158)
    | ~ class_Orderings_Opreorder(U_1157) ),
    inference(clausify,[status(thm)],[f_341_3]) ).

fof(f_342_1,plain,
    ! [T_a] :
      ( c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
      | ~ class_RealVector_Oreal__normed__algebra__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_norm__one]) ).

fof(f_342_2,plain,
    ! [U_1159] :
      ( c_RealVector_Onorm__class_Onorm(U_1159,c_Groups_Oone__class_Oone(U_1159)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
      | ~ class_RealVector_Oreal__normed__algebra__1(U_1159) ),
    inference(variable_rename,[status(thm)],[f_342_1]) ).

fof(f_342_3,plain,
    ! [U_1159] :
      ( c_RealVector_Onorm__class_Onorm(U_1159,c_Groups_Oone__class_Oone(U_1159)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
      | ~ class_RealVector_Oreal__normed__algebra__1(U_1159) ),
    inference(definitional_conversion,[status(esa)],[f_342_2]) ).

cnf(f_342_4,plain,
    ( c_RealVector_Onorm__class_Onorm(U_1159,c_Groups_Oone__class_Oone(U_1159)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
    | ~ class_RealVector_Oreal__normed__algebra__1(U_1159) ),
    inference(clausify,[status(thm)],[f_342_3]) ).

fof(f_343_1,plain,
    ! [V_P_2,V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
      | ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) )
      | ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
        & V_m_2 = V_n_2 )
      | ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__less__cases]) ).

fof(f_343_2,plain,
    ! [U_1162,U_1161,U_1160] :
      ( hBOOL(hAPP(hAPP(U_1162,U_1161),U_1160))
      | ( ~ hBOOL(hAPP(hAPP(U_1162,U_1161),U_1160))
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1161,U_1160) )
      | ( ~ hBOOL(hAPP(hAPP(U_1162,U_1161),U_1160))
        & U_1160 = U_1161 )
      | ( ~ hBOOL(hAPP(hAPP(U_1162,U_1161),U_1160))
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1160,U_1161) ) ),
    inference(variable_rename,[status(thm)],[f_343_1]) ).

fof(f_343_3,plain,
    ( ! [U_1160,U_1161,U_1162] :
        ( ~ hBOOL(hAPP(hAPP(U_1162,U_1161),U_1160))
        | ~ sP92(U_1160,U_1161,U_1162) )
    & ! [U_1160,U_1161,U_1162] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1161,U_1160)
        | ~ sP92(U_1160,U_1161,U_1162) )
    & ! [U_1160,U_1161,U_1162] :
        ( ~ hBOOL(hAPP(hAPP(U_1162,U_1161),U_1160))
        | ~ sP91(U_1160,U_1161,U_1162) )
    & ! [U_1160,U_1161,U_1162] :
        ( U_1160 = U_1161
        | ~ sP91(U_1160,U_1161,U_1162) )
    & ! [U_1160,U_1161,U_1162] :
        ( ~ hBOOL(hAPP(hAPP(U_1162,U_1161),U_1160))
        | ~ sP90(U_1160,U_1161,U_1162) )
    & ! [U_1160,U_1161,U_1162] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1160,U_1161)
        | ~ sP90(U_1160,U_1161,U_1162) )
    & ! [U_1160,U_1161,U_1162] :
        ( hBOOL(hAPP(hAPP(U_1162,U_1161),U_1160))
        | sP92(U_1160,U_1161,U_1162)
        | sP91(U_1160,U_1161,U_1162)
        | sP90(U_1160,U_1161,U_1162) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP90,sP91,sP92])],[f_343_2]) ).

cnf(f_343_4,plain,
    ( hBOOL(hAPP(hAPP(U_1162,U_1161),U_1160))
    | sP92(U_1160,U_1161,U_1162)
    | sP91(U_1160,U_1161,U_1162)
    | sP90(U_1160,U_1161,U_1162) ),
    inference(clausify,[status(thm)],[f_343_3]) ).

cnf(f_343_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1160,U_1161)
    | ~ sP90(U_1160,U_1161,U_1162) ),
    inference(clausify,[status(thm)],[f_343_3]) ).

cnf(f_343_6,plain,
    ( ~ hBOOL(hAPP(hAPP(U_1162,U_1161),U_1160))
    | ~ sP90(U_1160,U_1161,U_1162) ),
    inference(clausify,[status(thm)],[f_343_3]) ).

cnf(f_343_7,plain,
    ( U_1160 = U_1161
    | ~ sP91(U_1160,U_1161,U_1162) ),
    inference(clausify,[status(thm)],[f_343_3]) ).

cnf(f_343_8,plain,
    ( ~ hBOOL(hAPP(hAPP(U_1162,U_1161),U_1160))
    | ~ sP91(U_1160,U_1161,U_1162) ),
    inference(clausify,[status(thm)],[f_343_3]) ).

cnf(f_343_9,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1161,U_1160)
    | ~ sP92(U_1160,U_1161,U_1162) ),
    inference(clausify,[status(thm)],[f_343_3]) ).

cnf(f_343_10,plain,
    ( ~ hBOOL(hAPP(hAPP(U_1162,U_1161),U_1160))
    | ~ sP92(U_1160,U_1161,U_1162) ),
    inference(clausify,[status(thm)],[f_343_3]) ).

fof(f_344_1,plain,
    ! [V_t,V_s] :
      ( V_s != V_t
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t) ),
    inference(fof_nnf,[status(thm)],[fact_less__not__refl3]) ).

fof(f_344_2,plain,
    ! [U_1164,U_1163] :
      ( U_1163 != U_1164
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1163,U_1164) ),
    inference(variable_rename,[status(thm)],[f_344_1]) ).

fof(f_344_3,plain,
    ! [U_1164,U_1163] :
      ( U_1163 != U_1164
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1163,U_1164) ),
    inference(definitional_conversion,[status(esa)],[f_344_2]) ).

cnf(f_344_4,plain,
    ( U_1163 != U_1164
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1163,U_1164) ),
    inference(clausify,[status(thm)],[f_344_3]) ).

fof(f_345_1,plain,
    ! [V_m,V_n] :
      ( V_m != V_n
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m) ),
    inference(fof_nnf,[status(thm)],[fact_less__not__refl2]) ).

fof(f_345_2,plain,
    ! [U_1166,U_1165] :
      ( U_1166 != U_1165
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1165,U_1166) ),
    inference(variable_rename,[status(thm)],[f_345_1]) ).

fof(f_345_3,plain,
    ! [U_1166,U_1165] :
      ( U_1166 != U_1165
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1165,U_1166) ),
    inference(definitional_conversion,[status(esa)],[f_345_2]) ).

cnf(f_345_4,plain,
    ( U_1166 != U_1165
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1165,U_1166) ),
    inference(clausify,[status(thm)],[f_345_3]) ).

fof(f_346_1,plain,
    ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n),
    inference(fof_nnf,[status(thm)],[fact_less__irrefl__nat]) ).

fof(f_346_2,plain,
    ! [U_1167] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1167,U_1167),
    inference(variable_rename,[status(thm)],[f_346_1]) ).

fof(f_346_3,plain,
    ! [U_1167] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1167,U_1167),
    inference(definitional_conversion,[status(esa)],[f_346_2]) ).

cnf(f_346_4,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1167,U_1167),
    inference(clausify,[status(thm)],[f_346_3]) ).

fof(f_347_1,plain,
    ! [V_y,V_x] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
      | V_x = V_y ),
    inference(fof_nnf,[status(thm)],[fact_linorder__neqE__nat]) ).

fof(f_347_2,plain,
    ! [U_1169,U_1168] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1169,U_1168)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1168,U_1169)
      | U_1168 = U_1169 ),
    inference(variable_rename,[status(thm)],[f_347_1]) ).

fof(f_347_3,plain,
    ! [U_1169,U_1168] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1169,U_1168)
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1168,U_1169)
      | U_1168 = U_1169 ),
    inference(definitional_conversion,[status(esa)],[f_347_2]) ).

cnf(f_347_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1169,U_1168)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1168,U_1169)
    | U_1168 = U_1169 ),
    inference(clausify,[status(thm)],[f_347_3]) ).

fof(f_348_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( V_m_2 != V_n_2
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
          & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
        | V_m_2 = V_n_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__neq__iff]) ).

fof(f_348_2,plain,
    ! [U_1171,U_1170] :
      ( ( U_1170 != U_1171
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1171,U_1170)
          & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1170,U_1171) ) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1171,U_1170)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1170,U_1171)
        | U_1170 = U_1171 ) ),
    inference(variable_rename,[status(thm)],[f_348_1]) ).

fof(f_348_3,plain,
    ( ! [U_1175,U_1173] :
        ( U_1173 != U_1175
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1175,U_1173)
          & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1173,U_1175) ) )
    & ! [U_1174,U_1172] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1174,U_1172)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1172,U_1174)
        | U_1172 = U_1174 ) ),
    inference(miniscope,[status(thm)],[f_348_2]) ).

fof(f_348_4,plain,
    ( ! [U_1175,U_1173] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1175,U_1173)
        | ~ sP93(U_1175,U_1173) )
    & ! [U_1175,U_1173] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1173,U_1175)
        | ~ sP93(U_1175,U_1173) )
    & ! [U_1175,U_1173] :
        ( U_1173 != U_1175
        | sP93(U_1175,U_1173) )
    & ! [U_1172,U_1174] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1174,U_1172)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1172,U_1174)
        | U_1172 = U_1174 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP93])],[f_348_3]) ).

cnf(f_348_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1174,U_1172)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1172,U_1174)
    | U_1172 = U_1174 ),
    inference(clausify,[status(thm)],[f_348_4]) ).

cnf(f_348_6,plain,
    ( U_1173 != U_1175
    | sP93(U_1175,U_1173) ),
    inference(clausify,[status(thm)],[f_348_4]) ).

cnf(f_348_7,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1173,U_1175)
    | ~ sP93(U_1175,U_1173) ),
    inference(clausify,[status(thm)],[f_348_4]) ).

cnf(f_348_8,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1175,U_1173)
    | ~ sP93(U_1175,U_1173) ),
    inference(clausify,[status(thm)],[f_348_4]) ).

fof(f_349_1,plain,
    ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n),
    inference(fof_nnf,[status(thm)],[fact_less__not__refl]) ).

fof(f_349_2,plain,
    ! [U_1176] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1176,U_1176),
    inference(variable_rename,[status(thm)],[f_349_1]) ).

fof(f_349_3,plain,
    ! [U_1176] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1176,U_1176),
    inference(definitional_conversion,[status(esa)],[f_349_2]) ).

cnf(f_349_4,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1176,U_1176),
    inference(clausify,[status(thm)],[f_349_3]) ).

fof(f_350_1,plain,
    ! [T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__two]) ).

fof(f_350_2,plain,
    ! [U_1177] :
      ( c_Orderings_Oord__class_Oless(U_1177,c_Groups_Ozero__class_Ozero(U_1177),c_Groups_Oplus__class_Oplus(U_1177,c_Groups_Oone__class_Oone(U_1177),c_Groups_Oone__class_Oone(U_1177)))
      | ~ class_Rings_Olinordered__semidom(U_1177) ),
    inference(variable_rename,[status(thm)],[f_350_1]) ).

fof(f_350_3,plain,
    ! [U_1177] :
      ( c_Orderings_Oord__class_Oless(U_1177,c_Groups_Ozero__class_Ozero(U_1177),c_Groups_Oplus__class_Oplus(U_1177,c_Groups_Oone__class_Oone(U_1177),c_Groups_Oone__class_Oone(U_1177)))
      | ~ class_Rings_Olinordered__semidom(U_1177) ),
    inference(definitional_conversion,[status(esa)],[f_350_2]) ).

cnf(f_350_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1177,c_Groups_Ozero__class_Ozero(U_1177),c_Groups_Oplus__class_Oplus(U_1177,c_Groups_Oone__class_Oone(U_1177),c_Groups_Oone__class_Oone(U_1177)))
    | ~ class_Rings_Olinordered__semidom(U_1177) ),
    inference(clausify,[status(thm)],[f_350_3]) ).

fof(f_351_1,plain,
    ! [T_a] :
      ( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_one__poly__def]) ).

fof(f_351_2,plain,
    ! [U_1178] :
      ( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1178)) = c_Polynomial_OpCons(U_1178,c_Groups_Oone__class_Oone(U_1178),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1178)))
      | ~ class_Rings_Ocomm__semiring__1(U_1178) ),
    inference(variable_rename,[status(thm)],[f_351_1]) ).

fof(f_351_3,plain,
    ! [U_1178] :
      ( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1178)) = c_Polynomial_OpCons(U_1178,c_Groups_Oone__class_Oone(U_1178),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1178)))
      | ~ class_Rings_Ocomm__semiring__1(U_1178) ),
    inference(definitional_conversion,[status(esa)],[f_351_2]) ).

cnf(f_351_4,plain,
    ( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1178)) = c_Polynomial_OpCons(U_1178,c_Groups_Oone__class_Oone(U_1178),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1178)))
    | ~ class_Rings_Ocomm__semiring__1(U_1178) ),
    inference(clausify,[status(thm)],[f_351_3]) ).

fof(f_352_1,plain,
    ! [V_z,V_x,V_y,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_z,V_y)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I8_J]) ).

fof(f_352_2,plain,
    ! [U_1182,U_1181,U_1180,U_1179] :
      ( c_Orderings_Oord__class_Oless(U_1179,U_1182,U_1181)
      | ~ c_Orderings_Oord__class_Oless(U_1179,U_1182,U_1180)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1179,U_1180,U_1181)
      | ~ class_Orderings_Oorder(U_1179) ),
    inference(variable_rename,[status(thm)],[f_352_1]) ).

fof(f_352_3,plain,
    ! [U_1179,U_1180,U_1181,U_1182] :
      ( c_Orderings_Oord__class_Oless(U_1179,U_1182,U_1181)
      | ~ c_Orderings_Oord__class_Oless(U_1179,U_1182,U_1180)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1179,U_1180,U_1181)
      | ~ class_Orderings_Oorder(U_1179) ),
    inference(definitional_conversion,[status(esa)],[f_352_2]) ).

cnf(f_352_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1179,U_1182,U_1181)
    | ~ c_Orderings_Oord__class_Oless(U_1179,U_1182,U_1180)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1179,U_1180,U_1181)
    | ~ class_Orderings_Oorder(U_1179) ),
    inference(clausify,[status(thm)],[f_352_3]) ).

fof(f_353_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_x,V_z)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_z)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__le__less__trans]) ).

fof(f_353_2,plain,
    ! [U_1186,U_1185,U_1184,U_1183] :
      ( c_Orderings_Oord__class_Oless(U_1183,U_1184,U_1186)
      | ~ c_Orderings_Oord__class_Oless(U_1183,U_1185,U_1186)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1183,U_1184,U_1185)
      | ~ class_Orderings_Opreorder(U_1183) ),
    inference(variable_rename,[status(thm)],[f_353_1]) ).

fof(f_353_3,plain,
    ! [U_1186,U_1185,U_1183,U_1184] :
      ( c_Orderings_Oord__class_Oless(U_1183,U_1184,U_1186)
      | ~ c_Orderings_Oord__class_Oless(U_1183,U_1185,U_1186)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1183,U_1184,U_1185)
      | ~ class_Orderings_Opreorder(U_1183) ),
    inference(definitional_conversion,[status(esa)],[f_353_2]) ).

cnf(f_353_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1183,U_1184,U_1186)
    | ~ c_Orderings_Oord__class_Oless(U_1183,U_1185,U_1186)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1183,U_1184,U_1185)
    | ~ class_Orderings_Opreorder(U_1183) ),
    inference(clausify,[status(thm)],[f_353_3]) ).

fof(f_354_1,plain,
    ! [V_z,V_x,V_y,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_z,V_x)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I7_J]) ).

fof(f_354_2,plain,
    ! [U_1190,U_1189,U_1188,U_1187] :
      ( c_Orderings_Oord__class_Oless(U_1187,U_1190,U_1189)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1187,U_1190,U_1188)
      | ~ c_Orderings_Oord__class_Oless(U_1187,U_1188,U_1189)
      | ~ class_Orderings_Oorder(U_1187) ),
    inference(variable_rename,[status(thm)],[f_354_1]) ).

fof(f_354_3,plain,
    ! [U_1189,U_1190,U_1187,U_1188] :
      ( c_Orderings_Oord__class_Oless(U_1187,U_1190,U_1189)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1187,U_1190,U_1188)
      | ~ c_Orderings_Oord__class_Oless(U_1187,U_1188,U_1189)
      | ~ class_Orderings_Oorder(U_1187) ),
    inference(definitional_conversion,[status(esa)],[f_354_2]) ).

cnf(f_354_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1187,U_1190,U_1189)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1187,U_1190,U_1188)
    | ~ c_Orderings_Oord__class_Oless(U_1187,U_1188,U_1189)
    | ~ class_Orderings_Oorder(U_1187) ),
    inference(clausify,[status(thm)],[f_354_3]) ).

fof(f_355_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_x,V_z)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__le__trans]) ).

fof(f_355_2,plain,
    ! [U_1194,U_1193,U_1192,U_1191] :
      ( c_Orderings_Oord__class_Oless(U_1191,U_1192,U_1194)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1191,U_1193,U_1194)
      | ~ c_Orderings_Oord__class_Oless(U_1191,U_1192,U_1193)
      | ~ class_Orderings_Opreorder(U_1191) ),
    inference(variable_rename,[status(thm)],[f_355_1]) ).

fof(f_355_3,plain,
    ! [U_1194,U_1193,U_1191,U_1192] :
      ( c_Orderings_Oord__class_Oless(U_1191,U_1192,U_1194)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1191,U_1193,U_1194)
      | ~ c_Orderings_Oord__class_Oless(U_1191,U_1192,U_1193)
      | ~ class_Orderings_Opreorder(U_1191) ),
    inference(definitional_conversion,[status(esa)],[f_355_2]) ).

cnf(f_355_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1191,U_1192,U_1194)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1191,U_1193,U_1194)
    | ~ c_Orderings_Oord__class_Oless(U_1191,U_1192,U_1193)
    | ~ class_Orderings_Opreorder(U_1191) ),
    inference(clausify,[status(thm)],[f_355_3]) ).

fof(f_356_1,plain,
    ! [V_a,V_b,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
      | V_a = V_b
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I11_J]) ).

fof(f_356_2,plain,
    ! [U_1197,U_1196,U_1195] :
      ( c_Orderings_Oord__class_Oless(U_1195,U_1196,U_1197)
      | U_1197 = U_1196
      | ~ c_Orderings_Oord__class_Oless__eq(U_1195,U_1196,U_1197)
      | ~ class_Orderings_Oorder(U_1195) ),
    inference(variable_rename,[status(thm)],[f_356_1]) ).

fof(f_356_3,plain,
    ! [U_1197,U_1195,U_1196] :
      ( c_Orderings_Oord__class_Oless(U_1195,U_1196,U_1197)
      | U_1197 = U_1196
      | ~ c_Orderings_Oord__class_Oless__eq(U_1195,U_1196,U_1197)
      | ~ class_Orderings_Oorder(U_1195) ),
    inference(definitional_conversion,[status(esa)],[f_356_2]) ).

cnf(f_356_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1195,U_1196,U_1197)
    | U_1197 = U_1196
    | ~ c_Orderings_Oord__class_Oless__eq(U_1195,U_1196,U_1197)
    | ~ class_Orderings_Oorder(U_1195) ),
    inference(clausify,[status(thm)],[f_356_3]) ).

fof(f_357_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
      | V_a = V_b
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans]) ).

fof(f_357_2,plain,
    ! [U_1200,U_1199,U_1198] :
      ( c_Orderings_Oord__class_Oless(U_1198,U_1199,U_1200)
      | U_1199 = U_1200
      | ~ c_Orderings_Oord__class_Oless__eq(U_1198,U_1199,U_1200)
      | ~ class_Orderings_Oorder(U_1198) ),
    inference(variable_rename,[status(thm)],[f_357_1]) ).

fof(f_357_3,plain,
    ! [U_1198,U_1199,U_1200] :
      ( c_Orderings_Oord__class_Oless(U_1198,U_1199,U_1200)
      | U_1199 = U_1200
      | ~ c_Orderings_Oord__class_Oless__eq(U_1198,U_1199,U_1200)
      | ~ class_Orderings_Oorder(U_1198) ),
    inference(definitional_conversion,[status(esa)],[f_357_2]) ).

cnf(f_357_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1198,U_1199,U_1200)
    | U_1199 = U_1200
    | ~ c_Orderings_Oord__class_Oless__eq(U_1198,U_1199,U_1200)
    | ~ class_Orderings_Oorder(U_1198) ),
    inference(clausify,[status(thm)],[f_357_3]) ).

fof(f_358_1,plain,
    ! [V_y,V_x,T_a] :
      ( V_x = V_y
      | c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq]) ).

fof(f_358_2,plain,
    ! [U_1203,U_1202,U_1201] :
      ( U_1202 = U_1203
      | c_Orderings_Oord__class_Oless(U_1201,U_1202,U_1203)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1201,U_1202,U_1203)
      | ~ class_Orderings_Oorder(U_1201) ),
    inference(variable_rename,[status(thm)],[f_358_1]) ).

fof(f_358_3,plain,
    ! [U_1201,U_1202,U_1203] :
      ( U_1202 = U_1203
      | c_Orderings_Oord__class_Oless(U_1201,U_1202,U_1203)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1201,U_1202,U_1203)
      | ~ class_Orderings_Oorder(U_1201) ),
    inference(definitional_conversion,[status(esa)],[f_358_2]) ).

cnf(f_358_4,plain,
    ( U_1202 = U_1203
    | c_Orderings_Oord__class_Oless(U_1201,U_1202,U_1203)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1201,U_1202,U_1203)
    | ~ class_Orderings_Oorder(U_1201) ),
    inference(clausify,[status(thm)],[f_358_3]) ).

fof(f_359_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv2]) ).

fof(f_359_2,plain,
    ! [U_1206,U_1205,U_1204] :
      ( ( ( ~ c_Orderings_Oord__class_Oless(U_1204,U_1205,U_1206)
          | U_1205 != U_1206 )
        & ( U_1205 = U_1206
          | c_Orderings_Oord__class_Oless(U_1204,U_1205,U_1206) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(U_1204,U_1205,U_1206)
      | ~ class_Orderings_Olinorder(U_1204) ),
    inference(variable_rename,[status(thm)],[f_359_1]) ).

fof(f_359_3,plain,
    ( ! [U_1204,U_1206,U_1205] :
        ( ~ c_Orderings_Oord__class_Oless(U_1204,U_1205,U_1206)
        | U_1205 != U_1206
        | ~ sP94(U_1204,U_1206,U_1205) )
    & ! [U_1204,U_1206,U_1205] :
        ( U_1205 = U_1206
        | c_Orderings_Oord__class_Oless(U_1204,U_1205,U_1206)
        | ~ sP94(U_1204,U_1206,U_1205) )
    & ! [U_1204,U_1206,U_1205] :
        ( sP94(U_1204,U_1206,U_1205)
        | ~ c_Orderings_Oord__class_Oless__eq(U_1204,U_1205,U_1206)
        | ~ class_Orderings_Olinorder(U_1204) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP94])],[f_359_2]) ).

cnf(f_359_4,plain,
    ( sP94(U_1204,U_1206,U_1205)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1204,U_1205,U_1206)
    | ~ class_Orderings_Olinorder(U_1204) ),
    inference(clausify,[status(thm)],[f_359_3]) ).

cnf(f_359_5,plain,
    ( U_1205 = U_1206
    | c_Orderings_Oord__class_Oless(U_1204,U_1205,U_1206)
    | ~ sP94(U_1204,U_1206,U_1205) ),
    inference(clausify,[status(thm)],[f_359_3]) ).

cnf(f_359_6,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1204,U_1205,U_1206)
    | U_1205 != U_1206
    | ~ sP94(U_1204,U_1206,U_1205) ),
    inference(clausify,[status(thm)],[f_359_3]) ).

fof(f_360_1,plain,
    ! [V_y,V_x,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__imp__le]) ).

fof(f_360_2,plain,
    ! [U_1209,U_1208,U_1207] :
      ( c_Orderings_Oord__class_Oless__eq(U_1207,U_1208,U_1209)
      | ~ c_Orderings_Oord__class_Oless(U_1207,U_1208,U_1209)
      | ~ class_Orderings_Opreorder(U_1207) ),
    inference(variable_rename,[status(thm)],[f_360_1]) ).

fof(f_360_3,plain,
    ! [U_1209,U_1208,U_1207] :
      ( c_Orderings_Oord__class_Oless__eq(U_1207,U_1208,U_1209)
      | ~ c_Orderings_Oord__class_Oless(U_1207,U_1208,U_1209)
      | ~ class_Orderings_Opreorder(U_1207) ),
    inference(definitional_conversion,[status(esa)],[f_360_2]) ).

cnf(f_360_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1207,U_1208,U_1209)
    | ~ c_Orderings_Oord__class_Oless(U_1207,U_1208,U_1209)
    | ~ class_Orderings_Opreorder(U_1207) ),
    inference(clausify,[status(thm)],[f_360_3]) ).

fof(f_361_1,plain,
    ! [V_x,V_y,T_a] :
      ( ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_leD]) ).

fof(f_361_2,plain,
    ! [U_1212,U_1211,U_1210] :
      ( ~ c_Orderings_Oord__class_Oless(U_1210,U_1212,U_1211)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1210,U_1211,U_1212)
      | ~ class_Orderings_Olinorder(U_1210) ),
    inference(variable_rename,[status(thm)],[f_361_1]) ).

fof(f_361_3,plain,
    ! [U_1210,U_1211,U_1212] :
      ( ~ c_Orderings_Oord__class_Oless(U_1210,U_1212,U_1211)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1210,U_1211,U_1212)
      | ~ class_Orderings_Olinorder(U_1210) ),
    inference(definitional_conversion,[status(esa)],[f_361_2]) ).

cnf(f_361_4,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1210,U_1212,U_1211)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1210,U_1211,U_1212)
    | ~ class_Orderings_Olinorder(U_1210) ),
    inference(clausify,[status(thm)],[f_361_3]) ).

fof(f_362_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
      | V_a = V_b
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_xt1_I12_J]) ).

fof(f_362_2,plain,
    ! [U_1215,U_1214,U_1213] :
      ( c_Orderings_Oord__class_Oless(U_1213,U_1215,U_1214)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1213,U_1215,U_1214)
      | U_1214 = U_1215
      | ~ class_Orderings_Oorder(U_1213) ),
    inference(variable_rename,[status(thm)],[f_362_1]) ).

fof(f_362_3,plain,
    ! [U_1214,U_1213,U_1215] :
      ( c_Orderings_Oord__class_Oless(U_1213,U_1215,U_1214)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1213,U_1215,U_1214)
      | U_1214 = U_1215
      | ~ class_Orderings_Oorder(U_1213) ),
    inference(definitional_conversion,[status(esa)],[f_362_2]) ).

cnf(f_362_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1213,U_1215,U_1214)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1213,U_1215,U_1214)
    | U_1214 = U_1215
    | ~ class_Orderings_Oorder(U_1213) ),
    inference(clausify,[status(thm)],[f_362_3]) ).

fof(f_363_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
      | V_a = V_b
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans]) ).

fof(f_363_2,plain,
    ! [U_1218,U_1217,U_1216] :
      ( c_Orderings_Oord__class_Oless(U_1216,U_1217,U_1218)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1216,U_1217,U_1218)
      | U_1217 = U_1218
      | ~ class_Orderings_Oorder(U_1216) ),
    inference(variable_rename,[status(thm)],[f_363_1]) ).

fof(f_363_3,plain,
    ! [U_1216,U_1217,U_1218] :
      ( c_Orderings_Oord__class_Oless(U_1216,U_1217,U_1218)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1216,U_1217,U_1218)
      | U_1217 = U_1218
      | ~ class_Orderings_Oorder(U_1216) ),
    inference(definitional_conversion,[status(esa)],[f_363_2]) ).

cnf(f_363_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1216,U_1217,U_1218)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1216,U_1217,U_1218)
    | U_1217 = U_1218
    | ~ class_Orderings_Oorder(U_1216) ),
    inference(clausify,[status(thm)],[f_363_3]) ).

fof(f_364_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) )
      | c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv1]) ).

fof(f_364_2,plain,
    ! [U_1221,U_1220,U_1219] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_1219,U_1220,U_1221)
          | U_1220 != U_1221 )
        & ( U_1220 = U_1221
          | ~ c_Orderings_Oord__class_Oless__eq(U_1219,U_1220,U_1221) ) )
      | c_Orderings_Oord__class_Oless(U_1219,U_1220,U_1221)
      | ~ class_Orderings_Olinorder(U_1219) ),
    inference(variable_rename,[status(thm)],[f_364_1]) ).

fof(f_364_3,plain,
    ( ! [U_1220,U_1219,U_1221] :
        ( c_Orderings_Oord__class_Oless__eq(U_1219,U_1220,U_1221)
        | U_1220 != U_1221
        | ~ sP95(U_1220,U_1219,U_1221) )
    & ! [U_1220,U_1219,U_1221] :
        ( U_1220 = U_1221
        | ~ c_Orderings_Oord__class_Oless__eq(U_1219,U_1220,U_1221)
        | ~ sP95(U_1220,U_1219,U_1221) )
    & ! [U_1220,U_1219,U_1221] :
        ( sP95(U_1220,U_1219,U_1221)
        | c_Orderings_Oord__class_Oless(U_1219,U_1220,U_1221)
        | ~ class_Orderings_Olinorder(U_1219) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP95])],[f_364_2]) ).

cnf(f_364_4,plain,
    ( sP95(U_1220,U_1219,U_1221)
    | c_Orderings_Oord__class_Oless(U_1219,U_1220,U_1221)
    | ~ class_Orderings_Olinorder(U_1219) ),
    inference(clausify,[status(thm)],[f_364_3]) ).

cnf(f_364_5,plain,
    ( U_1220 = U_1221
    | ~ c_Orderings_Oord__class_Oless__eq(U_1219,U_1220,U_1221)
    | ~ sP95(U_1220,U_1219,U_1221) ),
    inference(clausify,[status(thm)],[f_364_3]) ).

cnf(f_364_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1219,U_1220,U_1221)
    | U_1220 != U_1221
    | ~ sP95(U_1220,U_1219,U_1221) ),
    inference(clausify,[status(thm)],[f_364_3]) ).

fof(f_365_1,plain,
    ! [V_x,V_y,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
      | c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_not__leE]) ).

fof(f_365_2,plain,
    ! [U_1224,U_1223,U_1222] :
      ( c_Orderings_Oord__class_Oless(U_1222,U_1224,U_1223)
      | c_Orderings_Oord__class_Oless__eq(U_1222,U_1223,U_1224)
      | ~ class_Orderings_Olinorder(U_1222) ),
    inference(variable_rename,[status(thm)],[f_365_1]) ).

fof(f_365_3,plain,
    ! [U_1223,U_1224,U_1222] :
      ( c_Orderings_Oord__class_Oless(U_1222,U_1224,U_1223)
      | c_Orderings_Oord__class_Oless__eq(U_1222,U_1223,U_1224)
      | ~ class_Orderings_Olinorder(U_1222) ),
    inference(definitional_conversion,[status(esa)],[f_365_2]) ).

cnf(f_365_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1222,U_1224,U_1223)
    | c_Orderings_Oord__class_Oless__eq(U_1222,U_1223,U_1224)
    | ~ class_Orderings_Olinorder(U_1222) ),
    inference(clausify,[status(thm)],[f_365_3]) ).

fof(f_366_1,plain,
    ! [V_y,V_x,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
      | c_Orderings_Oord__class_Oless(T_a,V_x,V_y)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_leI]) ).

fof(f_366_2,plain,
    ! [U_1227,U_1226,U_1225] :
      ( c_Orderings_Oord__class_Oless__eq(U_1225,U_1227,U_1226)
      | c_Orderings_Oord__class_Oless(U_1225,U_1226,U_1227)
      | ~ class_Orderings_Olinorder(U_1225) ),
    inference(variable_rename,[status(thm)],[f_366_1]) ).

fof(f_366_3,plain,
    ! [U_1225,U_1227,U_1226] :
      ( c_Orderings_Oord__class_Oless__eq(U_1225,U_1227,U_1226)
      | c_Orderings_Oord__class_Oless(U_1225,U_1226,U_1227)
      | ~ class_Orderings_Olinorder(U_1225) ),
    inference(definitional_conversion,[status(esa)],[f_366_2]) ).

cnf(f_366_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1225,U_1227,U_1226)
    | c_Orderings_Oord__class_Oless(U_1225,U_1226,U_1227)
    | ~ class_Orderings_Olinorder(U_1225) ),
    inference(clausify,[status(thm)],[f_366_3]) ).

fof(f_367_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
          | ( V_x_2 != V_y_2
            & ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
        & ( V_x_2 = V_y_2
          | c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) )
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__le__less]) ).

fof(f_367_2,plain,
    ! [U_1230,U_1229,U_1228] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_1228,U_1229,U_1230)
          | ( U_1229 != U_1230
            & ~ c_Orderings_Oord__class_Oless(U_1228,U_1229,U_1230) ) )
        & ( U_1229 = U_1230
          | c_Orderings_Oord__class_Oless(U_1228,U_1229,U_1230)
          | ~ c_Orderings_Oord__class_Oless__eq(U_1228,U_1229,U_1230) ) )
      | ~ class_Orderings_Oorder(U_1228) ),
    inference(variable_rename,[status(thm)],[f_367_1]) ).

fof(f_367_3,plain,
    ( ! [U_1228,U_1229,U_1230] :
        ( U_1229 != U_1230
        | ~ sP96(U_1228,U_1229,U_1230) )
    & ! [U_1228,U_1229,U_1230] :
        ( ~ c_Orderings_Oord__class_Oless(U_1228,U_1229,U_1230)
        | ~ sP96(U_1228,U_1229,U_1230) )
    & ! [U_1228,U_1229,U_1230] :
        ( c_Orderings_Oord__class_Oless__eq(U_1228,U_1229,U_1230)
        | sP96(U_1228,U_1229,U_1230)
        | ~ sP97(U_1228,U_1229,U_1230) )
    & ! [U_1228,U_1229,U_1230] :
        ( U_1229 = U_1230
        | c_Orderings_Oord__class_Oless(U_1228,U_1229,U_1230)
        | ~ c_Orderings_Oord__class_Oless__eq(U_1228,U_1229,U_1230)
        | ~ sP97(U_1228,U_1229,U_1230) )
    & ! [U_1228,U_1229,U_1230] :
        ( sP97(U_1228,U_1229,U_1230)
        | ~ class_Orderings_Oorder(U_1228) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP96,sP97])],[f_367_2]) ).

cnf(f_367_4,plain,
    ( sP97(U_1228,U_1229,U_1230)
    | ~ class_Orderings_Oorder(U_1228) ),
    inference(clausify,[status(thm)],[f_367_3]) ).

cnf(f_367_5,plain,
    ( U_1229 = U_1230
    | c_Orderings_Oord__class_Oless(U_1228,U_1229,U_1230)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1228,U_1229,U_1230)
    | ~ sP97(U_1228,U_1229,U_1230) ),
    inference(clausify,[status(thm)],[f_367_3]) ).

cnf(f_367_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1228,U_1229,U_1230)
    | sP96(U_1228,U_1229,U_1230)
    | ~ sP97(U_1228,U_1229,U_1230) ),
    inference(clausify,[status(thm)],[f_367_3]) ).

cnf(f_367_7,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1228,U_1229,U_1230)
    | ~ sP96(U_1228,U_1229,U_1230) ),
    inference(clausify,[status(thm)],[f_367_3]) ).

cnf(f_367_8,plain,
    ( U_1229 != U_1230
    | ~ sP96(U_1228,U_1229,U_1230) ),
    inference(clausify,[status(thm)],[f_367_3]) ).

fof(f_368_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
          | c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
        & ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
            & c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
          | ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
      | ~ class_Orderings_Opreorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__le__not__le]) ).

fof(f_368_2,plain,
    ! [U_1233,U_1232,U_1231] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1231,U_1232,U_1233)
          | c_Orderings_Oord__class_Oless__eq(U_1231,U_1233,U_1232)
          | ~ c_Orderings_Oord__class_Oless__eq(U_1231,U_1232,U_1233) )
        & ( ( ~ c_Orderings_Oord__class_Oless__eq(U_1231,U_1233,U_1232)
            & c_Orderings_Oord__class_Oless__eq(U_1231,U_1232,U_1233) )
          | ~ c_Orderings_Oord__class_Oless(U_1231,U_1232,U_1233) ) )
      | ~ class_Orderings_Opreorder(U_1231) ),
    inference(variable_rename,[status(thm)],[f_368_1]) ).

fof(f_368_3,plain,
    ( ! [U_1232,U_1231,U_1233] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_1231,U_1233,U_1232)
        | ~ sP98(U_1232,U_1231,U_1233) )
    & ! [U_1232,U_1231,U_1233] :
        ( c_Orderings_Oord__class_Oless__eq(U_1231,U_1232,U_1233)
        | ~ sP98(U_1232,U_1231,U_1233) )
    & ! [U_1232,U_1231,U_1233] :
        ( c_Orderings_Oord__class_Oless(U_1231,U_1232,U_1233)
        | c_Orderings_Oord__class_Oless__eq(U_1231,U_1233,U_1232)
        | ~ c_Orderings_Oord__class_Oless__eq(U_1231,U_1232,U_1233)
        | ~ sP99(U_1232,U_1231,U_1233) )
    & ! [U_1232,U_1231,U_1233] :
        ( sP98(U_1232,U_1231,U_1233)
        | ~ c_Orderings_Oord__class_Oless(U_1231,U_1232,U_1233)
        | ~ sP99(U_1232,U_1231,U_1233) )
    & ! [U_1232,U_1231,U_1233] :
        ( sP99(U_1232,U_1231,U_1233)
        | ~ class_Orderings_Opreorder(U_1231) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP98,sP99])],[f_368_2]) ).

cnf(f_368_4,plain,
    ( sP99(U_1232,U_1231,U_1233)
    | ~ class_Orderings_Opreorder(U_1231) ),
    inference(clausify,[status(thm)],[f_368_3]) ).

cnf(f_368_5,plain,
    ( sP98(U_1232,U_1231,U_1233)
    | ~ c_Orderings_Oord__class_Oless(U_1231,U_1232,U_1233)
    | ~ sP99(U_1232,U_1231,U_1233) ),
    inference(clausify,[status(thm)],[f_368_3]) ).

cnf(f_368_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1231,U_1232,U_1233)
    | c_Orderings_Oord__class_Oless__eq(U_1231,U_1233,U_1232)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1231,U_1232,U_1233)
    | ~ sP99(U_1232,U_1231,U_1233) ),
    inference(clausify,[status(thm)],[f_368_3]) ).

cnf(f_368_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1231,U_1232,U_1233)
    | ~ sP98(U_1232,U_1231,U_1233) ),
    inference(clausify,[status(thm)],[f_368_3]) ).

cnf(f_368_8,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_1231,U_1233,U_1232)
    | ~ sP98(U_1232,U_1231,U_1233) ),
    inference(clausify,[status(thm)],[f_368_3]) ).

fof(f_369_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
          | V_x_2 = V_y_2
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
        & ( ( V_x_2 != V_y_2
            & c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
          | ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
      | ~ class_Orderings_Oorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__less__le]) ).

fof(f_369_2,plain,
    ! [U_1236,U_1235,U_1234] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1234,U_1235,U_1236)
          | U_1235 = U_1236
          | ~ c_Orderings_Oord__class_Oless__eq(U_1234,U_1235,U_1236) )
        & ( ( U_1235 != U_1236
            & c_Orderings_Oord__class_Oless__eq(U_1234,U_1235,U_1236) )
          | ~ c_Orderings_Oord__class_Oless(U_1234,U_1235,U_1236) ) )
      | ~ class_Orderings_Oorder(U_1234) ),
    inference(variable_rename,[status(thm)],[f_369_1]) ).

fof(f_369_3,plain,
    ( ! [U_1236,U_1234,U_1235] :
        ( U_1235 != U_1236
        | ~ sP100(U_1236,U_1234,U_1235) )
    & ! [U_1236,U_1234,U_1235] :
        ( c_Orderings_Oord__class_Oless__eq(U_1234,U_1235,U_1236)
        | ~ sP100(U_1236,U_1234,U_1235) )
    & ! [U_1236,U_1234,U_1235] :
        ( c_Orderings_Oord__class_Oless(U_1234,U_1235,U_1236)
        | U_1235 = U_1236
        | ~ c_Orderings_Oord__class_Oless__eq(U_1234,U_1235,U_1236)
        | ~ sP101(U_1236,U_1234,U_1235) )
    & ! [U_1236,U_1234,U_1235] :
        ( sP100(U_1236,U_1234,U_1235)
        | ~ c_Orderings_Oord__class_Oless(U_1234,U_1235,U_1236)
        | ~ sP101(U_1236,U_1234,U_1235) )
    & ! [U_1236,U_1234,U_1235] :
        ( sP101(U_1236,U_1234,U_1235)
        | ~ class_Orderings_Oorder(U_1234) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP100,sP101])],[f_369_2]) ).

cnf(f_369_4,plain,
    ( sP101(U_1236,U_1234,U_1235)
    | ~ class_Orderings_Oorder(U_1234) ),
    inference(clausify,[status(thm)],[f_369_3]) ).

cnf(f_369_5,plain,
    ( sP100(U_1236,U_1234,U_1235)
    | ~ c_Orderings_Oord__class_Oless(U_1234,U_1235,U_1236)
    | ~ sP101(U_1236,U_1234,U_1235) ),
    inference(clausify,[status(thm)],[f_369_3]) ).

cnf(f_369_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1234,U_1235,U_1236)
    | U_1235 = U_1236
    | ~ c_Orderings_Oord__class_Oless__eq(U_1234,U_1235,U_1236)
    | ~ sP101(U_1236,U_1234,U_1235) ),
    inference(clausify,[status(thm)],[f_369_3]) ).

cnf(f_369_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1234,U_1235,U_1236)
    | ~ sP100(U_1236,U_1234,U_1235) ),
    inference(clausify,[status(thm)],[f_369_3]) ).

cnf(f_369_8,plain,
    ( U_1235 != U_1236
    | ~ sP100(U_1236,U_1234,U_1235) ),
    inference(clausify,[status(thm)],[f_369_3]) ).

fof(f_370_1,plain,
    ! [V_y,V_x,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_y,V_x)
      | c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear]) ).

fof(f_370_2,plain,
    ! [U_1239,U_1238,U_1237] :
      ( c_Orderings_Oord__class_Oless(U_1237,U_1239,U_1238)
      | c_Orderings_Oord__class_Oless__eq(U_1237,U_1238,U_1239)
      | ~ class_Orderings_Olinorder(U_1237) ),
    inference(variable_rename,[status(thm)],[f_370_1]) ).

fof(f_370_3,plain,
    ! [U_1237,U_1239,U_1238] :
      ( c_Orderings_Oord__class_Oless(U_1237,U_1239,U_1238)
      | c_Orderings_Oord__class_Oless__eq(U_1237,U_1238,U_1239)
      | ~ class_Orderings_Olinorder(U_1237) ),
    inference(definitional_conversion,[status(esa)],[f_370_2]) ).

cnf(f_370_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1237,U_1239,U_1238)
    | c_Orderings_Oord__class_Oless__eq(U_1237,U_1238,U_1239)
    | ~ class_Orderings_Olinorder(U_1237) ),
    inference(clausify,[status(thm)],[f_370_3]) ).

fof(f_371_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) )
        & ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
          | c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__not__le]) ).

fof(f_371_2,plain,
    ! [U_1242,U_1241,U_1240] :
      ( ( ( ~ c_Orderings_Oord__class_Oless__eq(U_1240,U_1241,U_1242)
          | ~ c_Orderings_Oord__class_Oless(U_1240,U_1242,U_1241) )
        & ( c_Orderings_Oord__class_Oless(U_1240,U_1242,U_1241)
          | c_Orderings_Oord__class_Oless__eq(U_1240,U_1241,U_1242) ) )
      | ~ class_Orderings_Olinorder(U_1240) ),
    inference(variable_rename,[status(thm)],[f_371_1]) ).

fof(f_371_3,plain,
    ( ! [U_1241,U_1240,U_1242] :
        ( ~ c_Orderings_Oord__class_Oless__eq(U_1240,U_1241,U_1242)
        | ~ c_Orderings_Oord__class_Oless(U_1240,U_1242,U_1241)
        | ~ sP102(U_1241,U_1240,U_1242) )
    & ! [U_1241,U_1240,U_1242] :
        ( c_Orderings_Oord__class_Oless(U_1240,U_1242,U_1241)
        | c_Orderings_Oord__class_Oless__eq(U_1240,U_1241,U_1242)
        | ~ sP102(U_1241,U_1240,U_1242) )
    & ! [U_1241,U_1240,U_1242] :
        ( sP102(U_1241,U_1240,U_1242)
        | ~ class_Orderings_Olinorder(U_1240) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP102])],[f_371_2]) ).

cnf(f_371_4,plain,
    ( sP102(U_1241,U_1240,U_1242)
    | ~ class_Orderings_Olinorder(U_1240) ),
    inference(clausify,[status(thm)],[f_371_3]) ).

cnf(f_371_5,plain,
    ( c_Orderings_Oord__class_Oless(U_1240,U_1242,U_1241)
    | c_Orderings_Oord__class_Oless__eq(U_1240,U_1241,U_1242)
    | ~ sP102(U_1241,U_1240,U_1242) ),
    inference(clausify,[status(thm)],[f_371_3]) ).

cnf(f_371_6,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_1240,U_1241,U_1242)
    | ~ c_Orderings_Oord__class_Oless(U_1240,U_1242,U_1241)
    | ~ sP102(U_1241,U_1240,U_1242) ),
    inference(clausify,[status(thm)],[f_371_3]) ).

fof(f_372_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
          | c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_linorder__not__less]) ).

fof(f_372_2,plain,
    ! [U_1245,U_1244,U_1243] :
      ( ( ( ~ c_Orderings_Oord__class_Oless(U_1243,U_1244,U_1245)
          | ~ c_Orderings_Oord__class_Oless__eq(U_1243,U_1245,U_1244) )
        & ( c_Orderings_Oord__class_Oless__eq(U_1243,U_1245,U_1244)
          | c_Orderings_Oord__class_Oless(U_1243,U_1244,U_1245) ) )
      | ~ class_Orderings_Olinorder(U_1243) ),
    inference(variable_rename,[status(thm)],[f_372_1]) ).

fof(f_372_3,plain,
    ( ! [U_1243,U_1245,U_1244] :
        ( ~ c_Orderings_Oord__class_Oless(U_1243,U_1244,U_1245)
        | ~ c_Orderings_Oord__class_Oless__eq(U_1243,U_1245,U_1244)
        | ~ sP103(U_1243,U_1245,U_1244) )
    & ! [U_1243,U_1245,U_1244] :
        ( c_Orderings_Oord__class_Oless__eq(U_1243,U_1245,U_1244)
        | c_Orderings_Oord__class_Oless(U_1243,U_1244,U_1245)
        | ~ sP103(U_1243,U_1245,U_1244) )
    & ! [U_1243,U_1245,U_1244] :
        ( sP103(U_1243,U_1245,U_1244)
        | ~ class_Orderings_Olinorder(U_1243) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP103])],[f_372_2]) ).

cnf(f_372_4,plain,
    ( sP103(U_1243,U_1245,U_1244)
    | ~ class_Orderings_Olinorder(U_1243) ),
    inference(clausify,[status(thm)],[f_372_3]) ).

cnf(f_372_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1243,U_1245,U_1244)
    | c_Orderings_Oord__class_Oless(U_1243,U_1244,U_1245)
    | ~ sP103(U_1243,U_1245,U_1244) ),
    inference(clausify,[status(thm)],[f_372_3]) ).

cnf(f_372_6,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1243,U_1244,U_1245)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1243,U_1245,U_1244)
    | ~ sP103(U_1243,U_1245,U_1244) ),
    inference(clausify,[status(thm)],[f_372_3]) ).

fof(f_373_1,plain,
    ! [T_a] :
      ( c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Ozero__neq__one(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_one__neq__zero]) ).

fof(f_373_2,plain,
    ! [U_1246] :
      ( c_Groups_Oone__class_Oone(U_1246) != c_Groups_Ozero__class_Ozero(U_1246)
      | ~ class_Rings_Ozero__neq__one(U_1246) ),
    inference(variable_rename,[status(thm)],[f_373_1]) ).

fof(f_373_3,plain,
    ! [U_1246] :
      ( c_Groups_Oone__class_Oone(U_1246) != c_Groups_Ozero__class_Ozero(U_1246)
      | ~ class_Rings_Ozero__neq__one(U_1246) ),
    inference(definitional_conversion,[status(esa)],[f_373_2]) ).

cnf(f_373_4,plain,
    ( c_Groups_Oone__class_Oone(U_1246) != c_Groups_Ozero__class_Ozero(U_1246)
    | ~ class_Rings_Ozero__neq__one(U_1246) ),
    inference(clausify,[status(thm)],[f_373_3]) ).

fof(f_374_1,plain,
    ! [T_a] :
      ( c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a)
      | ~ class_Rings_Ozero__neq__one(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__neq__one]) ).

fof(f_374_2,plain,
    ! [U_1247] :
      ( c_Groups_Ozero__class_Ozero(U_1247) != c_Groups_Oone__class_Oone(U_1247)
      | ~ class_Rings_Ozero__neq__one(U_1247) ),
    inference(variable_rename,[status(thm)],[f_374_1]) ).

fof(f_374_3,plain,
    ! [U_1247] :
      ( c_Groups_Ozero__class_Ozero(U_1247) != c_Groups_Oone__class_Oone(U_1247)
      | ~ class_Rings_Ozero__neq__one(U_1247) ),
    inference(definitional_conversion,[status(esa)],[f_374_2]) ).

cnf(f_374_4,plain,
    ( c_Groups_Ozero__class_Ozero(U_1247) != c_Groups_Oone__class_Oone(U_1247)
    | ~ class_Rings_Ozero__neq__one(U_1247) ),
    inference(clausify,[status(thm)],[f_374_3]) ).

fof(f_375_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left]) ).

fof(f_375_2,plain,
    ! [U_1251,U_1250,U_1249,U_1248] :
      ( c_Orderings_Oord__class_Oless(U_1248,U_1250,U_1251)
      | ~ c_Orderings_Oord__class_Oless(U_1248,c_Groups_Oplus__class_Oplus(U_1248,U_1249,U_1250),c_Groups_Oplus__class_Oplus(U_1248,U_1249,U_1251))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1248) ),
    inference(variable_rename,[status(thm)],[f_375_1]) ).

fof(f_375_3,plain,
    ! [U_1248,U_1249,U_1250,U_1251] :
      ( c_Orderings_Oord__class_Oless(U_1248,U_1250,U_1251)
      | ~ c_Orderings_Oord__class_Oless(U_1248,c_Groups_Oplus__class_Oplus(U_1248,U_1249,U_1250),c_Groups_Oplus__class_Oplus(U_1248,U_1249,U_1251))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1248) ),
    inference(definitional_conversion,[status(esa)],[f_375_2]) ).

cnf(f_375_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1248,U_1250,U_1251)
    | ~ c_Orderings_Oord__class_Oless(U_1248,c_Groups_Oplus__class_Oplus(U_1248,U_1249,U_1250),c_Groups_Oplus__class_Oplus(U_1248,U_1249,U_1251))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1248) ),
    inference(clausify,[status(thm)],[f_375_3]) ).

fof(f_376_1,plain,
    ! [V_b,V_c,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right]) ).

fof(f_376_2,plain,
    ! [U_1255,U_1254,U_1253,U_1252] :
      ( c_Orderings_Oord__class_Oless(U_1252,U_1253,U_1255)
      | ~ c_Orderings_Oord__class_Oless(U_1252,c_Groups_Oplus__class_Oplus(U_1252,U_1253,U_1254),c_Groups_Oplus__class_Oplus(U_1252,U_1255,U_1254))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1252) ),
    inference(variable_rename,[status(thm)],[f_376_1]) ).

fof(f_376_3,plain,
    ! [U_1254,U_1255,U_1252,U_1253] :
      ( c_Orderings_Oord__class_Oless(U_1252,U_1253,U_1255)
      | ~ c_Orderings_Oord__class_Oless(U_1252,c_Groups_Oplus__class_Oplus(U_1252,U_1253,U_1254),c_Groups_Oplus__class_Oplus(U_1252,U_1255,U_1254))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1252) ),
    inference(definitional_conversion,[status(esa)],[f_376_2]) ).

cnf(f_376_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1252,U_1253,U_1255)
    | ~ c_Orderings_Oord__class_Oless(U_1252,c_Groups_Oplus__class_Oplus(U_1252,U_1253,U_1254),c_Groups_Oplus__class_Oplus(U_1252,U_1255,U_1254))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1252) ),
    inference(clausify,[status(thm)],[f_376_3]) ).

fof(f_377_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
      | ~ c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__strict__mono]) ).

fof(f_377_2,plain,
    ! [U_1260,U_1259,U_1258,U_1257,U_1256] :
      ( c_Orderings_Oord__class_Oless(U_1256,c_Groups_Oplus__class_Oplus(U_1256,U_1257,U_1259),c_Groups_Oplus__class_Oplus(U_1256,U_1258,U_1260))
      | ~ c_Orderings_Oord__class_Oless(U_1256,U_1259,U_1260)
      | ~ c_Orderings_Oord__class_Oless(U_1256,U_1257,U_1258)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1256) ),
    inference(variable_rename,[status(thm)],[f_377_1]) ).

fof(f_377_3,plain,
    ! [U_1256,U_1257,U_1258,U_1259,U_1260] :
      ( c_Orderings_Oord__class_Oless(U_1256,c_Groups_Oplus__class_Oplus(U_1256,U_1257,U_1259),c_Groups_Oplus__class_Oplus(U_1256,U_1258,U_1260))
      | ~ c_Orderings_Oord__class_Oless(U_1256,U_1259,U_1260)
      | ~ c_Orderings_Oord__class_Oless(U_1256,U_1257,U_1258)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1256) ),
    inference(definitional_conversion,[status(esa)],[f_377_2]) ).

cnf(f_377_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1256,c_Groups_Oplus__class_Oplus(U_1256,U_1257,U_1259),c_Groups_Oplus__class_Oplus(U_1256,U_1258,U_1260))
    | ~ c_Orderings_Oord__class_Oless(U_1256,U_1259,U_1260)
    | ~ c_Orderings_Oord__class_Oless(U_1256,U_1257,U_1258)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1256) ),
    inference(clausify,[status(thm)],[f_377_3]) ).

fof(f_378_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))
      | ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono]) ).

fof(f_378_2,plain,
    ! [U_1264,U_1263,U_1262,U_1261] :
      ( c_Orderings_Oord__class_Oless(U_1261,c_Groups_Oplus__class_Oplus(U_1261,U_1264,U_1262),c_Groups_Oplus__class_Oplus(U_1261,U_1264,U_1263))
      | ~ c_Orderings_Oord__class_Oless(U_1261,U_1262,U_1263)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1261) ),
    inference(variable_rename,[status(thm)],[f_378_1]) ).

fof(f_378_3,plain,
    ! [U_1261,U_1264,U_1262,U_1263] :
      ( c_Orderings_Oord__class_Oless(U_1261,c_Groups_Oplus__class_Oplus(U_1261,U_1264,U_1262),c_Groups_Oplus__class_Oplus(U_1261,U_1264,U_1263))
      | ~ c_Orderings_Oord__class_Oless(U_1261,U_1262,U_1263)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1261) ),
    inference(definitional_conversion,[status(esa)],[f_378_2]) ).

cnf(f_378_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1261,c_Groups_Oplus__class_Oplus(U_1261,U_1264,U_1262),c_Groups_Oplus__class_Oplus(U_1261,U_1264,U_1263))
    | ~ c_Orderings_Oord__class_Oless(U_1261,U_1262,U_1263)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1261) ),
    inference(clausify,[status(thm)],[f_378_3]) ).

fof(f_379_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
      | ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono]) ).

fof(f_379_2,plain,
    ! [U_1268,U_1267,U_1266,U_1265] :
      ( c_Orderings_Oord__class_Oless(U_1265,c_Groups_Oplus__class_Oplus(U_1265,U_1266,U_1268),c_Groups_Oplus__class_Oplus(U_1265,U_1267,U_1268))
      | ~ c_Orderings_Oord__class_Oless(U_1265,U_1266,U_1267)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1265) ),
    inference(variable_rename,[status(thm)],[f_379_1]) ).

fof(f_379_3,plain,
    ! [U_1267,U_1266,U_1265,U_1268] :
      ( c_Orderings_Oord__class_Oless(U_1265,c_Groups_Oplus__class_Oplus(U_1265,U_1266,U_1268),c_Groups_Oplus__class_Oplus(U_1265,U_1267,U_1268))
      | ~ c_Orderings_Oord__class_Oless(U_1265,U_1266,U_1267)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1265) ),
    inference(definitional_conversion,[status(esa)],[f_379_2]) ).

cnf(f_379_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1265,c_Groups_Oplus__class_Oplus(U_1265,U_1266,U_1268),c_Groups_Oplus__class_Oplus(U_1265,U_1267,U_1268))
    | ~ c_Orderings_Oord__class_Oless(U_1265,U_1266,U_1267)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1265) ),
    inference(clausify,[status(thm)],[f_379_3]) ).

fof(f_380_1,plain,
    ! [V_b_2,V_ab_2,V_ca_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2))
          | ~ c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2) )
        & ( c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_ab_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_b_2)) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left]) ).

fof(f_380_2,plain,
    ! [U_1272,U_1271,U_1270,U_1269] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1269,c_Groups_Oplus__class_Oplus(U_1269,U_1270,U_1271),c_Groups_Oplus__class_Oplus(U_1269,U_1270,U_1272))
          | ~ c_Orderings_Oord__class_Oless(U_1269,U_1271,U_1272) )
        & ( c_Orderings_Oord__class_Oless(U_1269,U_1271,U_1272)
          | ~ c_Orderings_Oord__class_Oless(U_1269,c_Groups_Oplus__class_Oplus(U_1269,U_1270,U_1271),c_Groups_Oplus__class_Oplus(U_1269,U_1270,U_1272)) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1269) ),
    inference(variable_rename,[status(thm)],[f_380_1]) ).

fof(f_380_3,plain,
    ( ! [U_1271,U_1270,U_1269,U_1272] :
        ( c_Orderings_Oord__class_Oless(U_1269,c_Groups_Oplus__class_Oplus(U_1269,U_1270,U_1271),c_Groups_Oplus__class_Oplus(U_1269,U_1270,U_1272))
        | ~ c_Orderings_Oord__class_Oless(U_1269,U_1271,U_1272)
        | ~ sP104(U_1271,U_1270,U_1269,U_1272) )
    & ! [U_1271,U_1270,U_1269,U_1272] :
        ( c_Orderings_Oord__class_Oless(U_1269,U_1271,U_1272)
        | ~ c_Orderings_Oord__class_Oless(U_1269,c_Groups_Oplus__class_Oplus(U_1269,U_1270,U_1271),c_Groups_Oplus__class_Oplus(U_1269,U_1270,U_1272))
        | ~ sP104(U_1271,U_1270,U_1269,U_1272) )
    & ! [U_1271,U_1270,U_1269,U_1272] :
        ( sP104(U_1271,U_1270,U_1269,U_1272)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1269) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP104])],[f_380_2]) ).

cnf(f_380_4,plain,
    ( sP104(U_1271,U_1270,U_1269,U_1272)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1269) ),
    inference(clausify,[status(thm)],[f_380_3]) ).

cnf(f_380_5,plain,
    ( c_Orderings_Oord__class_Oless(U_1269,U_1271,U_1272)
    | ~ c_Orderings_Oord__class_Oless(U_1269,c_Groups_Oplus__class_Oplus(U_1269,U_1270,U_1271),c_Groups_Oplus__class_Oplus(U_1269,U_1270,U_1272))
    | ~ sP104(U_1271,U_1270,U_1269,U_1272) ),
    inference(clausify,[status(thm)],[f_380_3]) ).

cnf(f_380_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1269,c_Groups_Oplus__class_Oplus(U_1269,U_1270,U_1271),c_Groups_Oplus__class_Oplus(U_1269,U_1270,U_1272))
    | ~ c_Orderings_Oord__class_Oless(U_1269,U_1271,U_1272)
    | ~ sP104(U_1271,U_1270,U_1269,U_1272) ),
    inference(clausify,[status(thm)],[f_380_3]) ).

fof(f_381_1,plain,
    ! [V_b_2,V_ca_2,V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2))
          | ~ c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2) )
        & ( c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2)) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right]) ).

fof(f_381_2,plain,
    ! [U_1276,U_1275,U_1274,U_1273] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1273,c_Groups_Oplus__class_Oplus(U_1273,U_1274,U_1275),c_Groups_Oplus__class_Oplus(U_1273,U_1276,U_1275))
          | ~ c_Orderings_Oord__class_Oless(U_1273,U_1274,U_1276) )
        & ( c_Orderings_Oord__class_Oless(U_1273,U_1274,U_1276)
          | ~ c_Orderings_Oord__class_Oless(U_1273,c_Groups_Oplus__class_Oplus(U_1273,U_1274,U_1275),c_Groups_Oplus__class_Oplus(U_1273,U_1276,U_1275)) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1273) ),
    inference(variable_rename,[status(thm)],[f_381_1]) ).

fof(f_381_3,plain,
    ( ! [U_1276,U_1274,U_1273,U_1275] :
        ( c_Orderings_Oord__class_Oless(U_1273,c_Groups_Oplus__class_Oplus(U_1273,U_1274,U_1275),c_Groups_Oplus__class_Oplus(U_1273,U_1276,U_1275))
        | ~ c_Orderings_Oord__class_Oless(U_1273,U_1274,U_1276)
        | ~ sP105(U_1276,U_1274,U_1273,U_1275) )
    & ! [U_1276,U_1274,U_1273,U_1275] :
        ( c_Orderings_Oord__class_Oless(U_1273,U_1274,U_1276)
        | ~ c_Orderings_Oord__class_Oless(U_1273,c_Groups_Oplus__class_Oplus(U_1273,U_1274,U_1275),c_Groups_Oplus__class_Oplus(U_1273,U_1276,U_1275))
        | ~ sP105(U_1276,U_1274,U_1273,U_1275) )
    & ! [U_1276,U_1274,U_1273,U_1275] :
        ( sP105(U_1276,U_1274,U_1273,U_1275)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1273) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP105])],[f_381_2]) ).

cnf(f_381_4,plain,
    ( sP105(U_1276,U_1274,U_1273,U_1275)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1273) ),
    inference(clausify,[status(thm)],[f_381_3]) ).

cnf(f_381_5,plain,
    ( c_Orderings_Oord__class_Oless(U_1273,U_1274,U_1276)
    | ~ c_Orderings_Oord__class_Oless(U_1273,c_Groups_Oplus__class_Oplus(U_1273,U_1274,U_1275),c_Groups_Oplus__class_Oplus(U_1273,U_1276,U_1275))
    | ~ sP105(U_1276,U_1274,U_1273,U_1275) ),
    inference(clausify,[status(thm)],[f_381_3]) ).

cnf(f_381_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1273,c_Groups_Oplus__class_Oplus(U_1273,U_1274,U_1275),c_Groups_Oplus__class_Oplus(U_1273,U_1276,U_1275))
    | ~ c_Orderings_Oord__class_Oless(U_1273,U_1274,U_1276)
    | ~ sP105(U_1276,U_1274,U_1273,U_1275) ),
    inference(clausify,[status(thm)],[f_381_3]) ).

fof(f_382_1,plain,
    ! [V_db_2,V_ca_2,V_b_2,V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,V_db_2) )
        & ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,V_db_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2) ) )
      | c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2) != c_Groups_Ominus__class_Ominus(T_a,V_ca_2,V_db_2)
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less]) ).

fof(f_382_2,plain,
    ! [U_1281,U_1280,U_1279,U_1278,U_1277] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1277,U_1278,U_1279)
          | ~ c_Orderings_Oord__class_Oless(U_1277,U_1280,U_1281) )
        & ( c_Orderings_Oord__class_Oless(U_1277,U_1280,U_1281)
          | ~ c_Orderings_Oord__class_Oless(U_1277,U_1278,U_1279) ) )
      | c_Groups_Ominus__class_Ominus(U_1277,U_1278,U_1279) != c_Groups_Ominus__class_Ominus(U_1277,U_1280,U_1281)
      | ~ class_Groups_Oordered__ab__group__add(U_1277) ),
    inference(variable_rename,[status(thm)],[f_382_1]) ).

fof(f_382_3,plain,
    ( ! [U_1280,U_1279,U_1281,U_1278,U_1277] :
        ( c_Orderings_Oord__class_Oless(U_1277,U_1278,U_1279)
        | ~ c_Orderings_Oord__class_Oless(U_1277,U_1280,U_1281)
        | ~ sP106(U_1280,U_1279,U_1281,U_1278,U_1277) )
    & ! [U_1280,U_1279,U_1281,U_1278,U_1277] :
        ( c_Orderings_Oord__class_Oless(U_1277,U_1280,U_1281)
        | ~ c_Orderings_Oord__class_Oless(U_1277,U_1278,U_1279)
        | ~ sP106(U_1280,U_1279,U_1281,U_1278,U_1277) )
    & ! [U_1280,U_1279,U_1281,U_1278,U_1277] :
        ( sP106(U_1280,U_1279,U_1281,U_1278,U_1277)
        | c_Groups_Ominus__class_Ominus(U_1277,U_1278,U_1279) != c_Groups_Ominus__class_Ominus(U_1277,U_1280,U_1281)
        | ~ class_Groups_Oordered__ab__group__add(U_1277) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP106])],[f_382_2]) ).

cnf(f_382_4,plain,
    ( sP106(U_1280,U_1279,U_1281,U_1278,U_1277)
    | c_Groups_Ominus__class_Ominus(U_1277,U_1278,U_1279) != c_Groups_Ominus__class_Ominus(U_1277,U_1280,U_1281)
    | ~ class_Groups_Oordered__ab__group__add(U_1277) ),
    inference(clausify,[status(thm)],[f_382_3]) ).

cnf(f_382_5,plain,
    ( c_Orderings_Oord__class_Oless(U_1277,U_1280,U_1281)
    | ~ c_Orderings_Oord__class_Oless(U_1277,U_1278,U_1279)
    | ~ sP106(U_1280,U_1279,U_1281,U_1278,U_1277) ),
    inference(clausify,[status(thm)],[f_382_3]) ).

cnf(f_382_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1277,U_1278,U_1279)
    | ~ c_Orderings_Oord__class_Oless(U_1277,U_1280,U_1281)
    | ~ sP106(U_1280,U_1279,U_1281,U_1278,U_1277) ),
    inference(clausify,[status(thm)],[f_382_3]) ).

fof(f_383_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J]) ).

fof(f_383_2,plain,
    ! [U_1283,U_1282] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1282),U_1283),c_Groups_Oone__class_Oone(U_1282)) = U_1283
      | ~ class_Rings_Ocomm__semiring__1(U_1282) ),
    inference(variable_rename,[status(thm)],[f_383_1]) ).

fof(f_383_3,plain,
    ! [U_1283,U_1282] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1282),U_1283),c_Groups_Oone__class_Oone(U_1282)) = U_1283
      | ~ class_Rings_Ocomm__semiring__1(U_1282) ),
    inference(definitional_conversion,[status(esa)],[f_383_2]) ).

cnf(f_383_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1282),U_1283),c_Groups_Oone__class_Oone(U_1282)) = U_1283
    | ~ class_Rings_Ocomm__semiring__1(U_1282) ),
    inference(clausify,[status(thm)],[f_383_3]) ).

fof(f_384_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J]) ).

fof(f_384_2,plain,
    ! [U_1285,U_1284] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1284),c_Groups_Oone__class_Oone(U_1284)),U_1285) = U_1285
      | ~ class_Rings_Ocomm__semiring__1(U_1284) ),
    inference(variable_rename,[status(thm)],[f_384_1]) ).

fof(f_384_3,plain,
    ! [U_1284,U_1285] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1284),c_Groups_Oone__class_Oone(U_1284)),U_1285) = U_1285
      | ~ class_Rings_Ocomm__semiring__1(U_1284) ),
    inference(definitional_conversion,[status(esa)],[f_384_2]) ).

cnf(f_384_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1284),c_Groups_Oone__class_Oone(U_1284)),U_1285) = U_1285
    | ~ class_Rings_Ocomm__semiring__1(U_1284) ),
    inference(clausify,[status(thm)],[f_384_3]) ).

fof(f_385_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a
      | ~ class_Groups_Ocomm__monoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult_Ocomm__neutral]) ).

fof(f_385_2,plain,
    ! [U_1287,U_1286] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1286),U_1287),c_Groups_Oone__class_Oone(U_1286)) = U_1287
      | ~ class_Groups_Ocomm__monoid__mult(U_1286) ),
    inference(variable_rename,[status(thm)],[f_385_1]) ).

fof(f_385_3,plain,
    ! [U_1287,U_1286] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1286),U_1287),c_Groups_Oone__class_Oone(U_1286)) = U_1287
      | ~ class_Groups_Ocomm__monoid__mult(U_1286) ),
    inference(definitional_conversion,[status(esa)],[f_385_2]) ).

cnf(f_385_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1286),U_1287),c_Groups_Oone__class_Oone(U_1286)) = U_1287
    | ~ class_Groups_Ocomm__monoid__mult(U_1286) ),
    inference(clausify,[status(thm)],[f_385_3]) ).

fof(f_386_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__1__right]) ).

fof(f_386_2,plain,
    ! [U_1289,U_1288] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1288),U_1289),c_Groups_Oone__class_Oone(U_1288)) = U_1289
      | ~ class_Groups_Omonoid__mult(U_1288) ),
    inference(variable_rename,[status(thm)],[f_386_1]) ).

fof(f_386_3,plain,
    ! [U_1288,U_1289] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1288),U_1289),c_Groups_Oone__class_Oone(U_1288)) = U_1289
      | ~ class_Groups_Omonoid__mult(U_1288) ),
    inference(definitional_conversion,[status(esa)],[f_386_2]) ).

cnf(f_386_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1288),U_1289),c_Groups_Oone__class_Oone(U_1288)) = U_1289
    | ~ class_Groups_Omonoid__mult(U_1288) ),
    inference(clausify,[status(thm)],[f_386_3]) ).

fof(f_387_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a
      | ~ class_Groups_Ocomm__monoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__1]) ).

fof(f_387_2,plain,
    ! [U_1291,U_1290] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1290),c_Groups_Oone__class_Oone(U_1290)),U_1291) = U_1291
      | ~ class_Groups_Ocomm__monoid__mult(U_1290) ),
    inference(variable_rename,[status(thm)],[f_387_1]) ).

fof(f_387_3,plain,
    ! [U_1290,U_1291] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1290),c_Groups_Oone__class_Oone(U_1290)),U_1291) = U_1291
      | ~ class_Groups_Ocomm__monoid__mult(U_1290) ),
    inference(definitional_conversion,[status(esa)],[f_387_2]) ).

cnf(f_387_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1290),c_Groups_Oone__class_Oone(U_1290)),U_1291) = U_1291
    | ~ class_Groups_Ocomm__monoid__mult(U_1290) ),
    inference(clausify,[status(thm)],[f_387_3]) ).

fof(f_388_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__1__left]) ).

fof(f_388_2,plain,
    ! [U_1293,U_1292] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1292),c_Groups_Oone__class_Oone(U_1292)),U_1293) = U_1293
      | ~ class_Groups_Omonoid__mult(U_1292) ),
    inference(variable_rename,[status(thm)],[f_388_1]) ).

fof(f_388_3,plain,
    ! [U_1292,U_1293] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1292),c_Groups_Oone__class_Oone(U_1292)),U_1293) = U_1293
      | ~ class_Groups_Omonoid__mult(U_1292) ),
    inference(definitional_conversion,[status(esa)],[f_388_2]) ).

cnf(f_388_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1292),c_Groups_Oone__class_Oone(U_1292)),U_1293) = U_1293
    | ~ class_Groups_Omonoid__mult(U_1292) ),
    inference(clausify,[status(thm)],[f_388_3]) ).

fof(f_389_1,plain,
    ! [V_n] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
      | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_nnf,[status(thm)],[fact_gr0I]) ).

fof(f_389_2,plain,
    ! [U_1294] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1294)
      | U_1294 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_389_1]) ).

fof(f_389_3,plain,
    ! [U_1294] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1294)
      | U_1294 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_389_2]) ).

cnf(f_389_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1294)
    | U_1294 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_389_3]) ).

fof(f_390_1,plain,
    ! [V_n,V_m] :
      ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
    inference(fof_nnf,[status(thm)],[fact_gr__implies__not0]) ).

fof(f_390_2,plain,
    ! [U_1296,U_1295] :
      ( U_1296 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1295,U_1296) ),
    inference(variable_rename,[status(thm)],[f_390_1]) ).

fof(f_390_3,plain,
    ! [U_1296] :
      ( ! [U_1295] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1295,U_1296)
      | U_1296 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(miniscope,[status(thm)],[f_390_2]) ).

fof(f_390_4,plain,
    ! [U_1295,U_1296] :
      ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1295,U_1296)
      | U_1296 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_390_3]) ).

cnf(f_390_5,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1295,U_1296)
    | U_1296 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_390_4]) ).

fof(f_391_1,plain,
    ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_less__nat__zero__code]) ).

fof(f_391_2,plain,
    ! [U_1297] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1297,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_391_1]) ).

fof(f_391_3,plain,
    ! [U_1297] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1297,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_391_2]) ).

cnf(f_391_4,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1297,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_391_3]) ).

fof(f_392_1,plain,
    ! [V_n_2] :
      ( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
        | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_neq0__conv]) ).

fof(f_392_2,plain,
    ! [U_1298] :
      ( ( U_1298 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1298) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1298)
        | U_1298 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_392_1]) ).

fof(f_392_3,plain,
    ( ! [U_1300] :
        ( U_1300 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1300) )
    & ! [U_1299] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1299)
        | U_1299 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_392_2]) ).

fof(f_392_4,plain,
    ( ! [U_1300] :
        ( U_1300 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1300) )
    & ! [U_1299] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1299)
        | U_1299 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_392_3]) ).

cnf(f_392_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1299)
    | U_1299 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_392_4]) ).

cnf(f_392_6,plain,
    ( U_1300 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1300) ),
    inference(clausify,[status(thm)],[f_392_4]) ).

fof(f_393_1,plain,
    ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_not__less0]) ).

fof(f_393_2,plain,
    ! [U_1301] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1301,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_393_1]) ).

fof(f_393_3,plain,
    ! [U_1301] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1301,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_393_2]) ).

cnf(f_393_4,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1301,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_393_3]) ).

fof(f_394_1,plain,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k) ),
    inference(fof_nnf,[status(thm)],[fact_add__lessD1]) ).

fof(f_394_2,plain,
    ! [U_1304,U_1303,U_1302] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1302,U_1304)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1302,U_1303),U_1304) ),
    inference(variable_rename,[status(thm)],[f_394_1]) ).

fof(f_394_3,plain,
    ! [U_1303,U_1302,U_1304] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1302,U_1304)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1302,U_1303),U_1304) ),
    inference(definitional_conversion,[status(esa)],[f_394_2]) ).

cnf(f_394_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1302,U_1304)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1302,U_1303),U_1304) ),
    inference(clausify,[status(thm)],[f_394_3]) ).

fof(f_395_1,plain,
    ! [V_n,V_m,V_l,V_k] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l) ),
    inference(fof_nnf,[status(thm)],[fact_less__add__eq__less]) ).

fof(f_395_2,plain,
    ! [U_1308,U_1307,U_1306,U_1305] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1307,U_1308)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1307,U_1306) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1305,U_1308)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1305,U_1306) ),
    inference(variable_rename,[status(thm)],[f_395_1]) ).

fof(f_395_3,plain,
    ! [U_1305,U_1306,U_1307,U_1308] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1307,U_1308)
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1307,U_1306) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1305,U_1308)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1305,U_1306) ),
    inference(definitional_conversion,[status(esa)],[f_395_2]) ).

cnf(f_395_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1307,U_1308)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1307,U_1306) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1305,U_1308)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1305,U_1306) ),
    inference(clausify,[status(thm)],[f_395_3]) ).

fof(f_396_1,plain,
    ! [V_l,V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_add__less__mono]) ).

fof(f_396_2,plain,
    ! [U_1312,U_1311,U_1310,U_1309] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1309,U_1311),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1310,U_1312))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1311,U_1312)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1309,U_1310) ),
    inference(variable_rename,[status(thm)],[f_396_1]) ).

fof(f_396_3,plain,
    ! [U_1311,U_1310,U_1309,U_1312] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1309,U_1311),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1310,U_1312))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1311,U_1312)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1309,U_1310) ),
    inference(definitional_conversion,[status(esa)],[f_396_2]) ).

cnf(f_396_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1309,U_1311),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1310,U_1312))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1311,U_1312)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1309,U_1310) ),
    inference(clausify,[status(thm)],[f_396_3]) ).

fof(f_397_1,plain,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_add__less__mono1]) ).

fof(f_397_2,plain,
    ! [U_1315,U_1314,U_1313] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1313,U_1315),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1314,U_1315))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1313,U_1314) ),
    inference(variable_rename,[status(thm)],[f_397_1]) ).

fof(f_397_3,plain,
    ! [U_1315,U_1314,U_1313] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1313,U_1315),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1314,U_1315))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1313,U_1314) ),
    inference(definitional_conversion,[status(esa)],[f_397_2]) ).

cnf(f_397_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1313,U_1315),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1314,U_1315))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1313,U_1314) ),
    inference(clausify,[status(thm)],[f_397_3]) ).

fof(f_398_1,plain,
    ! [V_m,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_trans__less__add2]) ).

fof(f_398_2,plain,
    ! [U_1318,U_1317,U_1316] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1316,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1318,U_1317))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1316,U_1317) ),
    inference(variable_rename,[status(thm)],[f_398_1]) ).

fof(f_398_3,plain,
    ! [U_1317,U_1316,U_1318] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1316,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1318,U_1317))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1316,U_1317) ),
    inference(definitional_conversion,[status(esa)],[f_398_2]) ).

cnf(f_398_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1316,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1318,U_1317))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1316,U_1317) ),
    inference(clausify,[status(thm)],[f_398_3]) ).

fof(f_399_1,plain,
    ! [V_m,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_trans__less__add1]) ).

fof(f_399_2,plain,
    ! [U_1321,U_1320,U_1319] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1319,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1320,U_1321))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1319,U_1320) ),
    inference(variable_rename,[status(thm)],[f_399_1]) ).

fof(f_399_3,plain,
    ! [U_1320,U_1319,U_1321] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1319,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1320,U_1321))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1319,U_1320) ),
    inference(definitional_conversion,[status(esa)],[f_399_2]) ).

cnf(f_399_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1319,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1320,U_1321))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1319,U_1320) ),
    inference(clausify,[status(thm)],[f_399_3]) ).

fof(f_400_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less]) ).

fof(f_400_2,plain,
    ! [U_1324,U_1323,U_1322] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1322,U_1323),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1322,U_1324))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1323,U_1324) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1323,U_1324)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1322,U_1323),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1322,U_1324)) ) ),
    inference(variable_rename,[status(thm)],[f_400_1]) ).

fof(f_400_3,plain,
    ( ! [U_1330,U_1328] :
        ( ! [U_1326] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1326,U_1328),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1326,U_1330))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1328,U_1330) )
    & ! [U_1329,U_1327] :
        ( ! [U_1325] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1325,U_1327),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1325,U_1329))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1327,U_1329) ) ),
    inference(miniscope,[status(thm)],[f_400_2]) ).

fof(f_400_4,plain,
    ( ! [U_1328,U_1326,U_1330] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1326,U_1328),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1326,U_1330))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1328,U_1330) )
    & ! [U_1325,U_1327,U_1329] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1325,U_1327),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1325,U_1329))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1327,U_1329) ) ),
    inference(definitional_conversion,[status(esa)],[f_400_3]) ).

cnf(f_400_5,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1325,U_1327),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1325,U_1329))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1327,U_1329) ),
    inference(clausify,[status(thm)],[f_400_4]) ).

cnf(f_400_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1326,U_1328),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1326,U_1330))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1328,U_1330) ),
    inference(clausify,[status(thm)],[f_400_4]) ).

fof(f_401_1,plain,
    ! [V_i,V_j] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i),
    inference(fof_nnf,[status(thm)],[fact_not__add__less2]) ).

fof(f_401_2,plain,
    ! [U_1332,U_1331] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1331,U_1332),U_1332),
    inference(variable_rename,[status(thm)],[f_401_1]) ).

fof(f_401_3,plain,
    ! [U_1332,U_1331] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1331,U_1332),U_1332),
    inference(definitional_conversion,[status(esa)],[f_401_2]) ).

cnf(f_401_4,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1331,U_1332),U_1332),
    inference(clausify,[status(thm)],[f_401_3]) ).

fof(f_402_1,plain,
    ! [V_j,V_i] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i),
    inference(fof_nnf,[status(thm)],[fact_not__add__less1]) ).

fof(f_402_2,plain,
    ! [U_1334,U_1333] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1333,U_1334),U_1333),
    inference(variable_rename,[status(thm)],[f_402_1]) ).

fof(f_402_3,plain,
    ! [U_1334,U_1333] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1333,U_1334),U_1333),
    inference(definitional_conversion,[status(esa)],[f_402_2]) ).

cnf(f_402_4,plain,
    ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1333,U_1334),U_1333),
    inference(clausify,[status(thm)],[f_402_3]) ).

fof(f_403_1,plain,
    ! [V_y,V_z,V_x] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z) ),
    inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J]) ).

fof(f_403_2,plain,
    ! [U_1337,U_1336,U_1335] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1335,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1337,U_1336))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1335,U_1336) ),
    inference(variable_rename,[status(thm)],[f_403_1]) ).

fof(f_403_3,plain,
    ! [U_1337,U_1336,U_1335] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1335,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1337,U_1336))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1335,U_1336) ),
    inference(definitional_conversion,[status(esa)],[f_403_2]) ).

cnf(f_403_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1335,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1337,U_1336))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1335,U_1336) ),
    inference(clausify,[status(thm)],[f_403_3]) ).

fof(f_404_1,plain,
    ! [V_z,V_y,V_x] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y) ),
    inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J]) ).

fof(f_404_2,plain,
    ! [U_1340,U_1339,U_1338] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1338,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1339,U_1340))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1338,U_1339) ),
    inference(variable_rename,[status(thm)],[f_404_1]) ).

fof(f_404_3,plain,
    ! [U_1340,U_1339,U_1338] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1338,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1339,U_1340))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1338,U_1339) ),
    inference(definitional_conversion,[status(esa)],[f_404_2]) ).

cnf(f_404_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1338,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1339,U_1340))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1338,U_1339) ),
    inference(clausify,[status(thm)],[f_404_3]) ).

fof(f_405_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
        | V_m_2 = V_n_2
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) )
      & ( ( V_m_2 != V_n_2
          & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__less__le]) ).

fof(f_405_2,plain,
    ! [U_1342,U_1341] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1341,U_1342)
        | U_1341 = U_1342
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1341,U_1342) )
      & ( ( U_1341 != U_1342
          & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1341,U_1342) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1341,U_1342) ) ),
    inference(variable_rename,[status(thm)],[f_405_1]) ).

fof(f_405_3,plain,
    ( ! [U_1346,U_1344] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1344,U_1346)
        | U_1344 = U_1346
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1344,U_1346) )
    & ! [U_1345,U_1343] :
        ( ( U_1343 != U_1345
          & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1343,U_1345) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1343,U_1345) ) ),
    inference(miniscope,[status(thm)],[f_405_2]) ).

fof(f_405_4,plain,
    ( ! [U_1343,U_1345] :
        ( U_1343 != U_1345
        | ~ sP107(U_1343,U_1345) )
    & ! [U_1343,U_1345] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1343,U_1345)
        | ~ sP107(U_1343,U_1345) )
    & ! [U_1346,U_1344] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1344,U_1346)
        | U_1344 = U_1346
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1344,U_1346) )
    & ! [U_1343,U_1345] :
        ( sP107(U_1343,U_1345)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1343,U_1345) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP107])],[f_405_3]) ).

cnf(f_405_5,plain,
    ( sP107(U_1343,U_1345)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1343,U_1345) ),
    inference(clausify,[status(thm)],[f_405_4]) ).

cnf(f_405_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1344,U_1346)
    | U_1344 = U_1346
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1344,U_1346) ),
    inference(clausify,[status(thm)],[f_405_4]) ).

cnf(f_405_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1343,U_1345)
    | ~ sP107(U_1343,U_1345) ),
    inference(clausify,[status(thm)],[f_405_4]) ).

cnf(f_405_8,plain,
    ( U_1343 != U_1345
    | ~ sP107(U_1343,U_1345) ),
    inference(clausify,[status(thm)],[f_405_4]) ).

fof(f_406_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
        | ( V_m_2 != V_n_2
          & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) )
      & ( V_m_2 = V_n_2
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq]) ).

fof(f_406_2,plain,
    ! [U_1348,U_1347] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1347,U_1348)
        | ( U_1347 != U_1348
          & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1347,U_1348) ) )
      & ( U_1347 = U_1348
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1347,U_1348)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1347,U_1348) ) ),
    inference(variable_rename,[status(thm)],[f_406_1]) ).

fof(f_406_3,plain,
    ( ! [U_1352,U_1350] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1350,U_1352)
        | ( U_1350 != U_1352
          & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1350,U_1352) ) )
    & ! [U_1351,U_1349] :
        ( U_1349 = U_1351
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1349,U_1351)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1349,U_1351) ) ),
    inference(miniscope,[status(thm)],[f_406_2]) ).

fof(f_406_4,plain,
    ( ! [U_1350,U_1352] :
        ( U_1350 != U_1352
        | ~ sP108(U_1350,U_1352) )
    & ! [U_1350,U_1352] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1350,U_1352)
        | ~ sP108(U_1350,U_1352) )
    & ! [U_1350,U_1352] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1350,U_1352)
        | sP108(U_1350,U_1352) )
    & ! [U_1349,U_1351] :
        ( U_1349 = U_1351
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1349,U_1351)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1349,U_1351) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP108])],[f_406_3]) ).

cnf(f_406_5,plain,
    ( U_1349 = U_1351
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1349,U_1351)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1349,U_1351) ),
    inference(clausify,[status(thm)],[f_406_4]) ).

cnf(f_406_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1350,U_1352)
    | sP108(U_1350,U_1352) ),
    inference(clausify,[status(thm)],[f_406_4]) ).

cnf(f_406_7,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1350,U_1352)
    | ~ sP108(U_1350,U_1352) ),
    inference(clausify,[status(thm)],[f_406_4]) ).

cnf(f_406_8,plain,
    ( U_1350 != U_1352
    | ~ sP108(U_1350,U_1352) ),
    inference(clausify,[status(thm)],[f_406_4]) ).

fof(f_407_1,plain,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
    inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat]) ).

fof(f_407_2,plain,
    ! [U_1354,U_1353] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1353,U_1354)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1353,U_1354) ),
    inference(variable_rename,[status(thm)],[f_407_1]) ).

fof(f_407_3,plain,
    ! [U_1354,U_1353] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1353,U_1354)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1353,U_1354) ),
    inference(definitional_conversion,[status(esa)],[f_407_2]) ).

cnf(f_407_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1353,U_1354)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1353,U_1354) ),
    inference(clausify,[status(thm)],[f_407_3]) ).

fof(f_408_1,plain,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
      | V_m = V_n
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
    inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less]) ).

fof(f_408_2,plain,
    ! [U_1356,U_1355] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1355,U_1356)
      | U_1355 = U_1356
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1355,U_1356) ),
    inference(variable_rename,[status(thm)],[f_408_1]) ).

fof(f_408_3,plain,
    ! [U_1355,U_1356] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1355,U_1356)
      | U_1355 = U_1356
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1355,U_1356) ),
    inference(definitional_conversion,[status(esa)],[f_408_2]) ).

cnf(f_408_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1355,U_1356)
    | U_1355 = U_1356
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1355,U_1356) ),
    inference(clausify,[status(thm)],[f_408_3]) ).

fof(f_409_1,plain,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
      | ( V_m != V_n
        & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le]) ).

fof(f_409_2,plain,
    ! [U_1358,U_1357] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1357,U_1358)
      | ( U_1357 != U_1358
        & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1357,U_1358) ) ),
    inference(variable_rename,[status(thm)],[f_409_1]) ).

fof(f_409_3,plain,
    ( ! [U_1358,U_1357] :
        ( U_1357 != U_1358
        | ~ sP109(U_1358,U_1357) )
    & ! [U_1358,U_1357] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1357,U_1358)
        | ~ sP109(U_1358,U_1357) )
    & ! [U_1358,U_1357] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1357,U_1358)
        | sP109(U_1358,U_1357) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP109])],[f_409_2]) ).

cnf(f_409_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1357,U_1358)
    | sP109(U_1358,U_1357) ),
    inference(clausify,[status(thm)],[f_409_3]) ).

cnf(f_409_5,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1357,U_1358)
    | ~ sP109(U_1358,U_1357) ),
    inference(clausify,[status(thm)],[f_409_3]) ).

cnf(f_409_6,plain,
    ( U_1357 != U_1358
    | ~ sP109(U_1358,U_1357) ),
    inference(clausify,[status(thm)],[f_409_3]) ).

fof(f_410_1,plain,
    ! [V_y,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y) ),
    inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J]) ).

fof(f_410_2,plain,
    ! [U_1360,U_1359] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1359,U_1360)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1359,U_1360) ),
    inference(variable_rename,[status(thm)],[f_410_1]) ).

fof(f_410_3,plain,
    ! [U_1359,U_1360] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1359,U_1360)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1359,U_1360) ),
    inference(definitional_conversion,[status(esa)],[f_410_2]) ).

cnf(f_410_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1359,U_1360)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1359,U_1360) ),
    inference(clausify,[status(thm)],[f_410_3]) ).

fof(f_411_1,plain,
    ! [V_l,V_n,V_m] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
    inference(fof_nnf,[status(thm)],[fact_diff__less__mono2]) ).

fof(f_411_2,plain,
    ! [U_1363,U_1362,U_1361] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1363,U_1362),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1363,U_1361))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1361,U_1363)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1361,U_1362) ),
    inference(variable_rename,[status(thm)],[f_411_1]) ).

fof(f_411_3,plain,
    ! [U_1362,U_1361,U_1363] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1363,U_1362),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1363,U_1361))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1361,U_1363)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1361,U_1362) ),
    inference(definitional_conversion,[status(esa)],[f_411_2]) ).

cnf(f_411_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1363,U_1362),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1363,U_1361))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1361,U_1363)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1361,U_1362) ),
    inference(clausify,[status(thm)],[f_411_3]) ).

fof(f_412_1,plain,
    ! [V_n,V_k,V_j] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k) ),
    inference(fof_nnf,[status(thm)],[fact_less__imp__diff__less]) ).

fof(f_412_2,plain,
    ! [U_1366,U_1365,U_1364] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1364,U_1366),U_1365)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1364,U_1365) ),
    inference(variable_rename,[status(thm)],[f_412_1]) ).

fof(f_412_3,plain,
    ! [U_1366,U_1364,U_1365] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1364,U_1366),U_1365)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1364,U_1365) ),
    inference(definitional_conversion,[status(esa)],[f_412_2]) ).

cnf(f_412_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1364,U_1366),U_1365)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1364,U_1365) ),
    inference(clausify,[status(thm)],[f_412_3]) ).

fof(f_413_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | V_n_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | V_m_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__1__iff]) ).

fof(f_413_2,plain,
    ! [U_1368,U_1367] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1367),U_1368) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_1368 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_1367 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ( U_1368 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_1367 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1367),U_1368) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_413_1]) ).

fof(f_413_3,plain,
    ( ! [U_1372,U_1370] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1370),U_1372) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_1372 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_1370 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_1371,U_1369] :
        ( ( U_1371 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_1369 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1369),U_1371) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_413_2]) ).

fof(f_413_4,plain,
    ( ! [U_1371,U_1369] :
        ( U_1371 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP110(U_1371,U_1369) )
    & ! [U_1371,U_1369] :
        ( U_1369 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP110(U_1371,U_1369) )
    & ! [U_1372,U_1370] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1370),U_1372) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_1372 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_1370 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_1371,U_1369] :
        ( sP110(U_1371,U_1369)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1369),U_1371) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP110])],[f_413_3]) ).

cnf(f_413_5,plain,
    ( sP110(U_1371,U_1369)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1369),U_1371) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_413_4]) ).

cnf(f_413_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1370),U_1372) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_1372 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_1370 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_413_4]) ).

cnf(f_413_7,plain,
    ( U_1369 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP110(U_1371,U_1369) ),
    inference(clausify,[status(thm)],[f_413_4]) ).

cnf(f_413_8,plain,
    ( U_1371 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP110(U_1371,U_1369) ),
    inference(clausify,[status(thm)],[f_413_4]) ).

fof(f_414_1,plain,
    ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n,
    inference(fof_nnf,[status(thm)],[fact_nat__mult__1__right]) ).

fof(f_414_2,plain,
    ! [U_1373] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1373),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1373,
    inference(variable_rename,[status(thm)],[f_414_1]) ).

fof(f_414_3,plain,
    ! [U_1373] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1373),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1373,
    inference(definitional_conversion,[status(esa)],[f_414_2]) ).

cnf(f_414_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1373),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1373,
    inference(clausify,[status(thm)],[f_414_3]) ).

fof(f_415_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
        | V_n_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | V_m_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff]) ).

fof(f_415_2,plain,
    ! [U_1375,U_1374] :
      ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1374),U_1375)
        | U_1375 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_1374 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ( U_1375 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_1374 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1374),U_1375) ) ),
    inference(variable_rename,[status(thm)],[f_415_1]) ).

fof(f_415_3,plain,
    ( ! [U_1379,U_1377] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1377),U_1379)
        | U_1379 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_1377 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_1378,U_1376] :
        ( ( U_1378 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_1376 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1376),U_1378) ) ),
    inference(miniscope,[status(thm)],[f_415_2]) ).

fof(f_415_4,plain,
    ( ! [U_1378,U_1376] :
        ( U_1378 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP111(U_1378,U_1376) )
    & ! [U_1378,U_1376] :
        ( U_1376 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP111(U_1378,U_1376) )
    & ! [U_1379,U_1377] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1377),U_1379)
        | U_1379 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_1377 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_1378,U_1376] :
        ( sP111(U_1378,U_1376)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1376),U_1378) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP111])],[f_415_3]) ).

cnf(f_415_5,plain,
    ( sP111(U_1378,U_1376)
    | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1376),U_1378) ),
    inference(clausify,[status(thm)],[f_415_4]) ).

cnf(f_415_6,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1377),U_1379)
    | U_1379 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_1377 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_415_4]) ).

cnf(f_415_7,plain,
    ( U_1376 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP111(U_1378,U_1376) ),
    inference(clausify,[status(thm)],[f_415_4]) ).

cnf(f_415_8,plain,
    ( U_1378 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP111(U_1378,U_1376) ),
    inference(clausify,[status(thm)],[f_415_4]) ).

fof(f_416_1,plain,
    ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n,
    inference(fof_nnf,[status(thm)],[fact_nat__mult__1]) ).

fof(f_416_2,plain,
    ! [U_1380] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1380) = U_1380,
    inference(variable_rename,[status(thm)],[f_416_1]) ).

fof(f_416_3,plain,
    ! [U_1380] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1380) = U_1380,
    inference(definitional_conversion,[status(esa)],[f_416_2]) ).

cnf(f_416_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1380) = U_1380,
    inference(clausify,[status(thm)],[f_416_3]) ).

fof(f_417_1,plain,
    ! [V_p,T_a] :
      ( c_Polynomial_Osmult(T_a,c_Groups_Oone__class_Oone(T_a),V_p) = V_p
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_smult__1__left]) ).

fof(f_417_2,plain,
    ! [U_1382,U_1381] :
      ( c_Polynomial_Osmult(U_1381,c_Groups_Oone__class_Oone(U_1381),U_1382) = U_1382
      | ~ class_Rings_Ocomm__semiring__1(U_1381) ),
    inference(variable_rename,[status(thm)],[f_417_1]) ).

fof(f_417_3,plain,
    ! [U_1381,U_1382] :
      ( c_Polynomial_Osmult(U_1381,c_Groups_Oone__class_Oone(U_1381),U_1382) = U_1382
      | ~ class_Rings_Ocomm__semiring__1(U_1381) ),
    inference(definitional_conversion,[status(esa)],[f_417_2]) ).

cnf(f_417_4,plain,
    ( c_Polynomial_Osmult(U_1381,c_Groups_Oone__class_Oone(U_1381),U_1382) = U_1382
    | ~ class_Rings_Ocomm__semiring__1(U_1381) ),
    inference(clausify,[status(thm)],[f_417_3]) ).

fof(f_418_1,plain,
    ! [V_v,V_u,V_y,V_a,V_x,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a)
      | c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) != c_Groups_Oone__class_Oone(T_a)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_a)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_a)
      | ~ class_Rings_Olinordered__semiring__1__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_convex__bound__lt]) ).

fof(f_418_2,plain,
    ! [U_1388,U_1387,U_1386,U_1385,U_1384,U_1383] :
      ( c_Orderings_Oord__class_Oless(U_1383,c_Groups_Oplus__class_Oplus(U_1383,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1383),U_1387),U_1384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1383),U_1388),U_1386)),U_1385)
      | c_Groups_Oplus__class_Oplus(U_1383,U_1387,U_1388) != c_Groups_Oone__class_Oone(U_1383)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1383,c_Groups_Ozero__class_Ozero(U_1383),U_1388)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1383,c_Groups_Ozero__class_Ozero(U_1383),U_1387)
      | ~ c_Orderings_Oord__class_Oless(U_1383,U_1386,U_1385)
      | ~ c_Orderings_Oord__class_Oless(U_1383,U_1384,U_1385)
      | ~ class_Rings_Olinordered__semiring__1__strict(U_1383) ),
    inference(variable_rename,[status(thm)],[f_418_1]) ).

fof(f_418_3,plain,
    ! [U_1383,U_1384,U_1385,U_1386,U_1387,U_1388] :
      ( c_Orderings_Oord__class_Oless(U_1383,c_Groups_Oplus__class_Oplus(U_1383,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1383),U_1387),U_1384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1383),U_1388),U_1386)),U_1385)
      | c_Groups_Oplus__class_Oplus(U_1383,U_1387,U_1388) != c_Groups_Oone__class_Oone(U_1383)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1383,c_Groups_Ozero__class_Ozero(U_1383),U_1388)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1383,c_Groups_Ozero__class_Ozero(U_1383),U_1387)
      | ~ c_Orderings_Oord__class_Oless(U_1383,U_1386,U_1385)
      | ~ c_Orderings_Oord__class_Oless(U_1383,U_1384,U_1385)
      | ~ class_Rings_Olinordered__semiring__1__strict(U_1383) ),
    inference(definitional_conversion,[status(esa)],[f_418_2]) ).

cnf(f_418_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1383,c_Groups_Oplus__class_Oplus(U_1383,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1383),U_1387),U_1384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1383),U_1388),U_1386)),U_1385)
    | c_Groups_Oplus__class_Oplus(U_1383,U_1387,U_1388) != c_Groups_Oone__class_Oone(U_1383)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1383,c_Groups_Ozero__class_Ozero(U_1383),U_1388)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1383,c_Groups_Ozero__class_Ozero(U_1383),U_1387)
    | ~ c_Orderings_Oord__class_Oless(U_1383,U_1386,U_1385)
    | ~ c_Orderings_Oord__class_Oless(U_1383,U_1384,U_1385)
    | ~ class_Rings_Olinordered__semiring__1__strict(U_1383) ),
    inference(clausify,[status(thm)],[f_418_3]) ).

fof(f_419_1,plain,
    ! [V_a,T_a] :
      ( ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a),c_Groups_Ozero__class_Ozero(T_a))
      | ~ class_Rings_Olinordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_not__square__less__zero]) ).

fof(f_419_2,plain,
    ! [U_1390,U_1389] :
      ( ~ c_Orderings_Oord__class_Oless(U_1389,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1389),U_1390),U_1390),c_Groups_Ozero__class_Ozero(U_1389))
      | ~ class_Rings_Olinordered__ring(U_1389) ),
    inference(variable_rename,[status(thm)],[f_419_1]) ).

fof(f_419_3,plain,
    ! [U_1390,U_1389] :
      ( ~ c_Orderings_Oord__class_Oless(U_1389,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1389),U_1390),U_1390),c_Groups_Ozero__class_Ozero(U_1389))
      | ~ class_Rings_Olinordered__ring(U_1389) ),
    inference(definitional_conversion,[status(esa)],[f_419_2]) ).

cnf(f_419_4,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1389,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1389),U_1390),U_1390),c_Groups_Ozero__class_Ozero(U_1389))
    | ~ class_Rings_Olinordered__ring(U_1389) ),
    inference(clausify,[status(thm)],[f_419_3]) ).

fof(f_420_1,plain,
    ! [V_b_2,V_ca_2,V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))
          | ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,V_ab_2)
              | ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) )
            & ( ~ c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2)
              | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) ) ) )
        & ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_ab_2)
            & c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) )
          | ( c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2)
            & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) )
          | ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj]) ).

fof(f_420_2,plain,
    ! [U_1394,U_1393,U_1392,U_1391] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1391,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1391),U_1392),U_1393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1391),U_1394),U_1393))
          | ( ( ~ c_Orderings_Oord__class_Oless(U_1391,U_1394,U_1392)
              | ~ c_Orderings_Oord__class_Oless(U_1391,U_1393,c_Groups_Ozero__class_Ozero(U_1391)) )
            & ( ~ c_Orderings_Oord__class_Oless(U_1391,U_1392,U_1394)
              | ~ c_Orderings_Oord__class_Oless(U_1391,c_Groups_Ozero__class_Ozero(U_1391),U_1393) ) ) )
        & ( ( c_Orderings_Oord__class_Oless(U_1391,U_1394,U_1392)
            & c_Orderings_Oord__class_Oless(U_1391,U_1393,c_Groups_Ozero__class_Ozero(U_1391)) )
          | ( c_Orderings_Oord__class_Oless(U_1391,U_1392,U_1394)
            & c_Orderings_Oord__class_Oless(U_1391,c_Groups_Ozero__class_Ozero(U_1391),U_1393) )
          | ~ c_Orderings_Oord__class_Oless(U_1391,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1391),U_1392),U_1393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1391),U_1394),U_1393)) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_1391) ),
    inference(variable_rename,[status(thm)],[f_420_1]) ).

fof(f_420_3,plain,
    ( ! [U_1391,U_1392,U_1393,U_1394] :
        ( ~ c_Orderings_Oord__class_Oless(U_1391,U_1394,U_1392)
        | ~ c_Orderings_Oord__class_Oless(U_1391,U_1393,c_Groups_Ozero__class_Ozero(U_1391))
        | ~ sP114(U_1391,U_1392,U_1393,U_1394) )
    & ! [U_1391,U_1392,U_1393,U_1394] :
        ( ~ c_Orderings_Oord__class_Oless(U_1391,U_1392,U_1394)
        | ~ c_Orderings_Oord__class_Oless(U_1391,c_Groups_Ozero__class_Ozero(U_1391),U_1393)
        | ~ sP114(U_1391,U_1392,U_1393,U_1394) )
    & ! [U_1391,U_1392,U_1393,U_1394] :
        ( c_Orderings_Oord__class_Oless(U_1391,U_1394,U_1392)
        | ~ sP113(U_1391,U_1392,U_1393,U_1394) )
    & ! [U_1391,U_1392,U_1393,U_1394] :
        ( c_Orderings_Oord__class_Oless(U_1391,U_1393,c_Groups_Ozero__class_Ozero(U_1391))
        | ~ sP113(U_1391,U_1392,U_1393,U_1394) )
    & ! [U_1391,U_1392,U_1393,U_1394] :
        ( c_Orderings_Oord__class_Oless(U_1391,U_1392,U_1394)
        | ~ sP112(U_1391,U_1392,U_1393,U_1394) )
    & ! [U_1391,U_1392,U_1393,U_1394] :
        ( c_Orderings_Oord__class_Oless(U_1391,c_Groups_Ozero__class_Ozero(U_1391),U_1393)
        | ~ sP112(U_1391,U_1392,U_1393,U_1394) )
    & ! [U_1391,U_1392,U_1393,U_1394] :
        ( c_Orderings_Oord__class_Oless(U_1391,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1391),U_1392),U_1393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1391),U_1394),U_1393))
        | sP114(U_1391,U_1392,U_1393,U_1394)
        | ~ sP115(U_1391,U_1392,U_1393,U_1394) )
    & ! [U_1391,U_1392,U_1393,U_1394] :
        ( sP113(U_1391,U_1392,U_1393,U_1394)
        | sP112(U_1391,U_1392,U_1393,U_1394)
        | ~ c_Orderings_Oord__class_Oless(U_1391,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1391),U_1392),U_1393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1391),U_1394),U_1393))
        | ~ sP115(U_1391,U_1392,U_1393,U_1394) )
    & ! [U_1391,U_1392,U_1393,U_1394] :
        ( sP115(U_1391,U_1392,U_1393,U_1394)
        | ~ class_Rings_Olinordered__ring__strict(U_1391) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP112,sP113,sP114,sP115])],[f_420_2]) ).

cnf(f_420_4,plain,
    ( sP115(U_1391,U_1392,U_1393,U_1394)
    | ~ class_Rings_Olinordered__ring__strict(U_1391) ),
    inference(clausify,[status(thm)],[f_420_3]) ).

cnf(f_420_5,plain,
    ( sP113(U_1391,U_1392,U_1393,U_1394)
    | sP112(U_1391,U_1392,U_1393,U_1394)
    | ~ c_Orderings_Oord__class_Oless(U_1391,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1391),U_1392),U_1393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1391),U_1394),U_1393))
    | ~ sP115(U_1391,U_1392,U_1393,U_1394) ),
    inference(clausify,[status(thm)],[f_420_3]) ).

cnf(f_420_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1391,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1391),U_1392),U_1393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1391),U_1394),U_1393))
    | sP114(U_1391,U_1392,U_1393,U_1394)
    | ~ sP115(U_1391,U_1392,U_1393,U_1394) ),
    inference(clausify,[status(thm)],[f_420_3]) ).

cnf(f_420_7,plain,
    ( c_Orderings_Oord__class_Oless(U_1391,c_Groups_Ozero__class_Ozero(U_1391),U_1393)
    | ~ sP112(U_1391,U_1392,U_1393,U_1394) ),
    inference(clausify,[status(thm)],[f_420_3]) ).

cnf(f_420_8,plain,
    ( c_Orderings_Oord__class_Oless(U_1391,U_1392,U_1394)
    | ~ sP112(U_1391,U_1392,U_1393,U_1394) ),
    inference(clausify,[status(thm)],[f_420_3]) ).

cnf(f_420_9,plain,
    ( c_Orderings_Oord__class_Oless(U_1391,U_1393,c_Groups_Ozero__class_Ozero(U_1391))
    | ~ sP113(U_1391,U_1392,U_1393,U_1394) ),
    inference(clausify,[status(thm)],[f_420_3]) ).

cnf(f_420_10,plain,
    ( c_Orderings_Oord__class_Oless(U_1391,U_1394,U_1392)
    | ~ sP113(U_1391,U_1392,U_1393,U_1394) ),
    inference(clausify,[status(thm)],[f_420_3]) ).

cnf(f_420_11,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1391,U_1392,U_1394)
    | ~ c_Orderings_Oord__class_Oless(U_1391,c_Groups_Ozero__class_Ozero(U_1391),U_1393)
    | ~ sP114(U_1391,U_1392,U_1393,U_1394) ),
    inference(clausify,[status(thm)],[f_420_3]) ).

cnf(f_420_12,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1391,U_1394,U_1392)
    | ~ c_Orderings_Oord__class_Oless(U_1391,U_1393,c_Groups_Ozero__class_Ozero(U_1391))
    | ~ sP114(U_1391,U_1392,U_1393,U_1394) ),
    inference(clausify,[status(thm)],[f_420_3]) ).

fof(f_421_1,plain,
    ! [V_b_2,V_ab_2,V_ca_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
          | ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,V_ab_2)
              | ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) )
            & ( ~ c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2)
              | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) ) ) )
        & ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_ab_2)
            & c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a)) )
          | ( c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2)
            & c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2) )
          | ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj]) ).

fof(f_421_2,plain,
    ! [U_1398,U_1397,U_1396,U_1395] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1395,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1395),U_1396),U_1397),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1395),U_1396),U_1398))
          | ( ( ~ c_Orderings_Oord__class_Oless(U_1395,U_1398,U_1397)
              | ~ c_Orderings_Oord__class_Oless(U_1395,U_1396,c_Groups_Ozero__class_Ozero(U_1395)) )
            & ( ~ c_Orderings_Oord__class_Oless(U_1395,U_1397,U_1398)
              | ~ c_Orderings_Oord__class_Oless(U_1395,c_Groups_Ozero__class_Ozero(U_1395),U_1396) ) ) )
        & ( ( c_Orderings_Oord__class_Oless(U_1395,U_1398,U_1397)
            & c_Orderings_Oord__class_Oless(U_1395,U_1396,c_Groups_Ozero__class_Ozero(U_1395)) )
          | ( c_Orderings_Oord__class_Oless(U_1395,U_1397,U_1398)
            & c_Orderings_Oord__class_Oless(U_1395,c_Groups_Ozero__class_Ozero(U_1395),U_1396) )
          | ~ c_Orderings_Oord__class_Oless(U_1395,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1395),U_1396),U_1397),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1395),U_1396),U_1398)) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_1395) ),
    inference(variable_rename,[status(thm)],[f_421_1]) ).

fof(f_421_3,plain,
    ( ! [U_1398,U_1395,U_1397,U_1396] :
        ( ~ c_Orderings_Oord__class_Oless(U_1395,U_1398,U_1397)
        | ~ c_Orderings_Oord__class_Oless(U_1395,U_1396,c_Groups_Ozero__class_Ozero(U_1395))
        | ~ sP118(U_1398,U_1395,U_1397,U_1396) )
    & ! [U_1398,U_1395,U_1397,U_1396] :
        ( ~ c_Orderings_Oord__class_Oless(U_1395,U_1397,U_1398)
        | ~ c_Orderings_Oord__class_Oless(U_1395,c_Groups_Ozero__class_Ozero(U_1395),U_1396)
        | ~ sP118(U_1398,U_1395,U_1397,U_1396) )
    & ! [U_1398,U_1395,U_1397,U_1396] :
        ( c_Orderings_Oord__class_Oless(U_1395,U_1398,U_1397)
        | ~ sP117(U_1398,U_1395,U_1397,U_1396) )
    & ! [U_1398,U_1395,U_1397,U_1396] :
        ( c_Orderings_Oord__class_Oless(U_1395,U_1396,c_Groups_Ozero__class_Ozero(U_1395))
        | ~ sP117(U_1398,U_1395,U_1397,U_1396) )
    & ! [U_1398,U_1395,U_1397,U_1396] :
        ( c_Orderings_Oord__class_Oless(U_1395,U_1397,U_1398)
        | ~ sP116(U_1398,U_1395,U_1397,U_1396) )
    & ! [U_1398,U_1395,U_1397,U_1396] :
        ( c_Orderings_Oord__class_Oless(U_1395,c_Groups_Ozero__class_Ozero(U_1395),U_1396)
        | ~ sP116(U_1398,U_1395,U_1397,U_1396) )
    & ! [U_1398,U_1395,U_1397,U_1396] :
        ( c_Orderings_Oord__class_Oless(U_1395,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1395),U_1396),U_1397),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1395),U_1396),U_1398))
        | sP118(U_1398,U_1395,U_1397,U_1396)
        | ~ sP119(U_1398,U_1395,U_1397,U_1396) )
    & ! [U_1398,U_1395,U_1397,U_1396] :
        ( sP117(U_1398,U_1395,U_1397,U_1396)
        | sP116(U_1398,U_1395,U_1397,U_1396)
        | ~ c_Orderings_Oord__class_Oless(U_1395,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1395),U_1396),U_1397),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1395),U_1396),U_1398))
        | ~ sP119(U_1398,U_1395,U_1397,U_1396) )
    & ! [U_1398,U_1395,U_1397,U_1396] :
        ( sP119(U_1398,U_1395,U_1397,U_1396)
        | ~ class_Rings_Olinordered__ring__strict(U_1395) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP116,sP117,sP118,sP119])],[f_421_2]) ).

cnf(f_421_4,plain,
    ( sP119(U_1398,U_1395,U_1397,U_1396)
    | ~ class_Rings_Olinordered__ring__strict(U_1395) ),
    inference(clausify,[status(thm)],[f_421_3]) ).

cnf(f_421_5,plain,
    ( sP117(U_1398,U_1395,U_1397,U_1396)
    | sP116(U_1398,U_1395,U_1397,U_1396)
    | ~ c_Orderings_Oord__class_Oless(U_1395,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1395),U_1396),U_1397),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1395),U_1396),U_1398))
    | ~ sP119(U_1398,U_1395,U_1397,U_1396) ),
    inference(clausify,[status(thm)],[f_421_3]) ).

cnf(f_421_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1395,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1395),U_1396),U_1397),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1395),U_1396),U_1398))
    | sP118(U_1398,U_1395,U_1397,U_1396)
    | ~ sP119(U_1398,U_1395,U_1397,U_1396) ),
    inference(clausify,[status(thm)],[f_421_3]) ).

cnf(f_421_7,plain,
    ( c_Orderings_Oord__class_Oless(U_1395,c_Groups_Ozero__class_Ozero(U_1395),U_1396)
    | ~ sP116(U_1398,U_1395,U_1397,U_1396) ),
    inference(clausify,[status(thm)],[f_421_3]) ).

cnf(f_421_8,plain,
    ( c_Orderings_Oord__class_Oless(U_1395,U_1397,U_1398)
    | ~ sP116(U_1398,U_1395,U_1397,U_1396) ),
    inference(clausify,[status(thm)],[f_421_3]) ).

cnf(f_421_9,plain,
    ( c_Orderings_Oord__class_Oless(U_1395,U_1396,c_Groups_Ozero__class_Ozero(U_1395))
    | ~ sP117(U_1398,U_1395,U_1397,U_1396) ),
    inference(clausify,[status(thm)],[f_421_3]) ).

cnf(f_421_10,plain,
    ( c_Orderings_Oord__class_Oless(U_1395,U_1398,U_1397)
    | ~ sP117(U_1398,U_1395,U_1397,U_1396) ),
    inference(clausify,[status(thm)],[f_421_3]) ).

cnf(f_421_11,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1395,U_1397,U_1398)
    | ~ c_Orderings_Oord__class_Oless(U_1395,c_Groups_Ozero__class_Ozero(U_1395),U_1396)
    | ~ sP118(U_1398,U_1395,U_1397,U_1396) ),
    inference(clausify,[status(thm)],[f_421_3]) ).

cnf(f_421_12,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1395,U_1398,U_1397)
    | ~ c_Orderings_Oord__class_Oless(U_1395,U_1396,c_Groups_Ozero__class_Ozero(U_1395))
    | ~ sP118(U_1398,U_1395,U_1397,U_1396) ),
    inference(clausify,[status(thm)],[f_421_3]) ).

fof(f_422_1,plain,
    ! [V_b_2,V_ab_2,V_ca_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
          | ~ c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2) )
        & ( c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)) ) )
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos]) ).

fof(f_422_2,plain,
    ! [U_1402,U_1401,U_1400,U_1399] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1399,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1399),U_1400),U_1401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1399),U_1400),U_1402))
          | ~ c_Orderings_Oord__class_Oless(U_1399,U_1401,U_1402) )
        & ( c_Orderings_Oord__class_Oless(U_1399,U_1401,U_1402)
          | ~ c_Orderings_Oord__class_Oless(U_1399,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1399),U_1400),U_1401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1399),U_1400),U_1402)) ) )
      | ~ c_Orderings_Oord__class_Oless(U_1399,c_Groups_Ozero__class_Ozero(U_1399),U_1400)
      | ~ class_Rings_Olinordered__ring__strict(U_1399) ),
    inference(variable_rename,[status(thm)],[f_422_1]) ).

fof(f_422_3,plain,
    ( ! [U_1402,U_1400,U_1401,U_1399] :
        ( c_Orderings_Oord__class_Oless(U_1399,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1399),U_1400),U_1401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1399),U_1400),U_1402))
        | ~ c_Orderings_Oord__class_Oless(U_1399,U_1401,U_1402)
        | ~ sP120(U_1402,U_1400,U_1401,U_1399) )
    & ! [U_1402,U_1400,U_1401,U_1399] :
        ( c_Orderings_Oord__class_Oless(U_1399,U_1401,U_1402)
        | ~ c_Orderings_Oord__class_Oless(U_1399,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1399),U_1400),U_1401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1399),U_1400),U_1402))
        | ~ sP120(U_1402,U_1400,U_1401,U_1399) )
    & ! [U_1402,U_1400,U_1401,U_1399] :
        ( sP120(U_1402,U_1400,U_1401,U_1399)
        | ~ c_Orderings_Oord__class_Oless(U_1399,c_Groups_Ozero__class_Ozero(U_1399),U_1400)
        | ~ class_Rings_Olinordered__ring__strict(U_1399) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP120])],[f_422_2]) ).

cnf(f_422_4,plain,
    ( sP120(U_1402,U_1400,U_1401,U_1399)
    | ~ c_Orderings_Oord__class_Oless(U_1399,c_Groups_Ozero__class_Ozero(U_1399),U_1400)
    | ~ class_Rings_Olinordered__ring__strict(U_1399) ),
    inference(clausify,[status(thm)],[f_422_3]) ).

cnf(f_422_5,plain,
    ( c_Orderings_Oord__class_Oless(U_1399,U_1401,U_1402)
    | ~ c_Orderings_Oord__class_Oless(U_1399,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1399),U_1400),U_1401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1399),U_1400),U_1402))
    | ~ sP120(U_1402,U_1400,U_1401,U_1399) ),
    inference(clausify,[status(thm)],[f_422_3]) ).

cnf(f_422_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1399,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1399),U_1400),U_1401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1399),U_1400),U_1402))
    | ~ c_Orderings_Oord__class_Oless(U_1399,U_1401,U_1402)
    | ~ sP120(U_1402,U_1400,U_1401,U_1399) ),
    inference(clausify,[status(thm)],[f_422_3]) ).

fof(f_423_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__pos__pos]) ).

fof(f_423_2,plain,
    ! [U_1405,U_1404,U_1403] :
      ( c_Orderings_Oord__class_Oless(U_1403,c_Groups_Ozero__class_Ozero(U_1403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1403),U_1404),U_1405))
      | ~ c_Orderings_Oord__class_Oless(U_1403,c_Groups_Ozero__class_Ozero(U_1403),U_1405)
      | ~ c_Orderings_Oord__class_Oless(U_1403,c_Groups_Ozero__class_Ozero(U_1403),U_1404)
      | ~ class_Rings_Olinordered__semiring__strict(U_1403) ),
    inference(variable_rename,[status(thm)],[f_423_1]) ).

fof(f_423_3,plain,
    ! [U_1405,U_1403,U_1404] :
      ( c_Orderings_Oord__class_Oless(U_1403,c_Groups_Ozero__class_Ozero(U_1403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1403),U_1404),U_1405))
      | ~ c_Orderings_Oord__class_Oless(U_1403,c_Groups_Ozero__class_Ozero(U_1403),U_1405)
      | ~ c_Orderings_Oord__class_Oless(U_1403,c_Groups_Ozero__class_Ozero(U_1403),U_1404)
      | ~ class_Rings_Olinordered__semiring__strict(U_1403) ),
    inference(definitional_conversion,[status(esa)],[f_423_2]) ).

cnf(f_423_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1403,c_Groups_Ozero__class_Ozero(U_1403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1403),U_1404),U_1405))
    | ~ c_Orderings_Oord__class_Oless(U_1403,c_Groups_Ozero__class_Ozero(U_1403),U_1405)
    | ~ c_Orderings_Oord__class_Oless(U_1403,c_Groups_Ozero__class_Ozero(U_1403),U_1404)
    | ~ class_Rings_Olinordered__semiring__strict(U_1403) ),
    inference(clausify,[status(thm)],[f_423_3]) ).

fof(f_424_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))
      | ~ c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__pos__neg]) ).

fof(f_424_2,plain,
    ! [U_1408,U_1407,U_1406] :
      ( c_Orderings_Oord__class_Oless(U_1406,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1406),U_1407),U_1408),c_Groups_Ozero__class_Ozero(U_1406))
      | ~ c_Orderings_Oord__class_Oless(U_1406,U_1408,c_Groups_Ozero__class_Ozero(U_1406))
      | ~ c_Orderings_Oord__class_Oless(U_1406,c_Groups_Ozero__class_Ozero(U_1406),U_1407)
      | ~ class_Rings_Olinordered__semiring__strict(U_1406) ),
    inference(variable_rename,[status(thm)],[f_424_1]) ).

fof(f_424_3,plain,
    ! [U_1407,U_1408,U_1406] :
      ( c_Orderings_Oord__class_Oless(U_1406,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1406),U_1407),U_1408),c_Groups_Ozero__class_Ozero(U_1406))
      | ~ c_Orderings_Oord__class_Oless(U_1406,U_1408,c_Groups_Ozero__class_Ozero(U_1406))
      | ~ c_Orderings_Oord__class_Oless(U_1406,c_Groups_Ozero__class_Ozero(U_1406),U_1407)
      | ~ class_Rings_Olinordered__semiring__strict(U_1406) ),
    inference(definitional_conversion,[status(esa)],[f_424_2]) ).

cnf(f_424_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1406,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1406),U_1407),U_1408),c_Groups_Ozero__class_Ozero(U_1406))
    | ~ c_Orderings_Oord__class_Oless(U_1406,U_1408,c_Groups_Ozero__class_Ozero(U_1406))
    | ~ c_Orderings_Oord__class_Oless(U_1406,c_Groups_Ozero__class_Ozero(U_1406),U_1407)
    | ~ class_Rings_Olinordered__semiring__strict(U_1406) ),
    inference(clausify,[status(thm)],[f_424_3]) ).

fof(f_425_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a),c_Groups_Ozero__class_Ozero(T_a))
      | ~ c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__pos__neg2]) ).

fof(f_425_2,plain,
    ! [U_1411,U_1410,U_1409] :
      ( c_Orderings_Oord__class_Oless(U_1409,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1409),U_1411),U_1410),c_Groups_Ozero__class_Ozero(U_1409))
      | ~ c_Orderings_Oord__class_Oless(U_1409,U_1411,c_Groups_Ozero__class_Ozero(U_1409))
      | ~ c_Orderings_Oord__class_Oless(U_1409,c_Groups_Ozero__class_Ozero(U_1409),U_1410)
      | ~ class_Rings_Olinordered__semiring__strict(U_1409) ),
    inference(variable_rename,[status(thm)],[f_425_1]) ).

fof(f_425_3,plain,
    ! [U_1410,U_1409,U_1411] :
      ( c_Orderings_Oord__class_Oless(U_1409,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1409),U_1411),U_1410),c_Groups_Ozero__class_Ozero(U_1409))
      | ~ c_Orderings_Oord__class_Oless(U_1409,U_1411,c_Groups_Ozero__class_Ozero(U_1409))
      | ~ c_Orderings_Oord__class_Oless(U_1409,c_Groups_Ozero__class_Ozero(U_1409),U_1410)
      | ~ class_Rings_Olinordered__semiring__strict(U_1409) ),
    inference(definitional_conversion,[status(esa)],[f_425_2]) ).

cnf(f_425_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1409,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1409),U_1411),U_1410),c_Groups_Ozero__class_Ozero(U_1409))
    | ~ c_Orderings_Oord__class_Oless(U_1409,U_1411,c_Groups_Ozero__class_Ozero(U_1409))
    | ~ c_Orderings_Oord__class_Oless(U_1409,c_Groups_Ozero__class_Ozero(U_1409),U_1410)
    | ~ class_Rings_Olinordered__semiring__strict(U_1409) ),
    inference(clausify,[status(thm)],[f_425_3]) ).

fof(f_426_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos]) ).

fof(f_426_2,plain,
    ! [U_1414,U_1413,U_1412] :
      ( c_Orderings_Oord__class_Oless(U_1412,c_Groups_Ozero__class_Ozero(U_1412),U_1414)
      | ~ c_Orderings_Oord__class_Oless(U_1412,c_Groups_Ozero__class_Ozero(U_1412),U_1413)
      | ~ c_Orderings_Oord__class_Oless(U_1412,c_Groups_Ozero__class_Ozero(U_1412),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1412),U_1413),U_1414))
      | ~ class_Rings_Olinordered__semiring__strict(U_1412) ),
    inference(variable_rename,[status(thm)],[f_426_1]) ).

fof(f_426_3,plain,
    ! [U_1413,U_1412,U_1414] :
      ( c_Orderings_Oord__class_Oless(U_1412,c_Groups_Ozero__class_Ozero(U_1412),U_1414)
      | ~ c_Orderings_Oord__class_Oless(U_1412,c_Groups_Ozero__class_Ozero(U_1412),U_1413)
      | ~ c_Orderings_Oord__class_Oless(U_1412,c_Groups_Ozero__class_Ozero(U_1412),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1412),U_1413),U_1414))
      | ~ class_Rings_Olinordered__semiring__strict(U_1412) ),
    inference(definitional_conversion,[status(esa)],[f_426_2]) ).

cnf(f_426_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1412,c_Groups_Ozero__class_Ozero(U_1412),U_1414)
    | ~ c_Orderings_Oord__class_Oless(U_1412,c_Groups_Ozero__class_Ozero(U_1412),U_1413)
    | ~ c_Orderings_Oord__class_Oless(U_1412,c_Groups_Ozero__class_Ozero(U_1412),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1412),U_1413),U_1414))
    | ~ class_Rings_Olinordered__semiring__strict(U_1412) ),
    inference(clausify,[status(thm)],[f_426_3]) ).

fof(f_427_1,plain,
    ! [V_a,V_b,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos2]) ).

fof(f_427_2,plain,
    ! [U_1417,U_1416,U_1415] :
      ( c_Orderings_Oord__class_Oless(U_1415,c_Groups_Ozero__class_Ozero(U_1415),U_1416)
      | ~ c_Orderings_Oord__class_Oless(U_1415,c_Groups_Ozero__class_Ozero(U_1415),U_1417)
      | ~ c_Orderings_Oord__class_Oless(U_1415,c_Groups_Ozero__class_Ozero(U_1415),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1415),U_1416),U_1417))
      | ~ class_Rings_Olinordered__semiring__strict(U_1415) ),
    inference(variable_rename,[status(thm)],[f_427_1]) ).

fof(f_427_3,plain,
    ! [U_1417,U_1415,U_1416] :
      ( c_Orderings_Oord__class_Oless(U_1415,c_Groups_Ozero__class_Ozero(U_1415),U_1416)
      | ~ c_Orderings_Oord__class_Oless(U_1415,c_Groups_Ozero__class_Ozero(U_1415),U_1417)
      | ~ c_Orderings_Oord__class_Oless(U_1415,c_Groups_Ozero__class_Ozero(U_1415),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1415),U_1416),U_1417))
      | ~ class_Rings_Olinordered__semiring__strict(U_1415) ),
    inference(definitional_conversion,[status(esa)],[f_427_2]) ).

cnf(f_427_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1415,c_Groups_Ozero__class_Ozero(U_1415),U_1416)
    | ~ c_Orderings_Oord__class_Oless(U_1415,c_Groups_Ozero__class_Ozero(U_1415),U_1417)
    | ~ c_Orderings_Oord__class_Oless(U_1415,c_Groups_Ozero__class_Ozero(U_1415),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1415),U_1416),U_1417))
    | ~ class_Rings_Olinordered__semiring__strict(U_1415) ),
    inference(clausify,[status(thm)],[f_427_3]) ).

fof(f_428_1,plain,
    ! [V_b_2,V_ab_2,V_ca_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
          | ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,V_ab_2) )
        & ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_ab_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)) ) )
      | ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg]) ).

fof(f_428_2,plain,
    ! [U_1421,U_1420,U_1419,U_1418] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1418,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1418),U_1419),U_1420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1418),U_1419),U_1421))
          | ~ c_Orderings_Oord__class_Oless(U_1418,U_1421,U_1420) )
        & ( c_Orderings_Oord__class_Oless(U_1418,U_1421,U_1420)
          | ~ c_Orderings_Oord__class_Oless(U_1418,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1418),U_1419),U_1420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1418),U_1419),U_1421)) ) )
      | ~ c_Orderings_Oord__class_Oless(U_1418,U_1419,c_Groups_Ozero__class_Ozero(U_1418))
      | ~ class_Rings_Olinordered__ring__strict(U_1418) ),
    inference(variable_rename,[status(thm)],[f_428_1]) ).

fof(f_428_3,plain,
    ( ! [U_1420,U_1419,U_1418,U_1421] :
        ( c_Orderings_Oord__class_Oless(U_1418,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1418),U_1419),U_1420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1418),U_1419),U_1421))
        | ~ c_Orderings_Oord__class_Oless(U_1418,U_1421,U_1420)
        | ~ sP121(U_1420,U_1419,U_1418,U_1421) )
    & ! [U_1420,U_1419,U_1418,U_1421] :
        ( c_Orderings_Oord__class_Oless(U_1418,U_1421,U_1420)
        | ~ c_Orderings_Oord__class_Oless(U_1418,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1418),U_1419),U_1420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1418),U_1419),U_1421))
        | ~ sP121(U_1420,U_1419,U_1418,U_1421) )
    & ! [U_1420,U_1419,U_1418,U_1421] :
        ( sP121(U_1420,U_1419,U_1418,U_1421)
        | ~ c_Orderings_Oord__class_Oless(U_1418,U_1419,c_Groups_Ozero__class_Ozero(U_1418))
        | ~ class_Rings_Olinordered__ring__strict(U_1418) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP121])],[f_428_2]) ).

cnf(f_428_4,plain,
    ( sP121(U_1420,U_1419,U_1418,U_1421)
    | ~ c_Orderings_Oord__class_Oless(U_1418,U_1419,c_Groups_Ozero__class_Ozero(U_1418))
    | ~ class_Rings_Olinordered__ring__strict(U_1418) ),
    inference(clausify,[status(thm)],[f_428_3]) ).

cnf(f_428_5,plain,
    ( c_Orderings_Oord__class_Oless(U_1418,U_1421,U_1420)
    | ~ c_Orderings_Oord__class_Oless(U_1418,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1418),U_1419),U_1420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1418),U_1419),U_1421))
    | ~ sP121(U_1420,U_1419,U_1418,U_1421) ),
    inference(clausify,[status(thm)],[f_428_3]) ).

cnf(f_428_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1418,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1418),U_1419),U_1420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1418),U_1419),U_1421))
    | ~ c_Orderings_Oord__class_Oless(U_1418,U_1421,U_1420)
    | ~ sP121(U_1420,U_1419,U_1418,U_1421) ),
    inference(clausify,[status(thm)],[f_428_3]) ).

fof(f_429_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),c_Groups_Ozero__class_Ozero(T_a))
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__neg__pos]) ).

fof(f_429_2,plain,
    ! [U_1424,U_1423,U_1422] :
      ( c_Orderings_Oord__class_Oless(U_1422,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1422),U_1423),U_1424),c_Groups_Ozero__class_Ozero(U_1422))
      | ~ c_Orderings_Oord__class_Oless(U_1422,c_Groups_Ozero__class_Ozero(U_1422),U_1424)
      | ~ c_Orderings_Oord__class_Oless(U_1422,U_1423,c_Groups_Ozero__class_Ozero(U_1422))
      | ~ class_Rings_Olinordered__semiring__strict(U_1422) ),
    inference(variable_rename,[status(thm)],[f_429_1]) ).

fof(f_429_3,plain,
    ! [U_1422,U_1424,U_1423] :
      ( c_Orderings_Oord__class_Oless(U_1422,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1422),U_1423),U_1424),c_Groups_Ozero__class_Ozero(U_1422))
      | ~ c_Orderings_Oord__class_Oless(U_1422,c_Groups_Ozero__class_Ozero(U_1422),U_1424)
      | ~ c_Orderings_Oord__class_Oless(U_1422,U_1423,c_Groups_Ozero__class_Ozero(U_1422))
      | ~ class_Rings_Olinordered__semiring__strict(U_1422) ),
    inference(definitional_conversion,[status(esa)],[f_429_2]) ).

cnf(f_429_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1422,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1422),U_1423),U_1424),c_Groups_Ozero__class_Ozero(U_1422))
    | ~ c_Orderings_Oord__class_Oless(U_1422,c_Groups_Ozero__class_Ozero(U_1422),U_1424)
    | ~ c_Orderings_Oord__class_Oless(U_1422,U_1423,c_Groups_Ozero__class_Ozero(U_1422))
    | ~ class_Rings_Olinordered__semiring__strict(U_1422) ),
    inference(clausify,[status(thm)],[f_429_3]) ).

fof(f_430_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
      | ~ c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
      | ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__neg__neg]) ).

fof(f_430_2,plain,
    ! [U_1427,U_1426,U_1425] :
      ( c_Orderings_Oord__class_Oless(U_1425,c_Groups_Ozero__class_Ozero(U_1425),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1425),U_1426),U_1427))
      | ~ c_Orderings_Oord__class_Oless(U_1425,U_1427,c_Groups_Ozero__class_Ozero(U_1425))
      | ~ c_Orderings_Oord__class_Oless(U_1425,U_1426,c_Groups_Ozero__class_Ozero(U_1425))
      | ~ class_Rings_Olinordered__ring__strict(U_1425) ),
    inference(variable_rename,[status(thm)],[f_430_1]) ).

fof(f_430_3,plain,
    ! [U_1425,U_1426,U_1427] :
      ( c_Orderings_Oord__class_Oless(U_1425,c_Groups_Ozero__class_Ozero(U_1425),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1425),U_1426),U_1427))
      | ~ c_Orderings_Oord__class_Oless(U_1425,U_1427,c_Groups_Ozero__class_Ozero(U_1425))
      | ~ c_Orderings_Oord__class_Oless(U_1425,U_1426,c_Groups_Ozero__class_Ozero(U_1425))
      | ~ class_Rings_Olinordered__ring__strict(U_1425) ),
    inference(definitional_conversion,[status(esa)],[f_430_2]) ).

cnf(f_430_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1425,c_Groups_Ozero__class_Ozero(U_1425),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1425),U_1426),U_1427))
    | ~ c_Orderings_Oord__class_Oless(U_1425,U_1427,c_Groups_Ozero__class_Ozero(U_1425))
    | ~ c_Orderings_Oord__class_Oless(U_1425,U_1426,c_Groups_Ozero__class_Ozero(U_1425))
    | ~ class_Rings_Olinordered__ring__strict(U_1425) ),
    inference(clausify,[status(thm)],[f_430_3]) ).

fof(f_431_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono]) ).

fof(f_431_2,plain,
    ! [U_1431,U_1430,U_1429,U_1428] :
      ( c_Orderings_Oord__class_Oless(U_1428,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1428),U_1429),U_1431),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1428),U_1430),U_1431))
      | ~ c_Orderings_Oord__class_Oless(U_1428,c_Groups_Ozero__class_Ozero(U_1428),U_1431)
      | ~ c_Orderings_Oord__class_Oless(U_1428,U_1429,U_1430)
      | ~ class_Rings_Olinordered__semiring__strict(U_1428) ),
    inference(variable_rename,[status(thm)],[f_431_1]) ).

fof(f_431_3,plain,
    ! [U_1428,U_1430,U_1429,U_1431] :
      ( c_Orderings_Oord__class_Oless(U_1428,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1428),U_1429),U_1431),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1428),U_1430),U_1431))
      | ~ c_Orderings_Oord__class_Oless(U_1428,c_Groups_Ozero__class_Ozero(U_1428),U_1431)
      | ~ c_Orderings_Oord__class_Oless(U_1428,U_1429,U_1430)
      | ~ class_Rings_Olinordered__semiring__strict(U_1428) ),
    inference(definitional_conversion,[status(esa)],[f_431_2]) ).

cnf(f_431_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1428,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1428),U_1429),U_1431),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1428),U_1430),U_1431))
    | ~ c_Orderings_Oord__class_Oless(U_1428,c_Groups_Ozero__class_Ozero(U_1428),U_1431)
    | ~ c_Orderings_Oord__class_Oless(U_1428,U_1429,U_1430)
    | ~ class_Rings_Olinordered__semiring__strict(U_1428) ),
    inference(clausify,[status(thm)],[f_431_3]) ).

fof(f_432_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono]) ).

fof(f_432_2,plain,
    ! [U_1435,U_1434,U_1433,U_1432] :
      ( c_Orderings_Oord__class_Oless(U_1432,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1432),U_1435),U_1433),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1432),U_1435),U_1434))
      | ~ c_Orderings_Oord__class_Oless(U_1432,c_Groups_Ozero__class_Ozero(U_1432),U_1435)
      | ~ c_Orderings_Oord__class_Oless(U_1432,U_1433,U_1434)
      | ~ class_Rings_Olinordered__semiring__strict(U_1432) ),
    inference(variable_rename,[status(thm)],[f_432_1]) ).

fof(f_432_3,plain,
    ! [U_1435,U_1433,U_1432,U_1434] :
      ( c_Orderings_Oord__class_Oless(U_1432,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1432),U_1435),U_1433),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1432),U_1435),U_1434))
      | ~ c_Orderings_Oord__class_Oless(U_1432,c_Groups_Ozero__class_Ozero(U_1432),U_1435)
      | ~ c_Orderings_Oord__class_Oless(U_1432,U_1433,U_1434)
      | ~ class_Rings_Olinordered__semiring__strict(U_1432) ),
    inference(definitional_conversion,[status(esa)],[f_432_2]) ).

cnf(f_432_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1432,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1432),U_1435),U_1433),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1432),U_1435),U_1434))
    | ~ c_Orderings_Oord__class_Oless(U_1432,c_Groups_Ozero__class_Ozero(U_1432),U_1435)
    | ~ c_Orderings_Oord__class_Oless(U_1432,U_1433,U_1434)
    | ~ class_Rings_Olinordered__semiring__strict(U_1432) ),
    inference(clausify,[status(thm)],[f_432_3]) ).

fof(f_433_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
      | ~ class_Rings_Olinordered__comm__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__mult__strict__left__mono]) ).

fof(f_433_2,plain,
    ! [U_1439,U_1438,U_1437,U_1436] :
      ( c_Orderings_Oord__class_Oless(U_1436,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1436),U_1439),U_1437),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1436),U_1439),U_1438))
      | ~ c_Orderings_Oord__class_Oless(U_1436,c_Groups_Ozero__class_Ozero(U_1436),U_1439)
      | ~ c_Orderings_Oord__class_Oless(U_1436,U_1437,U_1438)
      | ~ class_Rings_Olinordered__comm__semiring__strict(U_1436) ),
    inference(variable_rename,[status(thm)],[f_433_1]) ).

fof(f_433_3,plain,
    ! [U_1439,U_1437,U_1438,U_1436] :
      ( c_Orderings_Oord__class_Oless(U_1436,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1436),U_1439),U_1437),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1436),U_1439),U_1438))
      | ~ c_Orderings_Oord__class_Oless(U_1436,c_Groups_Ozero__class_Ozero(U_1436),U_1439)
      | ~ c_Orderings_Oord__class_Oless(U_1436,U_1437,U_1438)
      | ~ class_Rings_Olinordered__comm__semiring__strict(U_1436) ),
    inference(definitional_conversion,[status(esa)],[f_433_2]) ).

cnf(f_433_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1436,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1436),U_1439),U_1437),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1436),U_1439),U_1438))
    | ~ c_Orderings_Oord__class_Oless(U_1436,c_Groups_Ozero__class_Ozero(U_1436),U_1439)
    | ~ c_Orderings_Oord__class_Oless(U_1436,U_1437,U_1438)
    | ~ class_Rings_Olinordered__comm__semiring__strict(U_1436) ),
    inference(clausify,[status(thm)],[f_433_3]) ).

fof(f_434_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
      | ~ c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
      | ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono__neg]) ).

fof(f_434_2,plain,
    ! [U_1443,U_1442,U_1441,U_1440] :
      ( c_Orderings_Oord__class_Oless(U_1440,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1440),U_1442),U_1443),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1440),U_1441),U_1443))
      | ~ c_Orderings_Oord__class_Oless(U_1440,U_1443,c_Groups_Ozero__class_Ozero(U_1440))
      | ~ c_Orderings_Oord__class_Oless(U_1440,U_1441,U_1442)
      | ~ class_Rings_Olinordered__ring__strict(U_1440) ),
    inference(variable_rename,[status(thm)],[f_434_1]) ).

fof(f_434_3,plain,
    ! [U_1440,U_1441,U_1442,U_1443] :
      ( c_Orderings_Oord__class_Oless(U_1440,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1440),U_1442),U_1443),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1440),U_1441),U_1443))
      | ~ c_Orderings_Oord__class_Oless(U_1440,U_1443,c_Groups_Ozero__class_Ozero(U_1440))
      | ~ c_Orderings_Oord__class_Oless(U_1440,U_1441,U_1442)
      | ~ class_Rings_Olinordered__ring__strict(U_1440) ),
    inference(definitional_conversion,[status(esa)],[f_434_2]) ).

cnf(f_434_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1440,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1440),U_1442),U_1443),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1440),U_1441),U_1443))
    | ~ c_Orderings_Oord__class_Oless(U_1440,U_1443,c_Groups_Ozero__class_Ozero(U_1440))
    | ~ c_Orderings_Oord__class_Oless(U_1440,U_1441,U_1442)
    | ~ class_Rings_Olinordered__ring__strict(U_1440) ),
    inference(clausify,[status(thm)],[f_434_3]) ).

fof(f_435_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
      | ~ c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))
      | ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_a)
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono__neg]) ).

fof(f_435_2,plain,
    ! [U_1447,U_1446,U_1445,U_1444] :
      ( c_Orderings_Oord__class_Oless(U_1444,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1444),U_1447),U_1446),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1444),U_1447),U_1445))
      | ~ c_Orderings_Oord__class_Oless(U_1444,U_1447,c_Groups_Ozero__class_Ozero(U_1444))
      | ~ c_Orderings_Oord__class_Oless(U_1444,U_1445,U_1446)
      | ~ class_Rings_Olinordered__ring__strict(U_1444) ),
    inference(variable_rename,[status(thm)],[f_435_1]) ).

fof(f_435_3,plain,
    ! [U_1447,U_1446,U_1444,U_1445] :
      ( c_Orderings_Oord__class_Oless(U_1444,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1444),U_1447),U_1446),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1444),U_1447),U_1445))
      | ~ c_Orderings_Oord__class_Oless(U_1444,U_1447,c_Groups_Ozero__class_Ozero(U_1444))
      | ~ c_Orderings_Oord__class_Oless(U_1444,U_1445,U_1446)
      | ~ class_Rings_Olinordered__ring__strict(U_1444) ),
    inference(definitional_conversion,[status(esa)],[f_435_2]) ).

cnf(f_435_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1444,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1444),U_1447),U_1446),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1444),U_1447),U_1445))
    | ~ c_Orderings_Oord__class_Oless(U_1444,U_1447,c_Groups_Ozero__class_Ozero(U_1444))
    | ~ c_Orderings_Oord__class_Oless(U_1444,U_1445,U_1446)
    | ~ class_Rings_Olinordered__ring__strict(U_1444) ),
    inference(clausify,[status(thm)],[f_435_3]) ).

fof(f_436_1,plain,
    ! [V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2))
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) )
        & ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__double__add__iff__zero__less__single__add]) ).

fof(f_436_2,plain,
    ! [U_1449,U_1448] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1448,c_Groups_Ozero__class_Ozero(U_1448),c_Groups_Oplus__class_Oplus(U_1448,U_1449,U_1449))
          | ~ c_Orderings_Oord__class_Oless(U_1448,c_Groups_Ozero__class_Ozero(U_1448),U_1449) )
        & ( c_Orderings_Oord__class_Oless(U_1448,c_Groups_Ozero__class_Ozero(U_1448),U_1449)
          | ~ c_Orderings_Oord__class_Oless(U_1448,c_Groups_Ozero__class_Ozero(U_1448),c_Groups_Oplus__class_Oplus(U_1448,U_1449,U_1449)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_1448) ),
    inference(variable_rename,[status(thm)],[f_436_1]) ).

fof(f_436_3,plain,
    ( ! [U_1448,U_1449] :
        ( c_Orderings_Oord__class_Oless(U_1448,c_Groups_Ozero__class_Ozero(U_1448),c_Groups_Oplus__class_Oplus(U_1448,U_1449,U_1449))
        | ~ c_Orderings_Oord__class_Oless(U_1448,c_Groups_Ozero__class_Ozero(U_1448),U_1449)
        | ~ sP122(U_1448,U_1449) )
    & ! [U_1448,U_1449] :
        ( c_Orderings_Oord__class_Oless(U_1448,c_Groups_Ozero__class_Ozero(U_1448),U_1449)
        | ~ c_Orderings_Oord__class_Oless(U_1448,c_Groups_Ozero__class_Ozero(U_1448),c_Groups_Oplus__class_Oplus(U_1448,U_1449,U_1449))
        | ~ sP122(U_1448,U_1449) )
    & ! [U_1448,U_1449] :
        ( sP122(U_1448,U_1449)
        | ~ class_Groups_Olinordered__ab__group__add(U_1448) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP122])],[f_436_2]) ).

cnf(f_436_4,plain,
    ( sP122(U_1448,U_1449)
    | ~ class_Groups_Olinordered__ab__group__add(U_1448) ),
    inference(clausify,[status(thm)],[f_436_3]) ).

cnf(f_436_5,plain,
    ( c_Orderings_Oord__class_Oless(U_1448,c_Groups_Ozero__class_Ozero(U_1448),U_1449)
    | ~ c_Orderings_Oord__class_Oless(U_1448,c_Groups_Ozero__class_Ozero(U_1448),c_Groups_Oplus__class_Oplus(U_1448,U_1449,U_1449))
    | ~ sP122(U_1448,U_1449) ),
    inference(clausify,[status(thm)],[f_436_3]) ).

cnf(f_436_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1448,c_Groups_Ozero__class_Ozero(U_1448),c_Groups_Oplus__class_Oplus(U_1448,U_1449,U_1449))
    | ~ c_Orderings_Oord__class_Oless(U_1448,c_Groups_Ozero__class_Ozero(U_1448),U_1449)
    | ~ sP122(U_1448,U_1449) ),
    inference(clausify,[status(thm)],[f_436_3]) ).

fof(f_437_1,plain,
    ! [V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2),c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) )
        & ( c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_double__add__less__zero__iff__single__add__less__zero]) ).

fof(f_437_2,plain,
    ! [U_1451,U_1450] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1450,c_Groups_Oplus__class_Oplus(U_1450,U_1451,U_1451),c_Groups_Ozero__class_Ozero(U_1450))
          | ~ c_Orderings_Oord__class_Oless(U_1450,U_1451,c_Groups_Ozero__class_Ozero(U_1450)) )
        & ( c_Orderings_Oord__class_Oless(U_1450,U_1451,c_Groups_Ozero__class_Ozero(U_1450))
          | ~ c_Orderings_Oord__class_Oless(U_1450,c_Groups_Oplus__class_Oplus(U_1450,U_1451,U_1451),c_Groups_Ozero__class_Ozero(U_1450)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_1450) ),
    inference(variable_rename,[status(thm)],[f_437_1]) ).

fof(f_437_3,plain,
    ( ! [U_1451,U_1450] :
        ( c_Orderings_Oord__class_Oless(U_1450,c_Groups_Oplus__class_Oplus(U_1450,U_1451,U_1451),c_Groups_Ozero__class_Ozero(U_1450))
        | ~ c_Orderings_Oord__class_Oless(U_1450,U_1451,c_Groups_Ozero__class_Ozero(U_1450))
        | ~ sP123(U_1451,U_1450) )
    & ! [U_1451,U_1450] :
        ( c_Orderings_Oord__class_Oless(U_1450,U_1451,c_Groups_Ozero__class_Ozero(U_1450))
        | ~ c_Orderings_Oord__class_Oless(U_1450,c_Groups_Oplus__class_Oplus(U_1450,U_1451,U_1451),c_Groups_Ozero__class_Ozero(U_1450))
        | ~ sP123(U_1451,U_1450) )
    & ! [U_1451,U_1450] :
        ( sP123(U_1451,U_1450)
        | ~ class_Groups_Olinordered__ab__group__add(U_1450) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP123])],[f_437_2]) ).

cnf(f_437_4,plain,
    ( sP123(U_1451,U_1450)
    | ~ class_Groups_Olinordered__ab__group__add(U_1450) ),
    inference(clausify,[status(thm)],[f_437_3]) ).

cnf(f_437_5,plain,
    ( c_Orderings_Oord__class_Oless(U_1450,U_1451,c_Groups_Ozero__class_Ozero(U_1450))
    | ~ c_Orderings_Oord__class_Oless(U_1450,c_Groups_Oplus__class_Oplus(U_1450,U_1451,U_1451),c_Groups_Ozero__class_Ozero(U_1450))
    | ~ sP123(U_1451,U_1450) ),
    inference(clausify,[status(thm)],[f_437_3]) ).

cnf(f_437_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1450,c_Groups_Oplus__class_Oplus(U_1450,U_1451,U_1451),c_Groups_Ozero__class_Ozero(U_1450))
    | ~ c_Orderings_Oord__class_Oless(U_1450,U_1451,c_Groups_Ozero__class_Ozero(U_1450))
    | ~ sP123(U_1451,U_1450) ),
    inference(clausify,[status(thm)],[f_437_3]) ).

fof(f_438_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__pos__pos]) ).

fof(f_438_2,plain,
    ! [U_1454,U_1453,U_1452] :
      ( c_Orderings_Oord__class_Oless(U_1452,c_Groups_Ozero__class_Ozero(U_1452),c_Groups_Oplus__class_Oplus(U_1452,U_1453,U_1454))
      | ~ c_Orderings_Oord__class_Oless(U_1452,c_Groups_Ozero__class_Ozero(U_1452),U_1454)
      | ~ c_Orderings_Oord__class_Oless(U_1452,c_Groups_Ozero__class_Ozero(U_1452),U_1453)
      | ~ class_Groups_Oordered__comm__monoid__add(U_1452) ),
    inference(variable_rename,[status(thm)],[f_438_1]) ).

fof(f_438_3,plain,
    ! [U_1453,U_1454,U_1452] :
      ( c_Orderings_Oord__class_Oless(U_1452,c_Groups_Ozero__class_Ozero(U_1452),c_Groups_Oplus__class_Oplus(U_1452,U_1453,U_1454))
      | ~ c_Orderings_Oord__class_Oless(U_1452,c_Groups_Ozero__class_Ozero(U_1452),U_1454)
      | ~ c_Orderings_Oord__class_Oless(U_1452,c_Groups_Ozero__class_Ozero(U_1452),U_1453)
      | ~ class_Groups_Oordered__comm__monoid__add(U_1452) ),
    inference(definitional_conversion,[status(esa)],[f_438_2]) ).

cnf(f_438_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1452,c_Groups_Ozero__class_Ozero(U_1452),c_Groups_Oplus__class_Oplus(U_1452,U_1453,U_1454))
    | ~ c_Orderings_Oord__class_Oless(U_1452,c_Groups_Ozero__class_Ozero(U_1452),U_1454)
    | ~ c_Orderings_Oord__class_Oless(U_1452,c_Groups_Ozero__class_Ozero(U_1452),U_1453)
    | ~ class_Groups_Oordered__comm__monoid__add(U_1452) ),
    inference(clausify,[status(thm)],[f_438_3]) ).

fof(f_439_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))
      | ~ c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
      | ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__neg__neg]) ).

fof(f_439_2,plain,
    ! [U_1457,U_1456,U_1455] :
      ( c_Orderings_Oord__class_Oless(U_1455,c_Groups_Oplus__class_Oplus(U_1455,U_1456,U_1457),c_Groups_Ozero__class_Ozero(U_1455))
      | ~ c_Orderings_Oord__class_Oless(U_1455,U_1457,c_Groups_Ozero__class_Ozero(U_1455))
      | ~ c_Orderings_Oord__class_Oless(U_1455,U_1456,c_Groups_Ozero__class_Ozero(U_1455))
      | ~ class_Groups_Oordered__comm__monoid__add(U_1455) ),
    inference(variable_rename,[status(thm)],[f_439_1]) ).

fof(f_439_3,plain,
    ! [U_1455,U_1457,U_1456] :
      ( c_Orderings_Oord__class_Oless(U_1455,c_Groups_Oplus__class_Oplus(U_1455,U_1456,U_1457),c_Groups_Ozero__class_Ozero(U_1455))
      | ~ c_Orderings_Oord__class_Oless(U_1455,U_1457,c_Groups_Ozero__class_Ozero(U_1455))
      | ~ c_Orderings_Oord__class_Oless(U_1455,U_1456,c_Groups_Ozero__class_Ozero(U_1455))
      | ~ class_Groups_Oordered__comm__monoid__add(U_1455) ),
    inference(definitional_conversion,[status(esa)],[f_439_2]) ).

cnf(f_439_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1455,c_Groups_Oplus__class_Oplus(U_1455,U_1456,U_1457),c_Groups_Ozero__class_Ozero(U_1455))
    | ~ c_Orderings_Oord__class_Oless(U_1455,U_1457,c_Groups_Ozero__class_Ozero(U_1455))
    | ~ c_Orderings_Oord__class_Oless(U_1455,U_1456,c_Groups_Ozero__class_Ozero(U_1455))
    | ~ class_Groups_Oordered__comm__monoid__add(U_1455) ),
    inference(clausify,[status(thm)],[f_439_3]) ).

fof(f_440_1,plain,
    ! [V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2),c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) )
        & ( c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_ab_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_even__less__0__iff]) ).

fof(f_440_2,plain,
    ! [U_1459,U_1458] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1458,c_Groups_Oplus__class_Oplus(U_1458,U_1459,U_1459),c_Groups_Ozero__class_Ozero(U_1458))
          | ~ c_Orderings_Oord__class_Oless(U_1458,U_1459,c_Groups_Ozero__class_Ozero(U_1458)) )
        & ( c_Orderings_Oord__class_Oless(U_1458,U_1459,c_Groups_Ozero__class_Ozero(U_1458))
          | ~ c_Orderings_Oord__class_Oless(U_1458,c_Groups_Oplus__class_Oplus(U_1458,U_1459,U_1459),c_Groups_Ozero__class_Ozero(U_1458)) ) )
      | ~ class_Rings_Olinordered__idom(U_1458) ),
    inference(variable_rename,[status(thm)],[f_440_1]) ).

fof(f_440_3,plain,
    ( ! [U_1459,U_1458] :
        ( c_Orderings_Oord__class_Oless(U_1458,c_Groups_Oplus__class_Oplus(U_1458,U_1459,U_1459),c_Groups_Ozero__class_Ozero(U_1458))
        | ~ c_Orderings_Oord__class_Oless(U_1458,U_1459,c_Groups_Ozero__class_Ozero(U_1458))
        | ~ sP124(U_1459,U_1458) )
    & ! [U_1459,U_1458] :
        ( c_Orderings_Oord__class_Oless(U_1458,U_1459,c_Groups_Ozero__class_Ozero(U_1458))
        | ~ c_Orderings_Oord__class_Oless(U_1458,c_Groups_Oplus__class_Oplus(U_1458,U_1459,U_1459),c_Groups_Ozero__class_Ozero(U_1458))
        | ~ sP124(U_1459,U_1458) )
    & ! [U_1459,U_1458] :
        ( sP124(U_1459,U_1458)
        | ~ class_Rings_Olinordered__idom(U_1458) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP124])],[f_440_2]) ).

cnf(f_440_4,plain,
    ( sP124(U_1459,U_1458)
    | ~ class_Rings_Olinordered__idom(U_1458) ),
    inference(clausify,[status(thm)],[f_440_3]) ).

cnf(f_440_5,plain,
    ( c_Orderings_Oord__class_Oless(U_1458,U_1459,c_Groups_Ozero__class_Ozero(U_1458))
    | ~ c_Orderings_Oord__class_Oless(U_1458,c_Groups_Oplus__class_Oplus(U_1458,U_1459,U_1459),c_Groups_Ozero__class_Ozero(U_1458))
    | ~ sP124(U_1459,U_1458) ),
    inference(clausify,[status(thm)],[f_440_3]) ).

cnf(f_440_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1458,c_Groups_Oplus__class_Oplus(U_1458,U_1459,U_1459),c_Groups_Ozero__class_Ozero(U_1458))
    | ~ c_Orderings_Oord__class_Oless(U_1458,U_1459,c_Groups_Ozero__class_Ozero(U_1458))
    | ~ sP124(U_1459,U_1458) ),
    inference(clausify,[status(thm)],[f_440_3]) ).

fof(f_441_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
      | ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_pos__add__strict]) ).

fof(f_441_2,plain,
    ! [U_1463,U_1462,U_1461,U_1460] :
      ( c_Orderings_Oord__class_Oless(U_1460,U_1462,c_Groups_Oplus__class_Oplus(U_1460,U_1461,U_1463))
      | ~ c_Orderings_Oord__class_Oless(U_1460,U_1462,U_1463)
      | ~ c_Orderings_Oord__class_Oless(U_1460,c_Groups_Ozero__class_Ozero(U_1460),U_1461)
      | ~ class_Rings_Olinordered__semidom(U_1460) ),
    inference(variable_rename,[status(thm)],[f_441_1]) ).

fof(f_441_3,plain,
    ! [U_1461,U_1462,U_1463,U_1460] :
      ( c_Orderings_Oord__class_Oless(U_1460,U_1462,c_Groups_Oplus__class_Oplus(U_1460,U_1461,U_1463))
      | ~ c_Orderings_Oord__class_Oless(U_1460,U_1462,U_1463)
      | ~ c_Orderings_Oord__class_Oless(U_1460,c_Groups_Ozero__class_Ozero(U_1460),U_1461)
      | ~ class_Rings_Olinordered__semidom(U_1460) ),
    inference(definitional_conversion,[status(esa)],[f_441_2]) ).

cnf(f_441_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1460,U_1462,c_Groups_Oplus__class_Oplus(U_1460,U_1461,U_1463))
    | ~ c_Orderings_Oord__class_Oless(U_1460,U_1462,U_1463)
    | ~ c_Orderings_Oord__class_Oless(U_1460,c_Groups_Ozero__class_Ozero(U_1460),U_1461)
    | ~ class_Rings_Olinordered__semidom(U_1460) ),
    inference(clausify,[status(thm)],[f_441_3]) ).

fof(f_442_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
      | ~ c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__le__less__mono]) ).

fof(f_442_2,plain,
    ! [U_1468,U_1467,U_1466,U_1465,U_1464] :
      ( c_Orderings_Oord__class_Oless(U_1464,c_Groups_Oplus__class_Oplus(U_1464,U_1465,U_1467),c_Groups_Oplus__class_Oplus(U_1464,U_1466,U_1468))
      | ~ c_Orderings_Oord__class_Oless(U_1464,U_1467,U_1468)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1464,U_1465,U_1466)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1464) ),
    inference(variable_rename,[status(thm)],[f_442_1]) ).

fof(f_442_3,plain,
    ! [U_1467,U_1466,U_1465,U_1464,U_1468] :
      ( c_Orderings_Oord__class_Oless(U_1464,c_Groups_Oplus__class_Oplus(U_1464,U_1465,U_1467),c_Groups_Oplus__class_Oplus(U_1464,U_1466,U_1468))
      | ~ c_Orderings_Oord__class_Oless(U_1464,U_1467,U_1468)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1464,U_1465,U_1466)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1464) ),
    inference(definitional_conversion,[status(esa)],[f_442_2]) ).

cnf(f_442_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1464,c_Groups_Oplus__class_Oplus(U_1464,U_1465,U_1467),c_Groups_Oplus__class_Oplus(U_1464,U_1466,U_1468))
    | ~ c_Orderings_Oord__class_Oless(U_1464,U_1467,U_1468)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1464,U_1465,U_1466)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1464) ),
    inference(clausify,[status(thm)],[f_442_3]) ).

fof(f_443_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__less__le__mono]) ).

fof(f_443_2,plain,
    ! [U_1473,U_1472,U_1471,U_1470,U_1469] :
      ( c_Orderings_Oord__class_Oless(U_1469,c_Groups_Oplus__class_Oplus(U_1469,U_1470,U_1472),c_Groups_Oplus__class_Oplus(U_1469,U_1471,U_1473))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1469,U_1472,U_1473)
      | ~ c_Orderings_Oord__class_Oless(U_1469,U_1470,U_1471)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1469) ),
    inference(variable_rename,[status(thm)],[f_443_1]) ).

fof(f_443_3,plain,
    ! [U_1472,U_1471,U_1469,U_1470,U_1473] :
      ( c_Orderings_Oord__class_Oless(U_1469,c_Groups_Oplus__class_Oplus(U_1469,U_1470,U_1472),c_Groups_Oplus__class_Oplus(U_1469,U_1471,U_1473))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1469,U_1472,U_1473)
      | ~ c_Orderings_Oord__class_Oless(U_1469,U_1470,U_1471)
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1469) ),
    inference(definitional_conversion,[status(esa)],[f_443_2]) ).

cnf(f_443_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1469,c_Groups_Oplus__class_Oplus(U_1469,U_1470,U_1472),c_Groups_Oplus__class_Oplus(U_1469,U_1471,U_1473))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1469,U_1472,U_1473)
    | ~ c_Orderings_Oord__class_Oless(U_1469,U_1470,U_1471)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1469) ),
    inference(clausify,[status(thm)],[f_443_3]) ).

fof(f_444_1,plain,
    ! [V_b_2,V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)) )
        & ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0]) ).

fof(f_444_2,plain,
    ! [U_1476,U_1475,U_1474] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1474,U_1475,U_1476)
          | ~ c_Orderings_Oord__class_Oless(U_1474,c_Groups_Ominus__class_Ominus(U_1474,U_1475,U_1476),c_Groups_Ozero__class_Ozero(U_1474)) )
        & ( c_Orderings_Oord__class_Oless(U_1474,c_Groups_Ominus__class_Ominus(U_1474,U_1475,U_1476),c_Groups_Ozero__class_Ozero(U_1474))
          | ~ c_Orderings_Oord__class_Oless(U_1474,U_1475,U_1476) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_1474) ),
    inference(variable_rename,[status(thm)],[f_444_1]) ).

fof(f_444_3,plain,
    ( ! [U_1476,U_1474,U_1475] :
        ( c_Orderings_Oord__class_Oless(U_1474,U_1475,U_1476)
        | ~ c_Orderings_Oord__class_Oless(U_1474,c_Groups_Ominus__class_Ominus(U_1474,U_1475,U_1476),c_Groups_Ozero__class_Ozero(U_1474))
        | ~ sP125(U_1476,U_1474,U_1475) )
    & ! [U_1476,U_1474,U_1475] :
        ( c_Orderings_Oord__class_Oless(U_1474,c_Groups_Ominus__class_Ominus(U_1474,U_1475,U_1476),c_Groups_Ozero__class_Ozero(U_1474))
        | ~ c_Orderings_Oord__class_Oless(U_1474,U_1475,U_1476)
        | ~ sP125(U_1476,U_1474,U_1475) )
    & ! [U_1476,U_1474,U_1475] :
        ( sP125(U_1476,U_1474,U_1475)
        | ~ class_Groups_Oordered__ab__group__add(U_1474) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP125])],[f_444_2]) ).

cnf(f_444_4,plain,
    ( sP125(U_1476,U_1474,U_1475)
    | ~ class_Groups_Oordered__ab__group__add(U_1474) ),
    inference(clausify,[status(thm)],[f_444_3]) ).

cnf(f_444_5,plain,
    ( c_Orderings_Oord__class_Oless(U_1474,c_Groups_Ominus__class_Ominus(U_1474,U_1475,U_1476),c_Groups_Ozero__class_Ozero(U_1474))
    | ~ c_Orderings_Oord__class_Oless(U_1474,U_1475,U_1476)
    | ~ sP125(U_1476,U_1474,U_1475) ),
    inference(clausify,[status(thm)],[f_444_3]) ).

cnf(f_444_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1474,U_1475,U_1476)
    | ~ c_Orderings_Oord__class_Oless(U_1474,c_Groups_Ominus__class_Ominus(U_1474,U_1475,U_1476),c_Groups_Ozero__class_Ozero(U_1474))
    | ~ sP125(U_1476,U_1474,U_1475) ),
    inference(clausify,[status(thm)],[f_444_3]) ).

fof(f_445_1,plain,
    ! [T_a] :
      ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_not__one__le__zero]) ).

fof(f_445_2,plain,
    ! [U_1477] :
      ( ~ c_Orderings_Oord__class_Oless__eq(U_1477,c_Groups_Oone__class_Oone(U_1477),c_Groups_Ozero__class_Ozero(U_1477))
      | ~ class_Rings_Olinordered__semidom(U_1477) ),
    inference(variable_rename,[status(thm)],[f_445_1]) ).

fof(f_445_3,plain,
    ! [U_1477] :
      ( ~ c_Orderings_Oord__class_Oless__eq(U_1477,c_Groups_Oone__class_Oone(U_1477),c_Groups_Ozero__class_Ozero(U_1477))
      | ~ class_Rings_Olinordered__semidom(U_1477) ),
    inference(definitional_conversion,[status(esa)],[f_445_2]) ).

cnf(f_445_4,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(U_1477,c_Groups_Oone__class_Oone(U_1477),c_Groups_Ozero__class_Ozero(U_1477))
    | ~ class_Rings_Olinordered__semidom(U_1477) ),
    inference(clausify,[status(thm)],[f_445_3]) ).

fof(f_446_1,plain,
    ! [T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__one]) ).

fof(f_446_2,plain,
    ! [U_1478] :
      ( c_Orderings_Oord__class_Oless__eq(U_1478,c_Groups_Ozero__class_Ozero(U_1478),c_Groups_Oone__class_Oone(U_1478))
      | ~ class_Rings_Olinordered__semidom(U_1478) ),
    inference(variable_rename,[status(thm)],[f_446_1]) ).

fof(f_446_3,plain,
    ! [U_1478] :
      ( c_Orderings_Oord__class_Oless__eq(U_1478,c_Groups_Ozero__class_Ozero(U_1478),c_Groups_Oone__class_Oone(U_1478))
      | ~ class_Rings_Olinordered__semidom(U_1478) ),
    inference(definitional_conversion,[status(esa)],[f_446_2]) ).

cnf(f_446_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1478,c_Groups_Ozero__class_Ozero(U_1478),c_Groups_Oone__class_Oone(U_1478))
    | ~ class_Rings_Olinordered__semidom(U_1478) ),
    inference(clausify,[status(thm)],[f_446_3]) ).

fof(f_447_1,plain,
    ! [V_m,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,V_m,V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_m)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J]) ).

fof(f_447_2,plain,
    ! [U_1480,U_1479] :
      ( c_Groups_Oplus__class_Oplus(U_1479,U_1480,U_1480) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1479),c_Groups_Oplus__class_Oplus(U_1479,c_Groups_Oone__class_Oone(U_1479),c_Groups_Oone__class_Oone(U_1479))),U_1480)
      | ~ class_Rings_Ocomm__semiring__1(U_1479) ),
    inference(variable_rename,[status(thm)],[f_447_1]) ).

fof(f_447_3,plain,
    ! [U_1479,U_1480] :
      ( c_Groups_Oplus__class_Oplus(U_1479,U_1480,U_1480) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1479),c_Groups_Oplus__class_Oplus(U_1479,c_Groups_Oone__class_Oone(U_1479),c_Groups_Oone__class_Oone(U_1479))),U_1480)
      | ~ class_Rings_Ocomm__semiring__1(U_1479) ),
    inference(definitional_conversion,[status(esa)],[f_447_2]) ).

cnf(f_447_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_1479,U_1480,U_1480) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1479),c_Groups_Oplus__class_Oplus(U_1479,c_Groups_Oone__class_Oone(U_1479),c_Groups_Oone__class_Oone(U_1479))),U_1480)
    | ~ class_Rings_Ocomm__semiring__1(U_1479) ),
    inference(clausify,[status(thm)],[f_447_3]) ).

fof(f_448_1,plain,
    ! [V_a,V_m,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J]) ).

fof(f_448_2,plain,
    ! [U_1483,U_1482,U_1481] :
      ( c_Groups_Oplus__class_Oplus(U_1481,U_1482,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1481),U_1483),U_1482)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1481),c_Groups_Oplus__class_Oplus(U_1481,U_1483,c_Groups_Oone__class_Oone(U_1481))),U_1482)
      | ~ class_Rings_Ocomm__semiring__1(U_1481) ),
    inference(variable_rename,[status(thm)],[f_448_1]) ).

fof(f_448_3,plain,
    ! [U_1481,U_1482,U_1483] :
      ( c_Groups_Oplus__class_Oplus(U_1481,U_1482,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1481),U_1483),U_1482)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1481),c_Groups_Oplus__class_Oplus(U_1481,U_1483,c_Groups_Oone__class_Oone(U_1481))),U_1482)
      | ~ class_Rings_Ocomm__semiring__1(U_1481) ),
    inference(definitional_conversion,[status(esa)],[f_448_2]) ).

cnf(f_448_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_1481,U_1482,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1481),U_1483),U_1482)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1481),c_Groups_Oplus__class_Oplus(U_1481,U_1483,c_Groups_Oone__class_Oone(U_1481))),U_1482)
    | ~ class_Rings_Ocomm__semiring__1(U_1481) ),
    inference(clausify,[status(thm)],[f_448_3]) ).

fof(f_449_1,plain,
    ! [V_m,V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J]) ).

fof(f_449_2,plain,
    ! [U_1486,U_1485,U_1484] :
      ( c_Groups_Oplus__class_Oplus(U_1484,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1484),U_1485),U_1486),U_1486) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1484),c_Groups_Oplus__class_Oplus(U_1484,U_1485,c_Groups_Oone__class_Oone(U_1484))),U_1486)
      | ~ class_Rings_Ocomm__semiring__1(U_1484) ),
    inference(variable_rename,[status(thm)],[f_449_1]) ).

fof(f_449_3,plain,
    ! [U_1484,U_1485,U_1486] :
      ( c_Groups_Oplus__class_Oplus(U_1484,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1484),U_1485),U_1486),U_1486) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1484),c_Groups_Oplus__class_Oplus(U_1484,U_1485,c_Groups_Oone__class_Oone(U_1484))),U_1486)
      | ~ class_Rings_Ocomm__semiring__1(U_1484) ),
    inference(definitional_conversion,[status(esa)],[f_449_2]) ).

cnf(f_449_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_1484,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1484),U_1485),U_1486),U_1486) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1484),c_Groups_Oplus__class_Oplus(U_1484,U_1485,c_Groups_Oone__class_Oone(U_1484))),U_1486)
    | ~ class_Rings_Ocomm__semiring__1(U_1484) ),
    inference(clausify,[status(thm)],[f_449_3]) ).

fof(f_450_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2))
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
          & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) ) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_add__gr__0]) ).

fof(f_450_2,plain,
    ! [U_1488,U_1487] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1487,U_1488))
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1488)
          & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1487) ) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1488)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1487)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1487,U_1488)) ) ),
    inference(variable_rename,[status(thm)],[f_450_1]) ).

fof(f_450_3,plain,
    ( ! [U_1492,U_1490] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1490,U_1492))
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1492)
          & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1490) ) )
    & ! [U_1491,U_1489] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1491)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1489)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1489,U_1491)) ) ),
    inference(miniscope,[status(thm)],[f_450_2]) ).

fof(f_450_4,plain,
    ( ! [U_1490,U_1492] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1492)
        | ~ sP126(U_1490,U_1492) )
    & ! [U_1490,U_1492] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1490)
        | ~ sP126(U_1490,U_1492) )
    & ! [U_1490,U_1492] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1490,U_1492))
        | sP126(U_1490,U_1492) )
    & ! [U_1489,U_1491] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1491)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1489)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1489,U_1491)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP126])],[f_450_3]) ).

cnf(f_450_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1491)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1489)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1489,U_1491)) ),
    inference(clausify,[status(thm)],[f_450_4]) ).

cnf(f_450_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1490,U_1492))
    | sP126(U_1490,U_1492) ),
    inference(clausify,[status(thm)],[f_450_4]) ).

cnf(f_450_7,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1490)
    | ~ sP126(U_1490,U_1492) ),
    inference(clausify,[status(thm)],[f_450_4]) ).

cnf(f_450_8,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1492)
    | ~ sP126(U_1490,U_1492) ),
    inference(clausify,[status(thm)],[f_450_4]) ).

fof(f_451_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
          | V_m_2 != V_n_2 )
        & ( V_m_2 = V_n_2
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel1]) ).

fof(f_451_2,plain,
    ! [U_1495,U_1494,U_1493] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1493),U_1494) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1493),U_1495)
          | U_1494 != U_1495 )
        & ( U_1494 = U_1495
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1493),U_1494) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1493),U_1495) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1493) ),
    inference(variable_rename,[status(thm)],[f_451_1]) ).

fof(f_451_3,plain,
    ( ! [U_1494,U_1495,U_1493] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1493),U_1494) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1493),U_1495)
        | U_1494 != U_1495
        | ~ sP127(U_1494,U_1495,U_1493) )
    & ! [U_1494,U_1495,U_1493] :
        ( U_1494 = U_1495
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1493),U_1494) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1493),U_1495)
        | ~ sP127(U_1494,U_1495,U_1493) )
    & ! [U_1494,U_1495,U_1493] :
        ( sP127(U_1494,U_1495,U_1493)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1493) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP127])],[f_451_2]) ).

cnf(f_451_4,plain,
    ( sP127(U_1494,U_1495,U_1493)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1493) ),
    inference(clausify,[status(thm)],[f_451_3]) ).

cnf(f_451_5,plain,
    ( U_1494 = U_1495
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1493),U_1494) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1493),U_1495)
    | ~ sP127(U_1494,U_1495,U_1493) ),
    inference(clausify,[status(thm)],[f_451_3]) ).

cnf(f_451_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1493),U_1494) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1493),U_1495)
    | U_1494 != U_1495
    | ~ sP127(U_1494,U_1495,U_1493) ),
    inference(clausify,[status(thm)],[f_451_3]) ).

fof(f_452_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) )
        & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__less__cancel1]) ).

fof(f_452_2,plain,
    ! [U_1498,U_1497,U_1496] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1496),U_1497),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1496),U_1498))
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1497,U_1498) )
        & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1497,U_1498)
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1496),U_1497),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1496),U_1498)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1496) ),
    inference(variable_rename,[status(thm)],[f_452_1]) ).

fof(f_452_3,plain,
    ( ! [U_1498,U_1497,U_1496] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1496),U_1497),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1496),U_1498))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1497,U_1498)
        | ~ sP128(U_1498,U_1497,U_1496) )
    & ! [U_1498,U_1497,U_1496] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1497,U_1498)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1496),U_1497),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1496),U_1498))
        | ~ sP128(U_1498,U_1497,U_1496) )
    & ! [U_1498,U_1497,U_1496] :
        ( sP128(U_1498,U_1497,U_1496)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1496) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP128])],[f_452_2]) ).

cnf(f_452_4,plain,
    ( sP128(U_1498,U_1497,U_1496)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1496) ),
    inference(clausify,[status(thm)],[f_452_3]) ).

cnf(f_452_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1497,U_1498)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1496),U_1497),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1496),U_1498))
    | ~ sP128(U_1498,U_1497,U_1496) ),
    inference(clausify,[status(thm)],[f_452_3]) ).

cnf(f_452_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1496),U_1497),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1496),U_1498))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1497,U_1498)
    | ~ sP128(U_1498,U_1497,U_1496) ),
    inference(clausify,[status(thm)],[f_452_3]) ).

fof(f_453_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) )
      & ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff]) ).

fof(f_453_2,plain,
    ! [U_1500,U_1499] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1499),U_1500))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1500)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1499) )
      & ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1500)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1499) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1499),U_1500)) ) ),
    inference(variable_rename,[status(thm)],[f_453_1]) ).

fof(f_453_3,plain,
    ( ! [U_1504,U_1502] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1502),U_1504))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1504)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1502) )
    & ! [U_1503,U_1501] :
        ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1503)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1501) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1501),U_1503)) ) ),
    inference(miniscope,[status(thm)],[f_453_2]) ).

fof(f_453_4,plain,
    ( ! [U_1501,U_1503] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1503)
        | ~ sP129(U_1501,U_1503) )
    & ! [U_1501,U_1503] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1501)
        | ~ sP129(U_1501,U_1503) )
    & ! [U_1502,U_1504] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1502),U_1504))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1504)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1502) )
    & ! [U_1501,U_1503] :
        ( sP129(U_1501,U_1503)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1501),U_1503)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP129])],[f_453_3]) ).

cnf(f_453_5,plain,
    ( sP129(U_1501,U_1503)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1501),U_1503)) ),
    inference(clausify,[status(thm)],[f_453_4]) ).

cnf(f_453_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1502),U_1504))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1504)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1502) ),
    inference(clausify,[status(thm)],[f_453_4]) ).

cnf(f_453_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1501)
    | ~ sP129(U_1501,U_1503) ),
    inference(clausify,[status(thm)],[f_453_4]) ).

cnf(f_453_8,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1503)
    | ~ sP129(U_1501,U_1503) ),
    inference(clausify,[status(thm)],[f_453_4]) ).

fof(f_454_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) )
      & ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1]) ).

fof(f_454_2,plain,
    ! [U_1507,U_1506,U_1505] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1505),U_1506),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1505),U_1507))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1506,U_1507)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1505) )
      & ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1506,U_1507)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1505) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1505),U_1506),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1505),U_1507)) ) ),
    inference(variable_rename,[status(thm)],[f_454_1]) ).

fof(f_454_3,plain,
    ( ! [U_1513,U_1511,U_1509] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1509),U_1511),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1509),U_1513))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1511,U_1513)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1509) )
    & ! [U_1512,U_1510,U_1508] :
        ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1510,U_1512)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1508) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1508),U_1510),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1508),U_1512)) ) ),
    inference(miniscope,[status(thm)],[f_454_2]) ).

fof(f_454_4,plain,
    ( ! [U_1508,U_1510,U_1512] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1510,U_1512)
        | ~ sP130(U_1508,U_1510,U_1512) )
    & ! [U_1508,U_1510,U_1512] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1508)
        | ~ sP130(U_1508,U_1510,U_1512) )
    & ! [U_1513,U_1509,U_1511] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1509),U_1511),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1509),U_1513))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1511,U_1513)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1509) )
    & ! [U_1508,U_1510,U_1512] :
        ( sP130(U_1508,U_1510,U_1512)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1508),U_1510),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1508),U_1512)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP130])],[f_454_3]) ).

cnf(f_454_5,plain,
    ( sP130(U_1508,U_1510,U_1512)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1508),U_1510),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1508),U_1512)) ),
    inference(clausify,[status(thm)],[f_454_4]) ).

cnf(f_454_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1509),U_1511),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1509),U_1513))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1511,U_1513)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1509) ),
    inference(clausify,[status(thm)],[f_454_4]) ).

cnf(f_454_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1508)
    | ~ sP130(U_1508,U_1510,U_1512) ),
    inference(clausify,[status(thm)],[f_454_4]) ).

cnf(f_454_8,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1510,U_1512)
    | ~ sP130(U_1508,U_1510,U_1512) ),
    inference(clausify,[status(thm)],[f_454_4]) ).

fof(f_455_1,plain,
    ! [V_n_2,V_k_2,V_m_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) )
      & ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2]) ).

fof(f_455_2,plain,
    ! [U_1516,U_1515,U_1514] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1514),U_1515),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1516),U_1515))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1514,U_1516)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1515) )
      & ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1514,U_1516)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1515) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1514),U_1515),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1516),U_1515)) ) ),
    inference(variable_rename,[status(thm)],[f_455_1]) ).

fof(f_455_3,plain,
    ( ! [U_1522,U_1520,U_1518] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1518),U_1520),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1522),U_1520))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1518,U_1522)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1520) )
    & ! [U_1521,U_1519,U_1517] :
        ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1517,U_1521)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1519) )
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1517),U_1519),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1521),U_1519)) ) ),
    inference(miniscope,[status(thm)],[f_455_2]) ).

fof(f_455_4,plain,
    ( ! [U_1517,U_1519,U_1521] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1517,U_1521)
        | ~ sP131(U_1517,U_1519,U_1521) )
    & ! [U_1517,U_1519,U_1521] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1519)
        | ~ sP131(U_1517,U_1519,U_1521) )
    & ! [U_1518,U_1520,U_1522] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1518),U_1520),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1522),U_1520))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1518,U_1522)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1520) )
    & ! [U_1517,U_1519,U_1521] :
        ( sP131(U_1517,U_1519,U_1521)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1517),U_1519),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1521),U_1519)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP131])],[f_455_3]) ).

cnf(f_455_5,plain,
    ( sP131(U_1517,U_1519,U_1521)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1517),U_1519),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1521),U_1519)) ),
    inference(clausify,[status(thm)],[f_455_4]) ).

cnf(f_455_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1518),U_1520),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1522),U_1520))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1518,U_1522)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1520) ),
    inference(clausify,[status(thm)],[f_455_4]) ).

cnf(f_455_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1519)
    | ~ sP131(U_1517,U_1519,U_1521) ),
    inference(clausify,[status(thm)],[f_455_4]) ).

cnf(f_455_8,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1517,U_1521)
    | ~ sP131(U_1517,U_1519,U_1521) ),
    inference(clausify,[status(thm)],[f_455_4]) ).

fof(f_456_1,plain,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__mono1]) ).

fof(f_456_2,plain,
    ! [U_1525,U_1524,U_1523] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1523),U_1525),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1524),U_1525))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1525)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1523,U_1524) ),
    inference(variable_rename,[status(thm)],[f_456_1]) ).

fof(f_456_3,plain,
    ! [U_1523,U_1525,U_1524] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1523),U_1525),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1524),U_1525))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1525)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1523,U_1524) ),
    inference(definitional_conversion,[status(esa)],[f_456_2]) ).

cnf(f_456_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1523),U_1525),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1524),U_1525))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1525)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1523,U_1524) ),
    inference(clausify,[status(thm)],[f_456_3]) ).

fof(f_457_1,plain,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__mono2]) ).

fof(f_457_2,plain,
    ! [U_1528,U_1527,U_1526] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1528),U_1526),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1528),U_1527))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1528)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1526,U_1527) ),
    inference(variable_rename,[status(thm)],[f_457_1]) ).

fof(f_457_3,plain,
    ! [U_1526,U_1528,U_1527] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1528),U_1526),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1528),U_1527))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1528)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1526,U_1527) ),
    inference(definitional_conversion,[status(esa)],[f_457_2]) ).

cnf(f_457_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1528),U_1526),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1528),U_1527))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1528)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1526,U_1527) ),
    inference(clausify,[status(thm)],[f_457_3]) ).

fof(f_458_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__diff]) ).

fof(f_458_2,plain,
    ! [U_1530,U_1529] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1529,U_1530))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1530,U_1529) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1530,U_1529)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1529,U_1530)) ) ),
    inference(variable_rename,[status(thm)],[f_458_1]) ).

fof(f_458_3,plain,
    ( ! [U_1534,U_1532] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1532,U_1534))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1534,U_1532) )
    & ! [U_1533,U_1531] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1533,U_1531)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1531,U_1533)) ) ),
    inference(miniscope,[status(thm)],[f_458_2]) ).

fof(f_458_4,plain,
    ( ! [U_1534,U_1532] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1532,U_1534))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1534,U_1532) )
    & ! [U_1531,U_1533] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1533,U_1531)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1531,U_1533)) ) ),
    inference(definitional_conversion,[status(esa)],[f_458_3]) ).

cnf(f_458_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1533,U_1531)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1531,U_1533)) ),
    inference(clausify,[status(thm)],[f_458_4]) ).

cnf(f_458_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1532,U_1534))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1534,U_1532) ),
    inference(clausify,[status(thm)],[f_458_4]) ).

fof(f_459_1,plain,
    ! [V_m,V_n] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
    inference(fof_nnf,[status(thm)],[fact_diff__less]) ).

fof(f_459_2,plain,
    ! [U_1536,U_1535] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1536,U_1535),U_1536)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1536)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1535) ),
    inference(variable_rename,[status(thm)],[f_459_1]) ).

fof(f_459_3,plain,
    ! [U_1536,U_1535] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1536,U_1535),U_1536)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1536)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1535) ),
    inference(definitional_conversion,[status(esa)],[f_459_2]) ).

cnf(f_459_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1536,U_1535),U_1536)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1536)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1535) ),
    inference(clausify,[status(thm)],[f_459_3]) ).

fof(f_460_1,plain,
    ! [V_n,V_m] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
    inference(fof_nnf,[status(thm)],[fact_add__diff__inverse]) ).

fof(f_460_2,plain,
    ! [U_1538,U_1537] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1538,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1537,U_1538)) = U_1537
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1537,U_1538) ),
    inference(variable_rename,[status(thm)],[f_460_1]) ).

fof(f_460_3,plain,
    ! [U_1538,U_1537] :
      ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1538,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1537,U_1538)) = U_1537
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1537,U_1538) ),
    inference(definitional_conversion,[status(esa)],[f_460_2]) ).

cnf(f_460_4,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1538,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1537,U_1538)) = U_1537
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1537,U_1538) ),
    inference(clausify,[status(thm)],[f_460_3]) ).

fof(f_461_1,plain,
    ! [V_k_2,V_j_2,V_i_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__diff__conv]) ).

fof(f_461_2,plain,
    ! [U_1541,U_1540,U_1539] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1539,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1540,U_1541))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1539,U_1541),U_1540) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1539,U_1541),U_1540)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1539,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1540,U_1541)) ) ),
    inference(variable_rename,[status(thm)],[f_461_1]) ).

fof(f_461_3,plain,
    ( ! [U_1547,U_1545,U_1543] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1543,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1545,U_1547))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1543,U_1547),U_1545) )
    & ! [U_1546,U_1544,U_1542] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1542,U_1546),U_1544)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1542,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1544,U_1546)) ) ),
    inference(miniscope,[status(thm)],[f_461_2]) ).

fof(f_461_4,plain,
    ( ! [U_1545,U_1543,U_1547] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1543,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1545,U_1547))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1543,U_1547),U_1545) )
    & ! [U_1546,U_1542,U_1544] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1542,U_1546),U_1544)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1542,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1544,U_1546)) ) ),
    inference(definitional_conversion,[status(esa)],[f_461_3]) ).

cnf(f_461_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1542,U_1546),U_1544)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1542,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1544,U_1546)) ),
    inference(clausify,[status(thm)],[f_461_4]) ).

cnf(f_461_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1543,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1545,U_1547))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1543,U_1547),U_1545) ),
    inference(clausify,[status(thm)],[f_461_4]) ).

fof(f_462_1,plain,
    ! [V_c,V_b,V_a] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c,V_a)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b) ),
    inference(fof_nnf,[status(thm)],[fact_diff__less__mono]) ).

fof(f_462_2,plain,
    ! [U_1550,U_1549,U_1548] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1548,U_1550),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1549,U_1550))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1550,U_1548)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1548,U_1549) ),
    inference(variable_rename,[status(thm)],[f_462_1]) ).

fof(f_462_3,plain,
    ! [U_1549,U_1548,U_1550] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1548,U_1550),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1549,U_1550))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1550,U_1548)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1548,U_1549) ),
    inference(definitional_conversion,[status(esa)],[f_462_2]) ).

cnf(f_462_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1548,U_1550),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1549,U_1550))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1550,U_1548)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1548,U_1549) ),
    inference(clausify,[status(thm)],[f_462_3]) ).

fof(f_463_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) )
        & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_m_2) ),
    inference(fof_nnf,[status(thm)],[fact_less__diff__iff]) ).

fof(f_463_2,plain,
    ! [U_1553,U_1552,U_1551] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1552,U_1551),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1553,U_1551))
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1552,U_1553) )
        & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1552,U_1553)
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1552,U_1551),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1553,U_1551)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1551,U_1553)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1551,U_1552) ),
    inference(variable_rename,[status(thm)],[f_463_1]) ).

fof(f_463_3,plain,
    ( ! [U_1553,U_1551,U_1552] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1552,U_1551),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1553,U_1551))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1552,U_1553)
        | ~ sP132(U_1553,U_1551,U_1552) )
    & ! [U_1553,U_1551,U_1552] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1552,U_1553)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1552,U_1551),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1553,U_1551))
        | ~ sP132(U_1553,U_1551,U_1552) )
    & ! [U_1553,U_1551,U_1552] :
        ( sP132(U_1553,U_1551,U_1552)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1551,U_1553)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1551,U_1552) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP132])],[f_463_2]) ).

cnf(f_463_4,plain,
    ( sP132(U_1553,U_1551,U_1552)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1551,U_1553)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1551,U_1552) ),
    inference(clausify,[status(thm)],[f_463_3]) ).

cnf(f_463_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1552,U_1553)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1552,U_1551),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1553,U_1551))
    | ~ sP132(U_1553,U_1551,U_1552) ),
    inference(clausify,[status(thm)],[f_463_3]) ).

cnf(f_463_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1552,U_1551),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1553,U_1551))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1552,U_1553)
    | ~ sP132(U_1553,U_1551,U_1552) ),
    inference(clausify,[status(thm)],[f_463_3]) ).

fof(f_464_1,plain,
    ! [V_n,V_m] :
      ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | V_m != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) ),
    inference(fof_nnf,[status(thm)],[fact_mult__eq__self__implies__10]) ).

fof(f_464_2,plain,
    ! [U_1555,U_1554] :
      ( U_1554 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | U_1555 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | U_1554 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1554),U_1555) ),
    inference(variable_rename,[status(thm)],[f_464_1]) ).

fof(f_464_3,plain,
    ! [U_1555,U_1554] :
      ( U_1554 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | U_1555 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | U_1554 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1554),U_1555) ),
    inference(definitional_conversion,[status(esa)],[f_464_2]) ).

cnf(f_464_4,plain,
    ( U_1554 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_1555 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_1554 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1554),U_1555) ),
    inference(clausify,[status(thm)],[f_464_3]) ).

fof(f_465_1,plain,
    ! [V_b_2,V_ab_2,V_ca_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)) ) )
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos]) ).

fof(f_465_2,plain,
    ! [U_1559,U_1558,U_1557,U_1556] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_1556,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1556),U_1557),U_1558),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1556),U_1557),U_1559))
          | ~ c_Orderings_Oord__class_Oless__eq(U_1556,U_1558,U_1559) )
        & ( c_Orderings_Oord__class_Oless__eq(U_1556,U_1558,U_1559)
          | ~ c_Orderings_Oord__class_Oless__eq(U_1556,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1556),U_1557),U_1558),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1556),U_1557),U_1559)) ) )
      | ~ c_Orderings_Oord__class_Oless(U_1556,c_Groups_Ozero__class_Ozero(U_1556),U_1557)
      | ~ class_Rings_Olinordered__ring__strict(U_1556) ),
    inference(variable_rename,[status(thm)],[f_465_1]) ).

fof(f_465_3,plain,
    ( ! [U_1557,U_1556,U_1559,U_1558] :
        ( c_Orderings_Oord__class_Oless__eq(U_1556,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1556),U_1557),U_1558),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1556),U_1557),U_1559))
        | ~ c_Orderings_Oord__class_Oless__eq(U_1556,U_1558,U_1559)
        | ~ sP133(U_1557,U_1556,U_1559,U_1558) )
    & ! [U_1557,U_1556,U_1559,U_1558] :
        ( c_Orderings_Oord__class_Oless__eq(U_1556,U_1558,U_1559)
        | ~ c_Orderings_Oord__class_Oless__eq(U_1556,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1556),U_1557),U_1558),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1556),U_1557),U_1559))
        | ~ sP133(U_1557,U_1556,U_1559,U_1558) )
    & ! [U_1557,U_1556,U_1559,U_1558] :
        ( sP133(U_1557,U_1556,U_1559,U_1558)
        | ~ c_Orderings_Oord__class_Oless(U_1556,c_Groups_Ozero__class_Ozero(U_1556),U_1557)
        | ~ class_Rings_Olinordered__ring__strict(U_1556) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP133])],[f_465_2]) ).

cnf(f_465_4,plain,
    ( sP133(U_1557,U_1556,U_1559,U_1558)
    | ~ c_Orderings_Oord__class_Oless(U_1556,c_Groups_Ozero__class_Ozero(U_1556),U_1557)
    | ~ class_Rings_Olinordered__ring__strict(U_1556) ),
    inference(clausify,[status(thm)],[f_465_3]) ).

cnf(f_465_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1556,U_1558,U_1559)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1556,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1556),U_1557),U_1558),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1556),U_1557),U_1559))
    | ~ sP133(U_1557,U_1556,U_1559,U_1558) ),
    inference(clausify,[status(thm)],[f_465_3]) ).

cnf(f_465_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1556,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1556),U_1557),U_1558),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1556),U_1557),U_1559))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1556,U_1558,U_1559)
    | ~ sP133(U_1557,U_1556,U_1559,U_1558) ),
    inference(clausify,[status(thm)],[f_465_3]) ).

fof(f_466_1,plain,
    ! [V_b_2,V_ab_2,V_ca_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_ab_2) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_ab_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)) ) )
      | ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Ozero__class_Ozero(T_a))
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__neg]) ).

fof(f_466_2,plain,
    ! [U_1563,U_1562,U_1561,U_1560] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_1560,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1560),U_1561),U_1562),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1560),U_1561),U_1563))
          | ~ c_Orderings_Oord__class_Oless__eq(U_1560,U_1563,U_1562) )
        & ( c_Orderings_Oord__class_Oless__eq(U_1560,U_1563,U_1562)
          | ~ c_Orderings_Oord__class_Oless__eq(U_1560,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1560),U_1561),U_1562),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1560),U_1561),U_1563)) ) )
      | ~ c_Orderings_Oord__class_Oless(U_1560,U_1561,c_Groups_Ozero__class_Ozero(U_1560))
      | ~ class_Rings_Olinordered__ring__strict(U_1560) ),
    inference(variable_rename,[status(thm)],[f_466_1]) ).

fof(f_466_3,plain,
    ( ! [U_1563,U_1562,U_1561,U_1560] :
        ( c_Orderings_Oord__class_Oless__eq(U_1560,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1560),U_1561),U_1562),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1560),U_1561),U_1563))
        | ~ c_Orderings_Oord__class_Oless__eq(U_1560,U_1563,U_1562)
        | ~ sP134(U_1563,U_1562,U_1561,U_1560) )
    & ! [U_1563,U_1562,U_1561,U_1560] :
        ( c_Orderings_Oord__class_Oless__eq(U_1560,U_1563,U_1562)
        | ~ c_Orderings_Oord__class_Oless__eq(U_1560,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1560),U_1561),U_1562),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1560),U_1561),U_1563))
        | ~ sP134(U_1563,U_1562,U_1561,U_1560) )
    & ! [U_1563,U_1562,U_1561,U_1560] :
        ( sP134(U_1563,U_1562,U_1561,U_1560)
        | ~ c_Orderings_Oord__class_Oless(U_1560,U_1561,c_Groups_Ozero__class_Ozero(U_1560))
        | ~ class_Rings_Olinordered__ring__strict(U_1560) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP134])],[f_466_2]) ).

cnf(f_466_4,plain,
    ( sP134(U_1563,U_1562,U_1561,U_1560)
    | ~ c_Orderings_Oord__class_Oless(U_1560,U_1561,c_Groups_Ozero__class_Ozero(U_1560))
    | ~ class_Rings_Olinordered__ring__strict(U_1560) ),
    inference(clausify,[status(thm)],[f_466_3]) ).

cnf(f_466_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1560,U_1563,U_1562)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1560,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1560),U_1561),U_1562),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1560),U_1561),U_1563))
    | ~ sP134(U_1563,U_1562,U_1561,U_1560) ),
    inference(clausify,[status(thm)],[f_466_3]) ).

cnf(f_466_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1560,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1560),U_1561),U_1562),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1560),U_1561),U_1563))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1560,U_1563,U_1562)
    | ~ sP134(U_1563,U_1562,U_1561,U_1560) ),
    inference(clausify,[status(thm)],[f_466_3]) ).

fof(f_467_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__strict__mono]) ).

fof(f_467_2,plain,
    ! [U_1568,U_1567,U_1566,U_1565,U_1564] :
      ( c_Orderings_Oord__class_Oless(U_1564,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1564),U_1565),U_1567),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1564),U_1566),U_1568))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1564,c_Groups_Ozero__class_Ozero(U_1564),U_1567)
      | ~ c_Orderings_Oord__class_Oless(U_1564,c_Groups_Ozero__class_Ozero(U_1564),U_1566)
      | ~ c_Orderings_Oord__class_Oless(U_1564,U_1567,U_1568)
      | ~ c_Orderings_Oord__class_Oless(U_1564,U_1565,U_1566)
      | ~ class_Rings_Olinordered__semiring__strict(U_1564) ),
    inference(variable_rename,[status(thm)],[f_467_1]) ).

fof(f_467_3,plain,
    ! [U_1566,U_1564,U_1568,U_1567,U_1565] :
      ( c_Orderings_Oord__class_Oless(U_1564,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1564),U_1565),U_1567),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1564),U_1566),U_1568))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1564,c_Groups_Ozero__class_Ozero(U_1564),U_1567)
      | ~ c_Orderings_Oord__class_Oless(U_1564,c_Groups_Ozero__class_Ozero(U_1564),U_1566)
      | ~ c_Orderings_Oord__class_Oless(U_1564,U_1567,U_1568)
      | ~ c_Orderings_Oord__class_Oless(U_1564,U_1565,U_1566)
      | ~ class_Rings_Olinordered__semiring__strict(U_1564) ),
    inference(definitional_conversion,[status(esa)],[f_467_2]) ).

cnf(f_467_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1564,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1564),U_1565),U_1567),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1564),U_1566),U_1568))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1564,c_Groups_Ozero__class_Ozero(U_1564),U_1567)
    | ~ c_Orderings_Oord__class_Oless(U_1564,c_Groups_Ozero__class_Ozero(U_1564),U_1566)
    | ~ c_Orderings_Oord__class_Oless(U_1564,U_1567,U_1568)
    | ~ c_Orderings_Oord__class_Oless(U_1564,U_1565,U_1566)
    | ~ class_Rings_Olinordered__semiring__strict(U_1564) ),
    inference(clausify,[status(thm)],[f_467_3]) ).

fof(f_468_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__strict__mono_H]) ).

fof(f_468_2,plain,
    ! [U_1573,U_1572,U_1571,U_1570,U_1569] :
      ( c_Orderings_Oord__class_Oless(U_1569,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1569),U_1570),U_1572),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1569),U_1571),U_1573))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1569,c_Groups_Ozero__class_Ozero(U_1569),U_1572)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1569,c_Groups_Ozero__class_Ozero(U_1569),U_1570)
      | ~ c_Orderings_Oord__class_Oless(U_1569,U_1572,U_1573)
      | ~ c_Orderings_Oord__class_Oless(U_1569,U_1570,U_1571)
      | ~ class_Rings_Olinordered__semiring__strict(U_1569) ),
    inference(variable_rename,[status(thm)],[f_468_1]) ).

fof(f_468_3,plain,
    ! [U_1570,U_1572,U_1571,U_1573,U_1569] :
      ( c_Orderings_Oord__class_Oless(U_1569,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1569),U_1570),U_1572),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1569),U_1571),U_1573))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1569,c_Groups_Ozero__class_Ozero(U_1569),U_1572)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1569,c_Groups_Ozero__class_Ozero(U_1569),U_1570)
      | ~ c_Orderings_Oord__class_Oless(U_1569,U_1572,U_1573)
      | ~ c_Orderings_Oord__class_Oless(U_1569,U_1570,U_1571)
      | ~ class_Rings_Olinordered__semiring__strict(U_1569) ),
    inference(definitional_conversion,[status(esa)],[f_468_2]) ).

cnf(f_468_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1569,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1569),U_1570),U_1572),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1569),U_1571),U_1573))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1569,c_Groups_Ozero__class_Ozero(U_1569),U_1572)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1569,c_Groups_Ozero__class_Ozero(U_1569),U_1570)
    | ~ c_Orderings_Oord__class_Oless(U_1569,U_1572,U_1573)
    | ~ c_Orderings_Oord__class_Oless(U_1569,U_1570,U_1571)
    | ~ class_Rings_Olinordered__semiring__strict(U_1569) ),
    inference(clausify,[status(thm)],[f_468_3]) ).

fof(f_469_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_d)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__le__imp__less]) ).

fof(f_469_2,plain,
    ! [U_1578,U_1577,U_1576,U_1575,U_1574] :
      ( c_Orderings_Oord__class_Oless(U_1574,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1574),U_1575),U_1577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1574),U_1576),U_1578))
      | ~ c_Orderings_Oord__class_Oless(U_1574,c_Groups_Ozero__class_Ozero(U_1574),U_1577)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1574,c_Groups_Ozero__class_Ozero(U_1574),U_1575)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1574,U_1577,U_1578)
      | ~ c_Orderings_Oord__class_Oless(U_1574,U_1575,U_1576)
      | ~ class_Rings_Olinordered__semiring__strict(U_1574) ),
    inference(variable_rename,[status(thm)],[f_469_1]) ).

fof(f_469_3,plain,
    ! [U_1577,U_1576,U_1574,U_1578,U_1575] :
      ( c_Orderings_Oord__class_Oless(U_1574,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1574),U_1575),U_1577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1574),U_1576),U_1578))
      | ~ c_Orderings_Oord__class_Oless(U_1574,c_Groups_Ozero__class_Ozero(U_1574),U_1577)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1574,c_Groups_Ozero__class_Ozero(U_1574),U_1575)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1574,U_1577,U_1578)
      | ~ c_Orderings_Oord__class_Oless(U_1574,U_1575,U_1576)
      | ~ class_Rings_Olinordered__semiring__strict(U_1574) ),
    inference(definitional_conversion,[status(esa)],[f_469_2]) ).

cnf(f_469_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1574,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1574),U_1575),U_1577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1574),U_1576),U_1578))
    | ~ c_Orderings_Oord__class_Oless(U_1574,c_Groups_Ozero__class_Ozero(U_1574),U_1577)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1574,c_Groups_Ozero__class_Ozero(U_1574),U_1575)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1574,U_1577,U_1578)
    | ~ c_Orderings_Oord__class_Oless(U_1574,U_1575,U_1576)
    | ~ class_Rings_Olinordered__semiring__strict(U_1574) ),
    inference(clausify,[status(thm)],[f_469_3]) ).

fof(f_470_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__less__imp__less]) ).

fof(f_470_2,plain,
    ! [U_1583,U_1582,U_1581,U_1580,U_1579] :
      ( c_Orderings_Oord__class_Oless(U_1579,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1579),U_1580),U_1582),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1579),U_1581),U_1583))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1579,c_Groups_Ozero__class_Ozero(U_1579),U_1582)
      | ~ c_Orderings_Oord__class_Oless(U_1579,c_Groups_Ozero__class_Ozero(U_1579),U_1580)
      | ~ c_Orderings_Oord__class_Oless(U_1579,U_1582,U_1583)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1579,U_1580,U_1581)
      | ~ class_Rings_Olinordered__semiring__strict(U_1579) ),
    inference(variable_rename,[status(thm)],[f_470_1]) ).

fof(f_470_3,plain,
    ! [U_1581,U_1579,U_1580,U_1583,U_1582] :
      ( c_Orderings_Oord__class_Oless(U_1579,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1579),U_1580),U_1582),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1579),U_1581),U_1583))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1579,c_Groups_Ozero__class_Ozero(U_1579),U_1582)
      | ~ c_Orderings_Oord__class_Oless(U_1579,c_Groups_Ozero__class_Ozero(U_1579),U_1580)
      | ~ c_Orderings_Oord__class_Oless(U_1579,U_1582,U_1583)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1579,U_1580,U_1581)
      | ~ class_Rings_Olinordered__semiring__strict(U_1579) ),
    inference(definitional_conversion,[status(esa)],[f_470_2]) ).

cnf(f_470_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1579,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1579),U_1580),U_1582),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1579),U_1581),U_1583))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1579,c_Groups_Ozero__class_Ozero(U_1579),U_1582)
    | ~ c_Orderings_Oord__class_Oless(U_1579,c_Groups_Ozero__class_Ozero(U_1579),U_1580)
    | ~ c_Orderings_Oord__class_Oless(U_1579,U_1582,U_1583)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1579,U_1580,U_1581)
    | ~ class_Rings_Olinordered__semiring__strict(U_1579) ),
    inference(clausify,[status(thm)],[f_470_3]) ).

fof(f_471_1,plain,
    ! [V_b,V_c,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
      | ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
      | ~ class_Rings_Olinordered__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__right__less__imp__less]) ).

fof(f_471_2,plain,
    ! [U_1587,U_1586,U_1585,U_1584] :
      ( c_Orderings_Oord__class_Oless(U_1584,U_1585,U_1587)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1584,c_Groups_Ozero__class_Ozero(U_1584),U_1586)
      | ~ c_Orderings_Oord__class_Oless(U_1584,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1584),U_1585),U_1586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1584),U_1587),U_1586))
      | ~ class_Rings_Olinordered__semiring(U_1584) ),
    inference(variable_rename,[status(thm)],[f_471_1]) ).

fof(f_471_3,plain,
    ! [U_1584,U_1585,U_1587,U_1586] :
      ( c_Orderings_Oord__class_Oless(U_1584,U_1585,U_1587)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1584,c_Groups_Ozero__class_Ozero(U_1584),U_1586)
      | ~ c_Orderings_Oord__class_Oless(U_1584,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1584),U_1585),U_1586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1584),U_1587),U_1586))
      | ~ class_Rings_Olinordered__semiring(U_1584) ),
    inference(definitional_conversion,[status(esa)],[f_471_2]) ).

cnf(f_471_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1584,U_1585,U_1587)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1584,c_Groups_Ozero__class_Ozero(U_1584),U_1586)
    | ~ c_Orderings_Oord__class_Oless(U_1584,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1584),U_1585),U_1586),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1584),U_1587),U_1586))
    | ~ class_Rings_Olinordered__semiring(U_1584) ),
    inference(clausify,[status(thm)],[f_471_3]) ).

fof(f_472_1,plain,
    ! [V_b,V_c,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
      | ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__right]) ).

fof(f_472_2,plain,
    ! [U_1591,U_1590,U_1589,U_1588] :
      ( c_Orderings_Oord__class_Oless(U_1588,U_1589,U_1591)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1588,c_Groups_Ozero__class_Ozero(U_1588),U_1590)
      | ~ c_Orderings_Oord__class_Oless(U_1588,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1588),U_1589),U_1590),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1588),U_1591),U_1590))
      | ~ class_Rings_Olinordered__semiring__strict(U_1588) ),
    inference(variable_rename,[status(thm)],[f_472_1]) ).

fof(f_472_3,plain,
    ! [U_1589,U_1588,U_1590,U_1591] :
      ( c_Orderings_Oord__class_Oless(U_1588,U_1589,U_1591)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1588,c_Groups_Ozero__class_Ozero(U_1588),U_1590)
      | ~ c_Orderings_Oord__class_Oless(U_1588,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1588),U_1589),U_1590),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1588),U_1591),U_1590))
      | ~ class_Rings_Olinordered__semiring__strict(U_1588) ),
    inference(definitional_conversion,[status(esa)],[f_472_2]) ).

cnf(f_472_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1588,U_1589,U_1591)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1588,c_Groups_Ozero__class_Ozero(U_1588),U_1590)
    | ~ c_Orderings_Oord__class_Oless(U_1588,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1588),U_1589),U_1590),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1588),U_1591),U_1590))
    | ~ class_Rings_Olinordered__semiring__strict(U_1588) ),
    inference(clausify,[status(thm)],[f_472_3]) ).

fof(f_473_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
      | ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
      | ~ class_Rings_Olinordered__semiring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__left__less__imp__less]) ).

fof(f_473_2,plain,
    ! [U_1595,U_1594,U_1593,U_1592] :
      ( c_Orderings_Oord__class_Oless(U_1592,U_1594,U_1595)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1592,c_Groups_Ozero__class_Ozero(U_1592),U_1593)
      | ~ c_Orderings_Oord__class_Oless(U_1592,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1592),U_1593),U_1594),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1592),U_1593),U_1595))
      | ~ class_Rings_Olinordered__semiring(U_1592) ),
    inference(variable_rename,[status(thm)],[f_473_1]) ).

fof(f_473_3,plain,
    ! [U_1595,U_1593,U_1594,U_1592] :
      ( c_Orderings_Oord__class_Oless(U_1592,U_1594,U_1595)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1592,c_Groups_Ozero__class_Ozero(U_1592),U_1593)
      | ~ c_Orderings_Oord__class_Oless(U_1592,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1592),U_1593),U_1594),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1592),U_1593),U_1595))
      | ~ class_Rings_Olinordered__semiring(U_1592) ),
    inference(definitional_conversion,[status(esa)],[f_473_2]) ).

cnf(f_473_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1592,U_1594,U_1595)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1592,c_Groups_Ozero__class_Ozero(U_1592),U_1593)
    | ~ c_Orderings_Oord__class_Oless(U_1592,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1592),U_1593),U_1594),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1592),U_1593),U_1595))
    | ~ class_Rings_Olinordered__semiring(U_1592) ),
    inference(clausify,[status(thm)],[f_473_3]) ).

fof(f_474_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
      | ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__left]) ).

fof(f_474_2,plain,
    ! [U_1599,U_1598,U_1597,U_1596] :
      ( c_Orderings_Oord__class_Oless(U_1596,U_1598,U_1599)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1596,c_Groups_Ozero__class_Ozero(U_1596),U_1597)
      | ~ c_Orderings_Oord__class_Oless(U_1596,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1596),U_1597),U_1598),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1596),U_1597),U_1599))
      | ~ class_Rings_Olinordered__semiring__strict(U_1596) ),
    inference(variable_rename,[status(thm)],[f_474_1]) ).

fof(f_474_3,plain,
    ! [U_1598,U_1597,U_1596,U_1599] :
      ( c_Orderings_Oord__class_Oless(U_1596,U_1598,U_1599)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1596,c_Groups_Ozero__class_Ozero(U_1596),U_1597)
      | ~ c_Orderings_Oord__class_Oless(U_1596,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1596),U_1597),U_1598),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1596),U_1597),U_1599))
      | ~ class_Rings_Olinordered__semiring__strict(U_1596) ),
    inference(definitional_conversion,[status(esa)],[f_474_2]) ).

cnf(f_474_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1596,U_1598,U_1599)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1596,c_Groups_Ozero__class_Ozero(U_1596),U_1597)
    | ~ c_Orderings_Oord__class_Oless(U_1596,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1596),U_1597),U_1598),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1596),U_1597),U_1599))
    | ~ class_Rings_Olinordered__semiring__strict(U_1596) ),
    inference(clausify,[status(thm)],[f_474_3]) ).

fof(f_475_1,plain,
    ! [V_b,V_c,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__right__le__imp__le]) ).

fof(f_475_2,plain,
    ! [U_1603,U_1602,U_1601,U_1600] :
      ( c_Orderings_Oord__class_Oless__eq(U_1600,U_1601,U_1603)
      | ~ c_Orderings_Oord__class_Oless(U_1600,c_Groups_Ozero__class_Ozero(U_1600),U_1602)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1600,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1600),U_1601),U_1602),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1600),U_1603),U_1602))
      | ~ class_Rings_Olinordered__semiring__strict(U_1600) ),
    inference(variable_rename,[status(thm)],[f_475_1]) ).

fof(f_475_3,plain,
    ! [U_1602,U_1600,U_1601,U_1603] :
      ( c_Orderings_Oord__class_Oless__eq(U_1600,U_1601,U_1603)
      | ~ c_Orderings_Oord__class_Oless(U_1600,c_Groups_Ozero__class_Ozero(U_1600),U_1602)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1600,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1600),U_1601),U_1602),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1600),U_1603),U_1602))
      | ~ class_Rings_Olinordered__semiring__strict(U_1600) ),
    inference(definitional_conversion,[status(esa)],[f_475_2]) ).

cnf(f_475_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1600,U_1601,U_1603)
    | ~ c_Orderings_Oord__class_Oless(U_1600,c_Groups_Ozero__class_Ozero(U_1600),U_1602)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1600,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1600),U_1601),U_1602),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1600),U_1603),U_1602))
    | ~ class_Rings_Olinordered__semiring__strict(U_1600) ),
    inference(clausify,[status(thm)],[f_475_3]) ).

fof(f_476_1,plain,
    ! [V_b,V_a,V_c,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
      | ~ class_Rings_Olinordered__semiring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__left__le__imp__le]) ).

fof(f_476_2,plain,
    ! [U_1607,U_1606,U_1605,U_1604] :
      ( c_Orderings_Oord__class_Oless__eq(U_1604,U_1606,U_1607)
      | ~ c_Orderings_Oord__class_Oless(U_1604,c_Groups_Ozero__class_Ozero(U_1604),U_1605)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1604,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1604),U_1605),U_1606),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1604),U_1605),U_1607))
      | ~ class_Rings_Olinordered__semiring__strict(U_1604) ),
    inference(variable_rename,[status(thm)],[f_476_1]) ).

fof(f_476_3,plain,
    ! [U_1607,U_1605,U_1606,U_1604] :
      ( c_Orderings_Oord__class_Oless__eq(U_1604,U_1606,U_1607)
      | ~ c_Orderings_Oord__class_Oless(U_1604,c_Groups_Ozero__class_Ozero(U_1604),U_1605)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1604,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1604),U_1605),U_1606),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1604),U_1605),U_1607))
      | ~ class_Rings_Olinordered__semiring__strict(U_1604) ),
    inference(definitional_conversion,[status(esa)],[f_476_2]) ).

cnf(f_476_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1604,U_1606,U_1607)
    | ~ c_Orderings_Oord__class_Oless(U_1604,c_Groups_Ozero__class_Ozero(U_1604),U_1605)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1604,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1604),U_1605),U_1606),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1604),U_1605),U_1607))
    | ~ class_Rings_Olinordered__semiring__strict(U_1604) ),
    inference(clausify,[status(thm)],[f_476_3]) ).

fof(f_477_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))
      | ~ c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg]) ).

fof(f_477_2,plain,
    ! [U_1610,U_1609,U_1608] :
      ( c_Orderings_Oord__class_Oless(U_1608,c_Groups_Oplus__class_Oplus(U_1608,U_1609,U_1610),c_Groups_Ozero__class_Ozero(U_1608))
      | ~ c_Orderings_Oord__class_Oless(U_1608,U_1610,c_Groups_Ozero__class_Ozero(U_1608))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1608,U_1609,c_Groups_Ozero__class_Ozero(U_1608))
      | ~ class_Groups_Oordered__comm__monoid__add(U_1608) ),
    inference(variable_rename,[status(thm)],[f_477_1]) ).

fof(f_477_3,plain,
    ! [U_1610,U_1608,U_1609] :
      ( c_Orderings_Oord__class_Oless(U_1608,c_Groups_Oplus__class_Oplus(U_1608,U_1609,U_1610),c_Groups_Ozero__class_Ozero(U_1608))
      | ~ c_Orderings_Oord__class_Oless(U_1608,U_1610,c_Groups_Ozero__class_Ozero(U_1608))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1608,U_1609,c_Groups_Ozero__class_Ozero(U_1608))
      | ~ class_Groups_Oordered__comm__monoid__add(U_1608) ),
    inference(definitional_conversion,[status(esa)],[f_477_2]) ).

cnf(f_477_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1608,c_Groups_Oplus__class_Oplus(U_1608,U_1609,U_1610),c_Groups_Ozero__class_Ozero(U_1608))
    | ~ c_Orderings_Oord__class_Oless(U_1608,U_1610,c_Groups_Ozero__class_Ozero(U_1608))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1608,U_1609,c_Groups_Ozero__class_Ozero(U_1608))
    | ~ class_Groups_Oordered__comm__monoid__add(U_1608) ),
    inference(clausify,[status(thm)],[f_477_3]) ).

fof(f_478_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
      | ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos]) ).

fof(f_478_2,plain,
    ! [U_1613,U_1612,U_1611] :
      ( c_Orderings_Oord__class_Oless(U_1611,c_Groups_Oplus__class_Oplus(U_1611,U_1612,U_1613),c_Groups_Ozero__class_Ozero(U_1611))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1611,U_1613,c_Groups_Ozero__class_Ozero(U_1611))
      | ~ c_Orderings_Oord__class_Oless(U_1611,U_1612,c_Groups_Ozero__class_Ozero(U_1611))
      | ~ class_Groups_Oordered__comm__monoid__add(U_1611) ),
    inference(variable_rename,[status(thm)],[f_478_1]) ).

fof(f_478_3,plain,
    ! [U_1612,U_1611,U_1613] :
      ( c_Orderings_Oord__class_Oless(U_1611,c_Groups_Oplus__class_Oplus(U_1611,U_1612,U_1613),c_Groups_Ozero__class_Ozero(U_1611))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1611,U_1613,c_Groups_Ozero__class_Ozero(U_1611))
      | ~ c_Orderings_Oord__class_Oless(U_1611,U_1612,c_Groups_Ozero__class_Ozero(U_1611))
      | ~ class_Groups_Oordered__comm__monoid__add(U_1611) ),
    inference(definitional_conversion,[status(esa)],[f_478_2]) ).

cnf(f_478_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1611,c_Groups_Oplus__class_Oplus(U_1611,U_1612,U_1613),c_Groups_Ozero__class_Ozero(U_1611))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1611,U_1613,c_Groups_Ozero__class_Ozero(U_1611))
    | ~ c_Orderings_Oord__class_Oless(U_1611,U_1612,c_Groups_Ozero__class_Ozero(U_1611))
    | ~ class_Groups_Oordered__comm__monoid__add(U_1611) ),
    inference(clausify,[status(thm)],[f_478_3]) ).

fof(f_479_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
      | ~ c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2]) ).

fof(f_479_2,plain,
    ! [U_1617,U_1616,U_1615,U_1614] :
      ( c_Orderings_Oord__class_Oless(U_1614,U_1616,c_Groups_Oplus__class_Oplus(U_1614,U_1615,U_1617))
      | ~ c_Orderings_Oord__class_Oless(U_1614,U_1616,U_1617)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1614,c_Groups_Ozero__class_Ozero(U_1614),U_1615)
      | ~ class_Groups_Oordered__comm__monoid__add(U_1614) ),
    inference(variable_rename,[status(thm)],[f_479_1]) ).

fof(f_479_3,plain,
    ! [U_1615,U_1614,U_1616,U_1617] :
      ( c_Orderings_Oord__class_Oless(U_1614,U_1616,c_Groups_Oplus__class_Oplus(U_1614,U_1615,U_1617))
      | ~ c_Orderings_Oord__class_Oless(U_1614,U_1616,U_1617)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1614,c_Groups_Ozero__class_Ozero(U_1614),U_1615)
      | ~ class_Groups_Oordered__comm__monoid__add(U_1614) ),
    inference(definitional_conversion,[status(esa)],[f_479_2]) ).

cnf(f_479_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1614,U_1616,c_Groups_Oplus__class_Oplus(U_1614,U_1615,U_1617))
    | ~ c_Orderings_Oord__class_Oless(U_1614,U_1616,U_1617)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1614,c_Groups_Ozero__class_Ozero(U_1614),U_1615)
    | ~ class_Groups_Oordered__comm__monoid__add(U_1614) ),
    inference(clausify,[status(thm)],[f_479_3]) ).

fof(f_480_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__strict__increasing]) ).

fof(f_480_2,plain,
    ! [U_1621,U_1620,U_1619,U_1618] :
      ( c_Orderings_Oord__class_Oless(U_1618,U_1620,c_Groups_Oplus__class_Oplus(U_1618,U_1619,U_1621))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1618,U_1620,U_1621)
      | ~ c_Orderings_Oord__class_Oless(U_1618,c_Groups_Ozero__class_Ozero(U_1618),U_1619)
      | ~ class_Groups_Oordered__comm__monoid__add(U_1618) ),
    inference(variable_rename,[status(thm)],[f_480_1]) ).

fof(f_480_3,plain,
    ! [U_1620,U_1621,U_1619,U_1618] :
      ( c_Orderings_Oord__class_Oless(U_1618,U_1620,c_Groups_Oplus__class_Oplus(U_1618,U_1619,U_1621))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1618,U_1620,U_1621)
      | ~ c_Orderings_Oord__class_Oless(U_1618,c_Groups_Ozero__class_Ozero(U_1618),U_1619)
      | ~ class_Groups_Oordered__comm__monoid__add(U_1618) ),
    inference(definitional_conversion,[status(esa)],[f_480_2]) ).

cnf(f_480_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1618,U_1620,c_Groups_Oplus__class_Oplus(U_1618,U_1619,U_1621))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1618,U_1620,U_1621)
    | ~ c_Orderings_Oord__class_Oless(U_1618,c_Groups_Ozero__class_Ozero(U_1618),U_1619)
    | ~ class_Groups_Oordered__comm__monoid__add(U_1618) ),
    inference(clausify,[status(thm)],[f_480_3]) ).

fof(f_481_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos]) ).

fof(f_481_2,plain,
    ! [U_1624,U_1623,U_1622] :
      ( c_Orderings_Oord__class_Oless(U_1622,c_Groups_Ozero__class_Ozero(U_1622),c_Groups_Oplus__class_Oplus(U_1622,U_1623,U_1624))
      | ~ c_Orderings_Oord__class_Oless(U_1622,c_Groups_Ozero__class_Ozero(U_1622),U_1624)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1622,c_Groups_Ozero__class_Ozero(U_1622),U_1623)
      | ~ class_Groups_Oordered__comm__monoid__add(U_1622) ),
    inference(variable_rename,[status(thm)],[f_481_1]) ).

fof(f_481_3,plain,
    ! [U_1623,U_1624,U_1622] :
      ( c_Orderings_Oord__class_Oless(U_1622,c_Groups_Ozero__class_Ozero(U_1622),c_Groups_Oplus__class_Oplus(U_1622,U_1623,U_1624))
      | ~ c_Orderings_Oord__class_Oless(U_1622,c_Groups_Ozero__class_Ozero(U_1622),U_1624)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1622,c_Groups_Ozero__class_Ozero(U_1622),U_1623)
      | ~ class_Groups_Oordered__comm__monoid__add(U_1622) ),
    inference(definitional_conversion,[status(esa)],[f_481_2]) ).

cnf(f_481_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1622,c_Groups_Ozero__class_Ozero(U_1622),c_Groups_Oplus__class_Oplus(U_1622,U_1623,U_1624))
    | ~ c_Orderings_Oord__class_Oless(U_1622,c_Groups_Ozero__class_Ozero(U_1622),U_1624)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1622,c_Groups_Ozero__class_Ozero(U_1622),U_1623)
    | ~ class_Groups_Oordered__comm__monoid__add(U_1622) ),
    inference(clausify,[status(thm)],[f_481_3]) ).

fof(f_482_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg]) ).

fof(f_482_2,plain,
    ! [U_1627,U_1626,U_1625] :
      ( c_Orderings_Oord__class_Oless(U_1625,c_Groups_Ozero__class_Ozero(U_1625),c_Groups_Oplus__class_Oplus(U_1625,U_1626,U_1627))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1625,c_Groups_Ozero__class_Ozero(U_1625),U_1627)
      | ~ c_Orderings_Oord__class_Oless(U_1625,c_Groups_Ozero__class_Ozero(U_1625),U_1626)
      | ~ class_Groups_Oordered__comm__monoid__add(U_1625) ),
    inference(variable_rename,[status(thm)],[f_482_1]) ).

fof(f_482_3,plain,
    ! [U_1626,U_1625,U_1627] :
      ( c_Orderings_Oord__class_Oless(U_1625,c_Groups_Ozero__class_Ozero(U_1625),c_Groups_Oplus__class_Oplus(U_1625,U_1626,U_1627))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1625,c_Groups_Ozero__class_Ozero(U_1625),U_1627)
      | ~ c_Orderings_Oord__class_Oless(U_1625,c_Groups_Ozero__class_Ozero(U_1625),U_1626)
      | ~ class_Groups_Oordered__comm__monoid__add(U_1625) ),
    inference(definitional_conversion,[status(esa)],[f_482_2]) ).

cnf(f_482_4,plain,
    ( c_Orderings_Oord__class_Oless(U_1625,c_Groups_Ozero__class_Ozero(U_1625),c_Groups_Oplus__class_Oplus(U_1625,U_1626,U_1627))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1625,c_Groups_Ozero__class_Ozero(U_1625),U_1627)
    | ~ c_Orderings_Oord__class_Oless(U_1625,c_Groups_Ozero__class_Ozero(U_1625),U_1626)
    | ~ class_Groups_Oordered__comm__monoid__add(U_1625) ),
    inference(clausify,[status(thm)],[f_482_3]) ).

fof(f_483_1,plain,
    ! [V_y,V_x,T_a] :
      ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a))
      | ~ class_Rings_Olinordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_not__sum__squares__lt__zero]) ).

fof(f_483_2,plain,
    ! [U_1630,U_1629,U_1628] :
      ( ~ c_Orderings_Oord__class_Oless(U_1628,c_Groups_Oplus__class_Oplus(U_1628,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1628),U_1629),U_1629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1628),U_1630),U_1630)),c_Groups_Ozero__class_Ozero(U_1628))
      | ~ class_Rings_Olinordered__ring(U_1628) ),
    inference(variable_rename,[status(thm)],[f_483_1]) ).

fof(f_483_3,plain,
    ! [U_1628,U_1629,U_1630] :
      ( ~ c_Orderings_Oord__class_Oless(U_1628,c_Groups_Oplus__class_Oplus(U_1628,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1628),U_1629),U_1629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1628),U_1630),U_1630)),c_Groups_Ozero__class_Ozero(U_1628))
      | ~ class_Rings_Olinordered__ring(U_1628) ),
    inference(definitional_conversion,[status(esa)],[f_483_2]) ).

cnf(f_483_4,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1628,c_Groups_Oplus__class_Oplus(U_1628,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1628),U_1629),U_1629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1628),U_1630),U_1630)),c_Groups_Ozero__class_Ozero(U_1628))
    | ~ class_Rings_Olinordered__ring(U_1628) ),
    inference(clausify,[status(thm)],[f_483_3]) ).

fof(f_484_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))
          | ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
            & V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) )
        & ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
          | V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))) ) )
      | ~ class_Rings_Olinordered__ring__strict(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sum__squares__gt__zero__iff]) ).

fof(f_484_2,plain,
    ! [U_1633,U_1632,U_1631] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1631,c_Groups_Ozero__class_Ozero(U_1631),c_Groups_Oplus__class_Oplus(U_1631,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1631),U_1632),U_1632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1631),U_1633),U_1633)))
          | ( U_1633 = c_Groups_Ozero__class_Ozero(U_1631)
            & U_1632 = c_Groups_Ozero__class_Ozero(U_1631) ) )
        & ( U_1633 != c_Groups_Ozero__class_Ozero(U_1631)
          | U_1632 != c_Groups_Ozero__class_Ozero(U_1631)
          | ~ c_Orderings_Oord__class_Oless(U_1631,c_Groups_Ozero__class_Ozero(U_1631),c_Groups_Oplus__class_Oplus(U_1631,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1631),U_1632),U_1632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1631),U_1633),U_1633))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_1631) ),
    inference(variable_rename,[status(thm)],[f_484_1]) ).

fof(f_484_3,plain,
    ( ! [U_1631,U_1632,U_1633] :
        ( U_1633 = c_Groups_Ozero__class_Ozero(U_1631)
        | ~ sP135(U_1631,U_1632,U_1633) )
    & ! [U_1631,U_1632,U_1633] :
        ( U_1632 = c_Groups_Ozero__class_Ozero(U_1631)
        | ~ sP135(U_1631,U_1632,U_1633) )
    & ! [U_1631,U_1632,U_1633] :
        ( c_Orderings_Oord__class_Oless(U_1631,c_Groups_Ozero__class_Ozero(U_1631),c_Groups_Oplus__class_Oplus(U_1631,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1631),U_1632),U_1632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1631),U_1633),U_1633)))
        | sP135(U_1631,U_1632,U_1633)
        | ~ sP136(U_1631,U_1632,U_1633) )
    & ! [U_1631,U_1632,U_1633] :
        ( U_1633 != c_Groups_Ozero__class_Ozero(U_1631)
        | U_1632 != c_Groups_Ozero__class_Ozero(U_1631)
        | ~ c_Orderings_Oord__class_Oless(U_1631,c_Groups_Ozero__class_Ozero(U_1631),c_Groups_Oplus__class_Oplus(U_1631,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1631),U_1632),U_1632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1631),U_1633),U_1633)))
        | ~ sP136(U_1631,U_1632,U_1633) )
    & ! [U_1631,U_1632,U_1633] :
        ( sP136(U_1631,U_1632,U_1633)
        | ~ class_Rings_Olinordered__ring__strict(U_1631) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP135,sP136])],[f_484_2]) ).

cnf(f_484_4,plain,
    ( sP136(U_1631,U_1632,U_1633)
    | ~ class_Rings_Olinordered__ring__strict(U_1631) ),
    inference(clausify,[status(thm)],[f_484_3]) ).

cnf(f_484_5,plain,
    ( U_1633 != c_Groups_Ozero__class_Ozero(U_1631)
    | U_1632 != c_Groups_Ozero__class_Ozero(U_1631)
    | ~ c_Orderings_Oord__class_Oless(U_1631,c_Groups_Ozero__class_Ozero(U_1631),c_Groups_Oplus__class_Oplus(U_1631,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1631),U_1632),U_1632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1631),U_1633),U_1633)))
    | ~ sP136(U_1631,U_1632,U_1633) ),
    inference(clausify,[status(thm)],[f_484_3]) ).

cnf(f_484_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1631,c_Groups_Ozero__class_Ozero(U_1631),c_Groups_Oplus__class_Oplus(U_1631,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1631),U_1632),U_1632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1631),U_1633),U_1633)))
    | sP135(U_1631,U_1632,U_1633)
    | ~ sP136(U_1631,U_1632,U_1633) ),
    inference(clausify,[status(thm)],[f_484_3]) ).

cnf(f_484_7,plain,
    ( U_1632 = c_Groups_Ozero__class_Ozero(U_1631)
    | ~ sP135(U_1631,U_1632,U_1633) ),
    inference(clausify,[status(thm)],[f_484_3]) ).

cnf(f_484_8,plain,
    ( U_1633 = c_Groups_Ozero__class_Ozero(U_1631)
    | ~ sP135(U_1631,U_1632,U_1633) ),
    inference(clausify,[status(thm)],[f_484_3]) ).

fof(f_485_1,plain,
    ! [V_y,V_x,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),V_x)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__right__le__one__le]) ).

fof(f_485_2,plain,
    ! [U_1636,U_1635,U_1634] :
      ( c_Orderings_Oord__class_Oless__eq(U_1634,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1634),U_1635),U_1636),U_1635)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1634,U_1636,c_Groups_Oone__class_Oone(U_1634))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1634,c_Groups_Ozero__class_Ozero(U_1634),U_1636)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1634,c_Groups_Ozero__class_Ozero(U_1634),U_1635)
      | ~ class_Rings_Olinordered__idom(U_1634) ),
    inference(variable_rename,[status(thm)],[f_485_1]) ).

fof(f_485_3,plain,
    ! [U_1636,U_1634,U_1635] :
      ( c_Orderings_Oord__class_Oless__eq(U_1634,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1634),U_1635),U_1636),U_1635)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1634,U_1636,c_Groups_Oone__class_Oone(U_1634))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1634,c_Groups_Ozero__class_Ozero(U_1634),U_1636)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1634,c_Groups_Ozero__class_Ozero(U_1634),U_1635)
      | ~ class_Rings_Olinordered__idom(U_1634) ),
    inference(definitional_conversion,[status(esa)],[f_485_2]) ).

cnf(f_485_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1634,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1634),U_1635),U_1636),U_1635)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1634,U_1636,c_Groups_Oone__class_Oone(U_1634))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1634,c_Groups_Ozero__class_Ozero(U_1634),U_1636)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1634,c_Groups_Ozero__class_Ozero(U_1634),U_1635)
    | ~ class_Rings_Olinordered__idom(U_1634) ),
    inference(clausify,[status(thm)],[f_485_3]) ).

fof(f_486_1,plain,
    ! [V_y,V_x,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__left__le__one__le]) ).

fof(f_486_2,plain,
    ! [U_1639,U_1638,U_1637] :
      ( c_Orderings_Oord__class_Oless__eq(U_1637,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1637),U_1639),U_1638),U_1638)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1637,U_1639,c_Groups_Oone__class_Oone(U_1637))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1637,c_Groups_Ozero__class_Ozero(U_1637),U_1639)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1637,c_Groups_Ozero__class_Ozero(U_1637),U_1638)
      | ~ class_Rings_Olinordered__idom(U_1637) ),
    inference(variable_rename,[status(thm)],[f_486_1]) ).

fof(f_486_3,plain,
    ! [U_1639,U_1637,U_1638] :
      ( c_Orderings_Oord__class_Oless__eq(U_1637,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1637),U_1639),U_1638),U_1638)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1637,U_1639,c_Groups_Oone__class_Oone(U_1637))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1637,c_Groups_Ozero__class_Ozero(U_1637),U_1639)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1637,c_Groups_Ozero__class_Ozero(U_1637),U_1638)
      | ~ class_Rings_Olinordered__idom(U_1637) ),
    inference(definitional_conversion,[status(esa)],[f_486_2]) ).

cnf(f_486_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1637,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1637),U_1639),U_1638),U_1638)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1637,U_1639,c_Groups_Oone__class_Oone(U_1637))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1637,c_Groups_Ozero__class_Ozero(U_1637),U_1639)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1637,c_Groups_Ozero__class_Ozero(U_1637),U_1638)
    | ~ class_Rings_Olinordered__idom(U_1637) ),
    inference(clausify,[status(thm)],[f_486_3]) ).

fof(f_487_1,plain,
    ! [V_db_2,V_b_2,V_ca_2,V_e_2,V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2))
          | ~ c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_ab_2)),V_e_2),V_db_2)) )
        & ( c_Orderings_Oord__class_Oless(T_a,V_ca_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_ab_2)),V_e_2),V_db_2))
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2)) ) )
      | ~ class_Rings_Oordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__add__iff2]) ).

fof(f_487_2,plain,
    ! [U_1645,U_1644,U_1643,U_1642,U_1641,U_1640] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1640,c_Groups_Oplus__class_Oplus(U_1640,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1640),U_1641),U_1642),U_1643),c_Groups_Oplus__class_Oplus(U_1640,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1640),U_1644),U_1642),U_1645))
          | ~ c_Orderings_Oord__class_Oless(U_1640,U_1643,c_Groups_Oplus__class_Oplus(U_1640,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1640),c_Groups_Ominus__class_Ominus(U_1640,U_1644,U_1641)),U_1642),U_1645)) )
        & ( c_Orderings_Oord__class_Oless(U_1640,U_1643,c_Groups_Oplus__class_Oplus(U_1640,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1640),c_Groups_Ominus__class_Ominus(U_1640,U_1644,U_1641)),U_1642),U_1645))
          | ~ c_Orderings_Oord__class_Oless(U_1640,c_Groups_Oplus__class_Oplus(U_1640,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1640),U_1641),U_1642),U_1643),c_Groups_Oplus__class_Oplus(U_1640,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1640),U_1644),U_1642),U_1645)) ) )
      | ~ class_Rings_Oordered__ring(U_1640) ),
    inference(variable_rename,[status(thm)],[f_487_1]) ).

fof(f_487_3,plain,
    ( ! [U_1640,U_1642,U_1641,U_1643,U_1644,U_1645] :
        ( c_Orderings_Oord__class_Oless(U_1640,c_Groups_Oplus__class_Oplus(U_1640,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1640),U_1641),U_1642),U_1643),c_Groups_Oplus__class_Oplus(U_1640,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1640),U_1644),U_1642),U_1645))
        | ~ c_Orderings_Oord__class_Oless(U_1640,U_1643,c_Groups_Oplus__class_Oplus(U_1640,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1640),c_Groups_Ominus__class_Ominus(U_1640,U_1644,U_1641)),U_1642),U_1645))
        | ~ sP137(U_1640,U_1642,U_1641,U_1643,U_1644,U_1645) )
    & ! [U_1640,U_1642,U_1641,U_1643,U_1644,U_1645] :
        ( c_Orderings_Oord__class_Oless(U_1640,U_1643,c_Groups_Oplus__class_Oplus(U_1640,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1640),c_Groups_Ominus__class_Ominus(U_1640,U_1644,U_1641)),U_1642),U_1645))
        | ~ c_Orderings_Oord__class_Oless(U_1640,c_Groups_Oplus__class_Oplus(U_1640,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1640),U_1641),U_1642),U_1643),c_Groups_Oplus__class_Oplus(U_1640,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1640),U_1644),U_1642),U_1645))
        | ~ sP137(U_1640,U_1642,U_1641,U_1643,U_1644,U_1645) )
    & ! [U_1640,U_1642,U_1641,U_1643,U_1644,U_1645] :
        ( sP137(U_1640,U_1642,U_1641,U_1643,U_1644,U_1645)
        | ~ class_Rings_Oordered__ring(U_1640) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP137])],[f_487_2]) ).

cnf(f_487_4,plain,
    ( sP137(U_1640,U_1642,U_1641,U_1643,U_1644,U_1645)
    | ~ class_Rings_Oordered__ring(U_1640) ),
    inference(clausify,[status(thm)],[f_487_3]) ).

cnf(f_487_5,plain,
    ( c_Orderings_Oord__class_Oless(U_1640,U_1643,c_Groups_Oplus__class_Oplus(U_1640,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1640),c_Groups_Ominus__class_Ominus(U_1640,U_1644,U_1641)),U_1642),U_1645))
    | ~ c_Orderings_Oord__class_Oless(U_1640,c_Groups_Oplus__class_Oplus(U_1640,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1640),U_1641),U_1642),U_1643),c_Groups_Oplus__class_Oplus(U_1640,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1640),U_1644),U_1642),U_1645))
    | ~ sP137(U_1640,U_1642,U_1641,U_1643,U_1644,U_1645) ),
    inference(clausify,[status(thm)],[f_487_3]) ).

cnf(f_487_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1640,c_Groups_Oplus__class_Oplus(U_1640,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1640),U_1641),U_1642),U_1643),c_Groups_Oplus__class_Oplus(U_1640,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1640),U_1644),U_1642),U_1645))
    | ~ c_Orderings_Oord__class_Oless(U_1640,U_1643,c_Groups_Oplus__class_Oplus(U_1640,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1640),c_Groups_Ominus__class_Ominus(U_1640,U_1644,U_1641)),U_1642),U_1645))
    | ~ sP137(U_1640,U_1642,U_1641,U_1643,U_1644,U_1645) ),
    inference(clausify,[status(thm)],[f_487_3]) ).

fof(f_488_1,plain,
    ! [V_db_2,V_b_2,V_ca_2,V_e_2,V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2))
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2)),V_e_2),V_ca_2),V_db_2) )
        & ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_ab_2,V_b_2)),V_e_2),V_ca_2),V_db_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_e_2),V_ca_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_db_2)) ) )
      | ~ class_Rings_Oordered__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__add__iff1]) ).

fof(f_488_2,plain,
    ! [U_1651,U_1650,U_1649,U_1648,U_1647,U_1646] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1646,c_Groups_Oplus__class_Oplus(U_1646,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1646),U_1647),U_1648),U_1649),c_Groups_Oplus__class_Oplus(U_1646,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1646),U_1650),U_1648),U_1651))
          | ~ c_Orderings_Oord__class_Oless(U_1646,c_Groups_Oplus__class_Oplus(U_1646,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1646),c_Groups_Ominus__class_Ominus(U_1646,U_1647,U_1650)),U_1648),U_1649),U_1651) )
        & ( c_Orderings_Oord__class_Oless(U_1646,c_Groups_Oplus__class_Oplus(U_1646,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1646),c_Groups_Ominus__class_Ominus(U_1646,U_1647,U_1650)),U_1648),U_1649),U_1651)
          | ~ c_Orderings_Oord__class_Oless(U_1646,c_Groups_Oplus__class_Oplus(U_1646,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1646),U_1647),U_1648),U_1649),c_Groups_Oplus__class_Oplus(U_1646,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1646),U_1650),U_1648),U_1651)) ) )
      | ~ class_Rings_Oordered__ring(U_1646) ),
    inference(variable_rename,[status(thm)],[f_488_1]) ).

fof(f_488_3,plain,
    ( ! [U_1647,U_1649,U_1646,U_1648,U_1650,U_1651] :
        ( c_Orderings_Oord__class_Oless(U_1646,c_Groups_Oplus__class_Oplus(U_1646,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1646),U_1647),U_1648),U_1649),c_Groups_Oplus__class_Oplus(U_1646,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1646),U_1650),U_1648),U_1651))
        | ~ c_Orderings_Oord__class_Oless(U_1646,c_Groups_Oplus__class_Oplus(U_1646,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1646),c_Groups_Ominus__class_Ominus(U_1646,U_1647,U_1650)),U_1648),U_1649),U_1651)
        | ~ sP138(U_1647,U_1649,U_1646,U_1648,U_1650,U_1651) )
    & ! [U_1647,U_1649,U_1646,U_1648,U_1650,U_1651] :
        ( c_Orderings_Oord__class_Oless(U_1646,c_Groups_Oplus__class_Oplus(U_1646,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1646),c_Groups_Ominus__class_Ominus(U_1646,U_1647,U_1650)),U_1648),U_1649),U_1651)
        | ~ c_Orderings_Oord__class_Oless(U_1646,c_Groups_Oplus__class_Oplus(U_1646,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1646),U_1647),U_1648),U_1649),c_Groups_Oplus__class_Oplus(U_1646,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1646),U_1650),U_1648),U_1651))
        | ~ sP138(U_1647,U_1649,U_1646,U_1648,U_1650,U_1651) )
    & ! [U_1647,U_1649,U_1646,U_1648,U_1650,U_1651] :
        ( sP138(U_1647,U_1649,U_1646,U_1648,U_1650,U_1651)
        | ~ class_Rings_Oordered__ring(U_1646) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP138])],[f_488_2]) ).

cnf(f_488_4,plain,
    ( sP138(U_1647,U_1649,U_1646,U_1648,U_1650,U_1651)
    | ~ class_Rings_Oordered__ring(U_1646) ),
    inference(clausify,[status(thm)],[f_488_3]) ).

cnf(f_488_5,plain,
    ( c_Orderings_Oord__class_Oless(U_1646,c_Groups_Oplus__class_Oplus(U_1646,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1646),c_Groups_Ominus__class_Ominus(U_1646,U_1647,U_1650)),U_1648),U_1649),U_1651)
    | ~ c_Orderings_Oord__class_Oless(U_1646,c_Groups_Oplus__class_Oplus(U_1646,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1646),U_1647),U_1648),U_1649),c_Groups_Oplus__class_Oplus(U_1646,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1646),U_1650),U_1648),U_1651))
    | ~ sP138(U_1647,U_1649,U_1646,U_1648,U_1650,U_1651) ),
    inference(clausify,[status(thm)],[f_488_3]) ).

cnf(f_488_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1646,c_Groups_Oplus__class_Oplus(U_1646,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1646),U_1647),U_1648),U_1649),c_Groups_Oplus__class_Oplus(U_1646,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1646),U_1650),U_1648),U_1651))
    | ~ c_Orderings_Oord__class_Oless(U_1646,c_Groups_Oplus__class_Oplus(U_1646,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1646),c_Groups_Ominus__class_Ominus(U_1646,U_1647,U_1650)),U_1648),U_1649),U_1651)
    | ~ sP138(U_1647,U_1649,U_1646,U_1648,U_1650,U_1651) ),
    inference(clausify,[status(thm)],[f_488_3]) ).

fof(f_489_1,plain,
    ! [V_x,T_a] :
      ( c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a)))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_real__squared__diff__one__factored]) ).

fof(f_489_2,plain,
    ! [U_1653,U_1652] :
      ( c_Groups_Ominus__class_Ominus(U_1652,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1652),U_1653),U_1653),c_Groups_Oone__class_Oone(U_1652)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1652),c_Groups_Oplus__class_Oplus(U_1652,U_1653,c_Groups_Oone__class_Oone(U_1652))),c_Groups_Ominus__class_Ominus(U_1652,U_1653,c_Groups_Oone__class_Oone(U_1652)))
      | ~ class_Rings_Oring__1(U_1652) ),
    inference(variable_rename,[status(thm)],[f_489_1]) ).

fof(f_489_3,plain,
    ! [U_1652,U_1653] :
      ( c_Groups_Ominus__class_Ominus(U_1652,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1652),U_1653),U_1653),c_Groups_Oone__class_Oone(U_1652)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1652),c_Groups_Oplus__class_Oplus(U_1652,U_1653,c_Groups_Oone__class_Oone(U_1652))),c_Groups_Ominus__class_Ominus(U_1652,U_1653,c_Groups_Oone__class_Oone(U_1652)))
      | ~ class_Rings_Oring__1(U_1652) ),
    inference(definitional_conversion,[status(esa)],[f_489_2]) ).

cnf(f_489_4,plain,
    ( c_Groups_Ominus__class_Ominus(U_1652,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1652),U_1653),U_1653),c_Groups_Oone__class_Oone(U_1652)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1652),c_Groups_Oplus__class_Oplus(U_1652,U_1653,c_Groups_Oone__class_Oone(U_1652))),c_Groups_Ominus__class_Ominus(U_1652,U_1653,c_Groups_Oone__class_Oone(U_1652)))
    | ~ class_Rings_Oring__1(U_1652) ),
    inference(clausify,[status(thm)],[f_489_3]) ).

fof(f_490_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__le__cancel1]) ).

fof(f_490_2,plain,
    ! [U_1656,U_1655,U_1654] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1654),U_1655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1654),U_1656))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1655,U_1656) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1655,U_1656)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1654),U_1655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1654),U_1656)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1654) ),
    inference(variable_rename,[status(thm)],[f_490_1]) ).

fof(f_490_3,plain,
    ( ! [U_1654,U_1655,U_1656] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1654),U_1655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1654),U_1656))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1655,U_1656)
        | ~ sP139(U_1654,U_1655,U_1656) )
    & ! [U_1654,U_1655,U_1656] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1655,U_1656)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1654),U_1655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1654),U_1656))
        | ~ sP139(U_1654,U_1655,U_1656) )
    & ! [U_1654,U_1655,U_1656] :
        ( sP139(U_1654,U_1655,U_1656)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1654) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP139])],[f_490_2]) ).

cnf(f_490_4,plain,
    ( sP139(U_1654,U_1655,U_1656)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1654) ),
    inference(clausify,[status(thm)],[f_490_3]) ).

cnf(f_490_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1655,U_1656)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1654),U_1655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1654),U_1656))
    | ~ sP139(U_1654,U_1655,U_1656) ),
    inference(clausify,[status(thm)],[f_490_3]) ).

cnf(f_490_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1654),U_1655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1654),U_1656))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1655,U_1656)
    | ~ sP139(U_1654,U_1655,U_1656) ),
    inference(clausify,[status(thm)],[f_490_3]) ).

fof(f_491_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
        | ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) ) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__cancel1]) ).

fof(f_491_2,plain,
    ! [U_1659,U_1658,U_1657] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1657),U_1658),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1657),U_1659))
        | ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1658,U_1659)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1657) ) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1658,U_1659)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1657)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1657),U_1658),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1657),U_1659)) ) ),
    inference(variable_rename,[status(thm)],[f_491_1]) ).

fof(f_491_3,plain,
    ( ! [U_1665,U_1663,U_1661] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1661),U_1663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1661),U_1665))
        | ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1663,U_1665)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1661) ) )
    & ! [U_1664,U_1662,U_1660] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1662,U_1664)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1660)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1660),U_1662),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1660),U_1664)) ) ),
    inference(miniscope,[status(thm)],[f_491_2]) ).

fof(f_491_4,plain,
    ( ! [U_1663,U_1665,U_1661] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1663,U_1665)
        | ~ sP140(U_1663,U_1665,U_1661) )
    & ! [U_1663,U_1665,U_1661] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1661)
        | ~ sP140(U_1663,U_1665,U_1661) )
    & ! [U_1663,U_1665,U_1661] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1661),U_1663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1661),U_1665))
        | sP140(U_1663,U_1665,U_1661) )
    & ! [U_1664,U_1662,U_1660] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1662,U_1664)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1660)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1660),U_1662),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1660),U_1664)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP140])],[f_491_3]) ).

cnf(f_491_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1662,U_1664)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1660)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1660),U_1662),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1660),U_1664)) ),
    inference(clausify,[status(thm)],[f_491_4]) ).

cnf(f_491_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1661),U_1663),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1661),U_1665))
    | sP140(U_1663,U_1665,U_1661) ),
    inference(clausify,[status(thm)],[f_491_4]) ).

cnf(f_491_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1661)
    | ~ sP140(U_1663,U_1665,U_1661) ),
    inference(clausify,[status(thm)],[f_491_4]) ).

cnf(f_491_8,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1663,U_1665)
    | ~ sP140(U_1663,U_1665,U_1661) ),
    inference(clausify,[status(thm)],[f_491_4]) ).

fof(f_492_1,plain,
    ! [V_n_2,V_k_2,V_m_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2))
        | ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) ) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__le__cancel2]) ).

fof(f_492_2,plain,
    ! [U_1668,U_1667,U_1666] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1666),U_1667),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1668),U_1667))
        | ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1666,U_1668)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1667) ) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1666,U_1668)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1667)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1666),U_1667),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1668),U_1667)) ) ),
    inference(variable_rename,[status(thm)],[f_492_1]) ).

fof(f_492_3,plain,
    ( ! [U_1674,U_1672,U_1670] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1670),U_1672),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1674),U_1672))
        | ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1670,U_1674)
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1672) ) )
    & ! [U_1673,U_1671,U_1669] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1669,U_1673)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1671)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1669),U_1671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1673),U_1671)) ) ),
    inference(miniscope,[status(thm)],[f_492_2]) ).

fof(f_492_4,plain,
    ( ! [U_1670,U_1674,U_1672] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1670,U_1674)
        | ~ sP141(U_1670,U_1674,U_1672) )
    & ! [U_1670,U_1674,U_1672] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1672)
        | ~ sP141(U_1670,U_1674,U_1672) )
    & ! [U_1670,U_1674,U_1672] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1670),U_1672),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1674),U_1672))
        | sP141(U_1670,U_1674,U_1672) )
    & ! [U_1669,U_1671,U_1673] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1669,U_1673)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1671)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1669),U_1671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1673),U_1671)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP141])],[f_492_3]) ).

cnf(f_492_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1669,U_1673)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1671)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1669),U_1671),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1673),U_1671)) ),
    inference(clausify,[status(thm)],[f_492_4]) ).

cnf(f_492_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1670),U_1672),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1674),U_1672))
    | sP141(U_1670,U_1674,U_1672) ),
    inference(clausify,[status(thm)],[f_492_4]) ).

cnf(f_492_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1672)
    | ~ sP141(U_1670,U_1674,U_1672) ),
    inference(clausify,[status(thm)],[f_492_4]) ).

cnf(f_492_8,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1670,U_1674)
    | ~ sP141(U_1670,U_1674,U_1672) ),
    inference(clausify,[status(thm)],[f_492_4]) ).

fof(f_493_1,plain,
    ! [V_b_2,V_ab_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ab_2,V_b_2)))
        | ? [B_d] :
            ( ~ hBOOL(hAPP(V_P_2,B_d))
            & V_ab_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d) )
        | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ab_2,V_b_2) ) )
      & ( ( ! [B_d] :
              ( hBOOL(hAPP(V_P_2,B_d))
              | V_ab_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d) )
          & ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ab_2,V_b_2) ) )
        | ~ hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ab_2,V_b_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__diff__split__asm]) ).

fof(f_493_2,plain,
    ! [U_1679,U_1678,U_1677] :
      ( ( hBOOL(hAPP(U_1677,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1678,U_1679)))
        | ? [U_1676] :
            ( ~ hBOOL(hAPP(U_1677,U_1676))
            & U_1678 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1679,U_1676) )
        | ( ~ hBOOL(hAPP(U_1677,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1678,U_1679) ) )
      & ( ( ! [U_1675] :
              ( hBOOL(hAPP(U_1677,U_1675))
              | U_1678 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1679,U_1675) )
          & ( hBOOL(hAPP(U_1677,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1678,U_1679) ) )
        | ~ hBOOL(hAPP(U_1677,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1678,U_1679))) ) ),
    inference(variable_rename,[status(thm)],[f_493_1]) ).

fof(f_493_3,plain,
    ( ! [U_1685,U_1683,U_1681] :
        ( hBOOL(hAPP(U_1681,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1683,U_1685)))
        | ? [U_1676] :
            ( ~ hBOOL(hAPP(U_1681,U_1676))
            & U_1683 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1685,U_1676) )
        | ( ~ hBOOL(hAPP(U_1681,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1683,U_1685) ) )
    & ! [U_1684,U_1682,U_1680] :
        ( ( ! [U_1675] :
              ( hBOOL(hAPP(U_1680,U_1675))
              | U_1682 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1684,U_1675) )
          & ( hBOOL(hAPP(U_1680,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1682,U_1684) ) )
        | ~ hBOOL(hAPP(U_1680,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1682,U_1684))) ) ),
    inference(miniscope,[status(thm)],[f_493_2]) ).

fof(f_493_4,plain,
    ( ! [U_1685,U_1683,U_1681] :
        ( hBOOL(hAPP(U_1681,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1683,U_1685)))
        | ( ~ hBOOL(hAPP(U_1681,sK13(U_1685,U_1683,U_1681)))
          & U_1683 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1685,sK13(U_1685,U_1683,U_1681)) )
        | ( ~ hBOOL(hAPP(U_1681,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1683,U_1685) ) )
    & ! [U_1684,U_1682,U_1680] :
        ( ( ! [U_1675] :
              ( hBOOL(hAPP(U_1680,U_1675))
              | U_1682 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1684,U_1675) )
          & ( hBOOL(hAPP(U_1680,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1682,U_1684) ) )
        | ~ hBOOL(hAPP(U_1680,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1682,U_1684))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_1676,sK13(U_1685,U_1683,U_1681))],[f_493_3]) ).

fof(f_493_5,plain,
    ( ! [U_1681,U_1683,U_1685] :
        ( ~ hBOOL(hAPP(U_1681,sK13(U_1685,U_1683,U_1681)))
        | ~ sP144(U_1681,U_1683,U_1685) )
    & ! [U_1681,U_1683,U_1685] :
        ( U_1683 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1685,sK13(U_1685,U_1683,U_1681))
        | ~ sP144(U_1681,U_1683,U_1685) )
    & ! [U_1681,U_1683,U_1685] :
        ( ~ hBOOL(hAPP(U_1681,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP143(U_1681,U_1683,U_1685) )
    & ! [U_1681,U_1683,U_1685] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1683,U_1685)
        | ~ sP143(U_1681,U_1683,U_1685) )
    & ! [U_1675,U_1682,U_1684,U_1680] :
        ( hBOOL(hAPP(U_1680,U_1675))
        | U_1682 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1684,U_1675)
        | ~ sP142(U_1675,U_1682,U_1684,U_1680) )
    & ! [U_1675,U_1682,U_1684,U_1680] :
        ( hBOOL(hAPP(U_1680,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1682,U_1684)
        | ~ sP142(U_1675,U_1682,U_1684,U_1680) )
    & ! [U_1681,U_1683,U_1685] :
        ( hBOOL(hAPP(U_1681,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1683,U_1685)))
        | sP144(U_1681,U_1683,U_1685)
        | sP143(U_1681,U_1683,U_1685) )
    & ! [U_1675,U_1682,U_1684,U_1680] :
        ( sP142(U_1675,U_1682,U_1684,U_1680)
        | ~ hBOOL(hAPP(U_1680,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1682,U_1684))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP142,sP143,sP144])],[f_493_4]) ).

cnf(f_493_6,plain,
    ( sP142(U_1675,U_1682,U_1684,U_1680)
    | ~ hBOOL(hAPP(U_1680,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1682,U_1684))) ),
    inference(clausify,[status(thm)],[f_493_5]) ).

cnf(f_493_7,plain,
    ( hBOOL(hAPP(U_1681,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1683,U_1685)))
    | sP144(U_1681,U_1683,U_1685)
    | sP143(U_1681,U_1683,U_1685) ),
    inference(clausify,[status(thm)],[f_493_5]) ).

cnf(f_493_8,plain,
    ( hBOOL(hAPP(U_1680,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1682,U_1684)
    | ~ sP142(U_1675,U_1682,U_1684,U_1680) ),
    inference(clausify,[status(thm)],[f_493_5]) ).

cnf(f_493_9,plain,
    ( hBOOL(hAPP(U_1680,U_1675))
    | U_1682 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1684,U_1675)
    | ~ sP142(U_1675,U_1682,U_1684,U_1680) ),
    inference(clausify,[status(thm)],[f_493_5]) ).

cnf(f_493_10,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1683,U_1685)
    | ~ sP143(U_1681,U_1683,U_1685) ),
    inference(clausify,[status(thm)],[f_493_5]) ).

cnf(f_493_11,plain,
    ( ~ hBOOL(hAPP(U_1681,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ sP143(U_1681,U_1683,U_1685) ),
    inference(clausify,[status(thm)],[f_493_5]) ).

cnf(f_493_12,plain,
    ( U_1683 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1685,sK13(U_1685,U_1683,U_1681))
    | ~ sP144(U_1681,U_1683,U_1685) ),
    inference(clausify,[status(thm)],[f_493_5]) ).

cnf(f_493_13,plain,
    ( ~ hBOOL(hAPP(U_1681,sK13(U_1685,U_1683,U_1681)))
    | ~ sP144(U_1681,U_1683,U_1685) ),
    inference(clausify,[status(thm)],[f_493_5]) ).

fof(f_494_1,plain,
    ! [V_b_2,V_ab_2,V_P_2] :
      ( ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ab_2,V_b_2)))
        | ? [B_d] :
            ( ~ hBOOL(hAPP(V_P_2,B_d))
            & V_ab_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d) )
        | ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ab_2,V_b_2) ) )
      & ( ( ! [B_d] :
              ( hBOOL(hAPP(V_P_2,B_d))
              | V_ab_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d) )
          & ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ab_2,V_b_2) ) )
        | ~ hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ab_2,V_b_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__diff__split]) ).

fof(f_494_2,plain,
    ! [U_1690,U_1689,U_1688] :
      ( ( hBOOL(hAPP(U_1688,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1689,U_1690)))
        | ? [U_1687] :
            ( ~ hBOOL(hAPP(U_1688,U_1687))
            & U_1689 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1690,U_1687) )
        | ( ~ hBOOL(hAPP(U_1688,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1689,U_1690) ) )
      & ( ( ! [U_1686] :
              ( hBOOL(hAPP(U_1688,U_1686))
              | U_1689 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1690,U_1686) )
          & ( hBOOL(hAPP(U_1688,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1689,U_1690) ) )
        | ~ hBOOL(hAPP(U_1688,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1689,U_1690))) ) ),
    inference(variable_rename,[status(thm)],[f_494_1]) ).

fof(f_494_3,plain,
    ( ! [U_1696,U_1694,U_1692] :
        ( hBOOL(hAPP(U_1692,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1694,U_1696)))
        | ? [U_1687] :
            ( ~ hBOOL(hAPP(U_1692,U_1687))
            & U_1694 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1696,U_1687) )
        | ( ~ hBOOL(hAPP(U_1692,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1694,U_1696) ) )
    & ! [U_1695,U_1693,U_1691] :
        ( ( ! [U_1686] :
              ( hBOOL(hAPP(U_1691,U_1686))
              | U_1693 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1695,U_1686) )
          & ( hBOOL(hAPP(U_1691,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1693,U_1695) ) )
        | ~ hBOOL(hAPP(U_1691,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1693,U_1695))) ) ),
    inference(miniscope,[status(thm)],[f_494_2]) ).

fof(f_494_4,plain,
    ( ! [U_1696,U_1694,U_1692] :
        ( hBOOL(hAPP(U_1692,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1694,U_1696)))
        | ( ~ hBOOL(hAPP(U_1692,sK14(U_1696,U_1694,U_1692)))
          & U_1694 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1696,sK14(U_1696,U_1694,U_1692)) )
        | ( ~ hBOOL(hAPP(U_1692,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1694,U_1696) ) )
    & ! [U_1695,U_1693,U_1691] :
        ( ( ! [U_1686] :
              ( hBOOL(hAPP(U_1691,U_1686))
              | U_1693 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1695,U_1686) )
          & ( hBOOL(hAPP(U_1691,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1693,U_1695) ) )
        | ~ hBOOL(hAPP(U_1691,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1693,U_1695))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_1687,sK14(U_1696,U_1694,U_1692))],[f_494_3]) ).

fof(f_494_5,plain,
    ( ! [U_1696,U_1694,U_1692] :
        ( ~ hBOOL(hAPP(U_1692,sK14(U_1696,U_1694,U_1692)))
        | ~ sP147(U_1696,U_1694,U_1692) )
    & ! [U_1696,U_1694,U_1692] :
        ( U_1694 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1696,sK14(U_1696,U_1694,U_1692))
        | ~ sP147(U_1696,U_1694,U_1692) )
    & ! [U_1696,U_1694,U_1692] :
        ( ~ hBOOL(hAPP(U_1692,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP146(U_1696,U_1694,U_1692) )
    & ! [U_1696,U_1694,U_1692] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1694,U_1696)
        | ~ sP146(U_1696,U_1694,U_1692) )
    & ! [U_1686,U_1693,U_1691,U_1695] :
        ( hBOOL(hAPP(U_1691,U_1686))
        | U_1693 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1695,U_1686)
        | ~ sP145(U_1686,U_1693,U_1691,U_1695) )
    & ! [U_1686,U_1693,U_1691,U_1695] :
        ( hBOOL(hAPP(U_1691,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1693,U_1695)
        | ~ sP145(U_1686,U_1693,U_1691,U_1695) )
    & ! [U_1696,U_1694,U_1692] :
        ( hBOOL(hAPP(U_1692,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1694,U_1696)))
        | sP147(U_1696,U_1694,U_1692)
        | sP146(U_1696,U_1694,U_1692) )
    & ! [U_1686,U_1693,U_1691,U_1695] :
        ( sP145(U_1686,U_1693,U_1691,U_1695)
        | ~ hBOOL(hAPP(U_1691,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1693,U_1695))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP145,sP146,sP147])],[f_494_4]) ).

cnf(f_494_6,plain,
    ( sP145(U_1686,U_1693,U_1691,U_1695)
    | ~ hBOOL(hAPP(U_1691,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1693,U_1695))) ),
    inference(clausify,[status(thm)],[f_494_5]) ).

cnf(f_494_7,plain,
    ( hBOOL(hAPP(U_1692,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1694,U_1696)))
    | sP147(U_1696,U_1694,U_1692)
    | sP146(U_1696,U_1694,U_1692) ),
    inference(clausify,[status(thm)],[f_494_5]) ).

cnf(f_494_8,plain,
    ( hBOOL(hAPP(U_1691,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1693,U_1695)
    | ~ sP145(U_1686,U_1693,U_1691,U_1695) ),
    inference(clausify,[status(thm)],[f_494_5]) ).

cnf(f_494_9,plain,
    ( hBOOL(hAPP(U_1691,U_1686))
    | U_1693 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1695,U_1686)
    | ~ sP145(U_1686,U_1693,U_1691,U_1695) ),
    inference(clausify,[status(thm)],[f_494_5]) ).

cnf(f_494_10,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1694,U_1696)
    | ~ sP146(U_1696,U_1694,U_1692) ),
    inference(clausify,[status(thm)],[f_494_5]) ).

cnf(f_494_11,plain,
    ( ~ hBOOL(hAPP(U_1692,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ sP146(U_1696,U_1694,U_1692) ),
    inference(clausify,[status(thm)],[f_494_5]) ).

cnf(f_494_12,plain,
    ( U_1694 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1696,sK14(U_1696,U_1694,U_1692))
    | ~ sP147(U_1696,U_1694,U_1692) ),
    inference(clausify,[status(thm)],[f_494_5]) ).

cnf(f_494_13,plain,
    ( ~ hBOOL(hAPP(U_1692,sK14(U_1696,U_1694,U_1692)))
    | ~ sP147(U_1696,U_1694,U_1692) ),
    inference(clausify,[status(thm)],[f_494_5]) ).

fof(f_495_1,plain,
    ! [V_v,V_u,V_y,V_a,V_x,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a)
      | c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) != c_Groups_Oone__class_Oone(T_a)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_a)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a)
      | ~ class_Rings_Olinordered__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_convex__bound__le]) ).

fof(f_495_2,plain,
    ! [U_1702,U_1701,U_1700,U_1699,U_1698,U_1697] :
      ( c_Orderings_Oord__class_Oless__eq(U_1697,c_Groups_Oplus__class_Oplus(U_1697,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1697),U_1701),U_1698),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1697),U_1702),U_1700)),U_1699)
      | c_Groups_Oplus__class_Oplus(U_1697,U_1701,U_1702) != c_Groups_Oone__class_Oone(U_1697)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1697,c_Groups_Ozero__class_Ozero(U_1697),U_1702)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1697,c_Groups_Ozero__class_Ozero(U_1697),U_1701)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1697,U_1700,U_1699)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1697,U_1698,U_1699)
      | ~ class_Rings_Olinordered__semiring__1(U_1697) ),
    inference(variable_rename,[status(thm)],[f_495_1]) ).

fof(f_495_3,plain,
    ! [U_1699,U_1698,U_1701,U_1702,U_1700,U_1697] :
      ( c_Orderings_Oord__class_Oless__eq(U_1697,c_Groups_Oplus__class_Oplus(U_1697,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1697),U_1701),U_1698),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1697),U_1702),U_1700)),U_1699)
      | c_Groups_Oplus__class_Oplus(U_1697,U_1701,U_1702) != c_Groups_Oone__class_Oone(U_1697)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1697,c_Groups_Ozero__class_Ozero(U_1697),U_1702)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1697,c_Groups_Ozero__class_Ozero(U_1697),U_1701)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1697,U_1700,U_1699)
      | ~ c_Orderings_Oord__class_Oless__eq(U_1697,U_1698,U_1699)
      | ~ class_Rings_Olinordered__semiring__1(U_1697) ),
    inference(definitional_conversion,[status(esa)],[f_495_2]) ).

cnf(f_495_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1697,c_Groups_Oplus__class_Oplus(U_1697,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1697),U_1701),U_1698),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1697),U_1702),U_1700)),U_1699)
    | c_Groups_Oplus__class_Oplus(U_1697,U_1701,U_1702) != c_Groups_Oone__class_Oone(U_1697)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1697,c_Groups_Ozero__class_Ozero(U_1697),U_1702)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1697,c_Groups_Ozero__class_Ozero(U_1697),U_1701)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1697,U_1700,U_1699)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1697,U_1698,U_1699)
    | ~ class_Rings_Olinordered__semiring__1(U_1697) ),
    inference(clausify,[status(thm)],[f_495_3]) ).

fof(f_496_1,plain,
    ! [V_p,V_c,T_a] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_c),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)),c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) = V_p
      | ~ class_Rings_Ocomm__ring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_synthetic__div__correct_H]) ).

fof(f_496_2,plain,
    ! [U_1705,U_1704,U_1703] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1703),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1703)),c_Polynomial_OpCons(U_1703,c_Groups_Ouminus__class_Ouminus(U_1703,U_1704),c_Polynomial_OpCons(U_1703,c_Groups_Oone__class_Oone(U_1703),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1703))))),c_Polynomial_Osynthetic__div(U_1703,U_1705,U_1704)),c_Polynomial_OpCons(U_1703,hAPP(c_Polynomial_Opoly(U_1703,U_1705),U_1704),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1703)))) = U_1705
      | ~ class_Rings_Ocomm__ring__1(U_1703) ),
    inference(variable_rename,[status(thm)],[f_496_1]) ).

fof(f_496_3,plain,
    ! [U_1704,U_1705,U_1703] :
      ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1703),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1703)),c_Polynomial_OpCons(U_1703,c_Groups_Ouminus__class_Ouminus(U_1703,U_1704),c_Polynomial_OpCons(U_1703,c_Groups_Oone__class_Oone(U_1703),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1703))))),c_Polynomial_Osynthetic__div(U_1703,U_1705,U_1704)),c_Polynomial_OpCons(U_1703,hAPP(c_Polynomial_Opoly(U_1703,U_1705),U_1704),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1703)))) = U_1705
      | ~ class_Rings_Ocomm__ring__1(U_1703) ),
    inference(definitional_conversion,[status(esa)],[f_496_2]) ).

cnf(f_496_4,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1703),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1703)),c_Polynomial_OpCons(U_1703,c_Groups_Ouminus__class_Ouminus(U_1703,U_1704),c_Polynomial_OpCons(U_1703,c_Groups_Oone__class_Oone(U_1703),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1703))))),c_Polynomial_Osynthetic__div(U_1703,U_1705,U_1704)),c_Polynomial_OpCons(U_1703,hAPP(c_Polynomial_Opoly(U_1703,U_1705),U_1704),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1703)))) = U_1705
    | ~ class_Rings_Ocomm__ring__1(U_1703) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

fof(f_497_1,plain,
    ! [V_pa_2,V_ab_2,T_a] :
      ( ( ( c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_ab_2,V_pa_2))
          | ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2)
              | V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
            & ~ c_Polynomial_Opos__poly(T_a,V_pa_2) ) )
        & ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2)
            & V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
          | c_Polynomial_Opos__poly(T_a,V_pa_2)
          | ~ c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_ab_2,V_pa_2)) ) )
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_pos__poly__pCons]) ).

fof(f_497_2,plain,
    ! [U_1708,U_1707,U_1706] :
      ( ( ( c_Polynomial_Opos__poly(U_1706,c_Polynomial_OpCons(U_1706,U_1707,U_1708))
          | ( ( ~ c_Orderings_Oord__class_Oless(U_1706,c_Groups_Ozero__class_Ozero(U_1706),U_1707)
              | U_1708 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1706)) )
            & ~ c_Polynomial_Opos__poly(U_1706,U_1708) ) )
        & ( ( c_Orderings_Oord__class_Oless(U_1706,c_Groups_Ozero__class_Ozero(U_1706),U_1707)
            & U_1708 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1706)) )
          | c_Polynomial_Opos__poly(U_1706,U_1708)
          | ~ c_Polynomial_Opos__poly(U_1706,c_Polynomial_OpCons(U_1706,U_1707,U_1708)) ) )
      | ~ class_Rings_Olinordered__idom(U_1706) ),
    inference(variable_rename,[status(thm)],[f_497_1]) ).

fof(f_497_3,plain,
    ( ! [U_1706,U_1707,U_1708] :
        ( ~ c_Orderings_Oord__class_Oless(U_1706,c_Groups_Ozero__class_Ozero(U_1706),U_1707)
        | U_1708 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1706))
        | ~ sP149(U_1706,U_1707,U_1708) )
    & ! [U_1706,U_1707,U_1708] :
        ( ~ c_Polynomial_Opos__poly(U_1706,U_1708)
        | ~ sP149(U_1706,U_1707,U_1708) )
    & ! [U_1706,U_1707,U_1708] :
        ( c_Orderings_Oord__class_Oless(U_1706,c_Groups_Ozero__class_Ozero(U_1706),U_1707)
        | ~ sP148(U_1706,U_1707,U_1708) )
    & ! [U_1706,U_1707,U_1708] :
        ( U_1708 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1706))
        | ~ sP148(U_1706,U_1707,U_1708) )
    & ! [U_1706,U_1707,U_1708] :
        ( c_Polynomial_Opos__poly(U_1706,c_Polynomial_OpCons(U_1706,U_1707,U_1708))
        | sP149(U_1706,U_1707,U_1708)
        | ~ sP150(U_1706,U_1707,U_1708) )
    & ! [U_1706,U_1707,U_1708] :
        ( sP148(U_1706,U_1707,U_1708)
        | c_Polynomial_Opos__poly(U_1706,U_1708)
        | ~ c_Polynomial_Opos__poly(U_1706,c_Polynomial_OpCons(U_1706,U_1707,U_1708))
        | ~ sP150(U_1706,U_1707,U_1708) )
    & ! [U_1706,U_1707,U_1708] :
        ( sP150(U_1706,U_1707,U_1708)
        | ~ class_Rings_Olinordered__idom(U_1706) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP148,sP149,sP150])],[f_497_2]) ).

cnf(f_497_4,plain,
    ( sP150(U_1706,U_1707,U_1708)
    | ~ class_Rings_Olinordered__idom(U_1706) ),
    inference(clausify,[status(thm)],[f_497_3]) ).

cnf(f_497_5,plain,
    ( sP148(U_1706,U_1707,U_1708)
    | c_Polynomial_Opos__poly(U_1706,U_1708)
    | ~ c_Polynomial_Opos__poly(U_1706,c_Polynomial_OpCons(U_1706,U_1707,U_1708))
    | ~ sP150(U_1706,U_1707,U_1708) ),
    inference(clausify,[status(thm)],[f_497_3]) ).

cnf(f_497_6,plain,
    ( c_Polynomial_Opos__poly(U_1706,c_Polynomial_OpCons(U_1706,U_1707,U_1708))
    | sP149(U_1706,U_1707,U_1708)
    | ~ sP150(U_1706,U_1707,U_1708) ),
    inference(clausify,[status(thm)],[f_497_3]) ).

cnf(f_497_7,plain,
    ( U_1708 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1706))
    | ~ sP148(U_1706,U_1707,U_1708) ),
    inference(clausify,[status(thm)],[f_497_3]) ).

cnf(f_497_8,plain,
    ( c_Orderings_Oord__class_Oless(U_1706,c_Groups_Ozero__class_Ozero(U_1706),U_1707)
    | ~ sP148(U_1706,U_1707,U_1708) ),
    inference(clausify,[status(thm)],[f_497_3]) ).

cnf(f_497_9,plain,
    ( ~ c_Polynomial_Opos__poly(U_1706,U_1708)
    | ~ sP149(U_1706,U_1707,U_1708) ),
    inference(clausify,[status(thm)],[f_497_3]) ).

cnf(f_497_10,plain,
    ( ~ c_Orderings_Oord__class_Oless(U_1706,c_Groups_Ozero__class_Ozero(U_1706),U_1707)
    | U_1708 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1706))
    | ~ sP149(U_1706,U_1707,U_1708) ),
    inference(clausify,[status(thm)],[f_497_3]) ).

fof(f_498_1,plain,
    ! [V_n_2,V_P_2] :
      ( ? [B_k] :
          ( hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B_k,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          & ! [B_i] :
              ( ~ hBOOL(hAPP(V_P_2,B_i))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i,B_k) )
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k,V_n_2) )
      | ~ hBOOL(hAPP(V_P_2,V_n_2))
      | hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(fof_nnf,[status(thm)],[fact_ex__least__nat__less]) ).

fof(f_498_2,plain,
    ! [U_1712,U_1711] :
      ( ? [U_1710] :
          ( hBOOL(hAPP(U_1711,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1710,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          & ! [U_1709] :
              ( ~ hBOOL(hAPP(U_1711,U_1709))
              | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1709,U_1710) )
          & c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1710,U_1712) )
      | ~ hBOOL(hAPP(U_1711,U_1712))
      | hBOOL(hAPP(U_1711,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[f_498_1]) ).

fof(f_498_3,plain,
    ! [U_1712,U_1711] :
      ( ( hBOOL(hAPP(U_1711,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK15(U_1712,U_1711),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        & ! [U_1709] :
            ( ~ hBOOL(hAPP(U_1711,U_1709))
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1709,sK15(U_1712,U_1711)) )
        & c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK15(U_1712,U_1711),U_1712) )
      | ~ hBOOL(hAPP(U_1711,U_1712))
      | hBOOL(hAPP(U_1711,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_1710,sK15(U_1712,U_1711))],[f_498_2]) ).

fof(f_498_4,plain,
    ( ! [U_1712,U_1709,U_1711] :
        ( hBOOL(hAPP(U_1711,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK15(U_1712,U_1711),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ sP151(U_1712,U_1709,U_1711) )
    & ! [U_1712,U_1709,U_1711] :
        ( ~ hBOOL(hAPP(U_1711,U_1709))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1709,sK15(U_1712,U_1711))
        | ~ sP151(U_1712,U_1709,U_1711) )
    & ! [U_1712,U_1709,U_1711] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK15(U_1712,U_1711),U_1712)
        | ~ sP151(U_1712,U_1709,U_1711) )
    & ! [U_1712,U_1709,U_1711] :
        ( sP151(U_1712,U_1709,U_1711)
        | ~ hBOOL(hAPP(U_1711,U_1712))
        | hBOOL(hAPP(U_1711,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP151])],[f_498_3]) ).

cnf(f_498_5,plain,
    ( sP151(U_1712,U_1709,U_1711)
    | ~ hBOOL(hAPP(U_1711,U_1712))
    | hBOOL(hAPP(U_1711,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_498_4]) ).

cnf(f_498_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK15(U_1712,U_1711),U_1712)
    | ~ sP151(U_1712,U_1709,U_1711) ),
    inference(clausify,[status(thm)],[f_498_4]) ).

cnf(f_498_7,plain,
    ( ~ hBOOL(hAPP(U_1711,U_1709))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1709,sK15(U_1712,U_1711))
    | ~ sP151(U_1712,U_1709,U_1711) ),
    inference(clausify,[status(thm)],[f_498_4]) ).

cnf(f_498_8,plain,
    ( hBOOL(hAPP(U_1711,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK15(U_1712,U_1711),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ sP151(U_1712,U_1709,U_1711) ),
    inference(clausify,[status(thm)],[f_498_4]) ).

fof(f_499_1,plain,
    ! [V_x,V_n,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_realpow__minus__mult]) ).

fof(f_499_2,plain,
    ! [U_1715,U_1714,U_1713] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1713),hAPP(hAPP(c_Power_Opower__class_Opower(U_1713),U_1715),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1714,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_1715) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1713),U_1715),U_1714)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1714)
      | ~ class_Groups_Omonoid__mult(U_1713) ),
    inference(variable_rename,[status(thm)],[f_499_1]) ).

fof(f_499_3,plain,
    ! [U_1715,U_1714,U_1713] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1713),hAPP(hAPP(c_Power_Opower__class_Opower(U_1713),U_1715),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1714,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_1715) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1713),U_1715),U_1714)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1714)
      | ~ class_Groups_Omonoid__mult(U_1713) ),
    inference(definitional_conversion,[status(esa)],[f_499_2]) ).

cnf(f_499_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1713),hAPP(hAPP(c_Power_Opower__class_Opower(U_1713),U_1715),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1714,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_1715) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1713),U_1715),U_1714)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1714)
    | ~ class_Groups_Omonoid__mult(U_1713) ),
    inference(clausify,[status(thm)],[f_499_3]) ).

fof(f_500_1,plain,
    ! [V_b,V_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(V_a)),c_RComplete_Onatfloor(V_b)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_b)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_b)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__mult__natfloor]) ).

fof(f_500_2,plain,
    ! [U_1717,U_1716] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(U_1716)),c_RComplete_Onatfloor(U_1717)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1716),U_1717)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1717)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1716) ),
    inference(variable_rename,[status(thm)],[f_500_1]) ).

fof(f_500_3,plain,
    ! [U_1716,U_1717] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(U_1716)),c_RComplete_Onatfloor(U_1717)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1716),U_1717)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1717)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1716) ),
    inference(definitional_conversion,[status(esa)],[f_500_2]) ).

cnf(f_500_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(U_1716)),c_RComplete_Onatfloor(U_1717)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1716),U_1717)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1717)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1716) ),
    inference(clausify,[status(thm)],[f_500_3]) ).

fof(f_501_1,plain,
    ! [V_n,V_m] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
        | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n) = V_n
        | V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_add__eq__if]) ).

fof(f_501_2,plain,
    ! [U_1719,U_1718] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1718,U_1719) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1718,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1719))
        | U_1718 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1718,U_1719) = U_1719
        | U_1718 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_501_1]) ).

fof(f_501_3,plain,
    ( ! [U_1723,U_1721] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1721,U_1723) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1721,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1723))
        | U_1721 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1722,U_1720] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1720,U_1722) = U_1722
        | U_1720 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_501_2]) ).

fof(f_501_4,plain,
    ( ! [U_1723,U_1721] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1721,U_1723) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1721,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1723))
        | U_1721 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1722,U_1720] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1720,U_1722) = U_1722
        | U_1720 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_501_3]) ).

cnf(f_501_5,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1720,U_1722) = U_1722
    | U_1720 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_501_4]) ).

cnf(f_501_6,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1721,U_1723) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1721,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1723))
    | U_1721 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_501_4]) ).

fof(f_502_1,plain,
    ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)),
    inference(fof_nnf,[status(thm)],[fact_lessI]) ).

fof(f_502_2,plain,
    ! [U_1724] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1724,c_Nat_OSuc(U_1724)),
    inference(variable_rename,[status(thm)],[f_502_1]) ).

fof(f_502_3,plain,
    ! [U_1724] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1724,c_Nat_OSuc(U_1724)),
    inference(definitional_conversion,[status(esa)],[f_502_2]) ).

cnf(f_502_4,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1724,c_Nat_OSuc(U_1724)),
    inference(clausify,[status(thm)],[f_502_3]) ).

fof(f_503_1,plain,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__mono]) ).

fof(f_503_2,plain,
    ! [U_1726,U_1725] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1725),c_Nat_OSuc(U_1726))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1725,U_1726) ),
    inference(variable_rename,[status(thm)],[f_503_1]) ).

fof(f_503_3,plain,
    ! [U_1725,U_1726] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1725),c_Nat_OSuc(U_1726))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1725,U_1726) ),
    inference(definitional_conversion,[status(esa)],[f_503_2]) ).

cnf(f_503_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1725),c_Nat_OSuc(U_1726))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1725,U_1726) ),
    inference(clausify,[status(thm)],[f_503_3]) ).

fof(f_504_1,plain,
    ! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)),
    inference(fof_nnf,[status(thm)],[fact_zero__less__Suc]) ).

fof(f_504_2,plain,
    ! [U_1727] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(U_1727)),
    inference(variable_rename,[status(thm)],[f_504_1]) ).

fof(f_504_3,plain,
    ! [U_1727] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(U_1727)),
    inference(definitional_conversion,[status(esa)],[f_504_2]) ).

cnf(f_504_4,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(U_1727)),
    inference(clausify,[status(thm)],[f_504_3]) ).

fof(f_505_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)
          | ~ c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)) )
        & ( c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2))
          | ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2) ) )
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__poly__def]) ).

fof(f_505_2,plain,
    ! [U_1730,U_1729,U_1728] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1728),U_1729,U_1730)
          | ~ c_Polynomial_Opos__poly(U_1728,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_1728),U_1730,U_1729)) )
        & ( c_Polynomial_Opos__poly(U_1728,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_1728),U_1730,U_1729))
          | ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1728),U_1729,U_1730) ) )
      | ~ class_Rings_Olinordered__idom(U_1728) ),
    inference(variable_rename,[status(thm)],[f_505_1]) ).

fof(f_505_3,plain,
    ( ! [U_1728,U_1729,U_1730] :
        ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1728),U_1729,U_1730)
        | ~ c_Polynomial_Opos__poly(U_1728,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_1728),U_1730,U_1729))
        | ~ sP152(U_1728,U_1729,U_1730) )
    & ! [U_1728,U_1729,U_1730] :
        ( c_Polynomial_Opos__poly(U_1728,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_1728),U_1730,U_1729))
        | ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1728),U_1729,U_1730)
        | ~ sP152(U_1728,U_1729,U_1730) )
    & ! [U_1728,U_1729,U_1730] :
        ( sP152(U_1728,U_1729,U_1730)
        | ~ class_Rings_Olinordered__idom(U_1728) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP152])],[f_505_2]) ).

cnf(f_505_4,plain,
    ( sP152(U_1728,U_1729,U_1730)
    | ~ class_Rings_Olinordered__idom(U_1728) ),
    inference(clausify,[status(thm)],[f_505_3]) ).

cnf(f_505_5,plain,
    ( c_Polynomial_Opos__poly(U_1728,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_1728),U_1730,U_1729))
    | ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1728),U_1729,U_1730)
    | ~ sP152(U_1728,U_1729,U_1730) ),
    inference(clausify,[status(thm)],[f_505_3]) ).

cnf(f_505_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1728),U_1729,U_1730)
    | ~ c_Polynomial_Opos__poly(U_1728,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_1728),U_1730,U_1729))
    | ~ sP152(U_1728,U_1729,U_1730) ),
    inference(clausify,[status(thm)],[f_505_3]) ).

fof(f_506_1,plain,
    c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_natfloor__one]) ).

fof(f_506_2,plain,
    c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_506_1]) ).

cnf(f_506_3,plain,
    c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_506_2]) ).

fof(f_507_1,plain,
    ! [V_n] : V_n != c_Nat_OSuc(V_n),
    inference(fof_nnf,[status(thm)],[fact_n__not__Suc__n]) ).

fof(f_507_2,plain,
    ! [U_1731] : U_1731 != c_Nat_OSuc(U_1731),
    inference(variable_rename,[status(thm)],[f_507_1]) ).

fof(f_507_3,plain,
    ! [U_1731] : U_1731 != c_Nat_OSuc(U_1731),
    inference(definitional_conversion,[status(esa)],[f_507_2]) ).

cnf(f_507_4,plain,
    U_1731 != c_Nat_OSuc(U_1731),
    inference(clausify,[status(thm)],[f_507_3]) ).

fof(f_508_1,plain,
    ! [V_n] : c_Nat_OSuc(V_n) != V_n,
    inference(fof_nnf,[status(thm)],[fact_Suc__n__not__n]) ).

fof(f_508_2,plain,
    ! [U_1732] : c_Nat_OSuc(U_1732) != U_1732,
    inference(variable_rename,[status(thm)],[f_508_1]) ).

fof(f_508_3,plain,
    ! [U_1732] : c_Nat_OSuc(U_1732) != U_1732,
    inference(definitional_conversion,[status(esa)],[f_508_2]) ).

cnf(f_508_4,plain,
    c_Nat_OSuc(U_1732) != U_1732,
    inference(clausify,[status(thm)],[f_508_3]) ).

fof(f_509_1,plain,
    ! [V_nat_H_2,V_nat_2] :
      ( ( c_Nat_OSuc(V_nat_2) = c_Nat_OSuc(V_nat_H_2)
        | V_nat_2 != V_nat_H_2 )
      & ( V_nat_2 = V_nat_H_2
        | c_Nat_OSuc(V_nat_2) != c_Nat_OSuc(V_nat_H_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat_Oinject]) ).

fof(f_509_2,plain,
    ! [U_1734,U_1733] :
      ( ( c_Nat_OSuc(U_1733) = c_Nat_OSuc(U_1734)
        | U_1733 != U_1734 )
      & ( U_1733 = U_1734
        | c_Nat_OSuc(U_1733) != c_Nat_OSuc(U_1734) ) ),
    inference(variable_rename,[status(thm)],[f_509_1]) ).

fof(f_509_3,plain,
    ( ! [U_1738,U_1736] :
        ( c_Nat_OSuc(U_1736) = c_Nat_OSuc(U_1738)
        | U_1736 != U_1738 )
    & ! [U_1737,U_1735] :
        ( U_1735 = U_1737
        | c_Nat_OSuc(U_1735) != c_Nat_OSuc(U_1737) ) ),
    inference(miniscope,[status(thm)],[f_509_2]) ).

fof(f_509_4,plain,
    ( ! [U_1736,U_1738] :
        ( c_Nat_OSuc(U_1736) = c_Nat_OSuc(U_1738)
        | U_1736 != U_1738 )
    & ! [U_1737,U_1735] :
        ( U_1735 = U_1737
        | c_Nat_OSuc(U_1735) != c_Nat_OSuc(U_1737) ) ),
    inference(definitional_conversion,[status(esa)],[f_509_3]) ).

cnf(f_509_5,plain,
    ( U_1735 = U_1737
    | c_Nat_OSuc(U_1735) != c_Nat_OSuc(U_1737) ),
    inference(clausify,[status(thm)],[f_509_4]) ).

cnf(f_509_6,plain,
    ( c_Nat_OSuc(U_1736) = c_Nat_OSuc(U_1738)
    | U_1736 != U_1738 ),
    inference(clausify,[status(thm)],[f_509_4]) ).

fof(f_510_1,plain,
    ! [V_y,V_x] :
      ( V_x = V_y
      | c_Nat_OSuc(V_x) != c_Nat_OSuc(V_y) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__inject]) ).

fof(f_510_2,plain,
    ! [U_1740,U_1739] :
      ( U_1739 = U_1740
      | c_Nat_OSuc(U_1739) != c_Nat_OSuc(U_1740) ),
    inference(variable_rename,[status(thm)],[f_510_1]) ).

fof(f_510_3,plain,
    ! [U_1739,U_1740] :
      ( U_1739 = U_1740
      | c_Nat_OSuc(U_1739) != c_Nat_OSuc(U_1740) ),
    inference(definitional_conversion,[status(esa)],[f_510_2]) ).

cnf(f_510_4,plain,
    ( U_1739 = U_1740
    | c_Nat_OSuc(U_1739) != c_Nat_OSuc(U_1740) ),
    inference(clausify,[status(thm)],[f_510_3]) ).

fof(f_511_1,plain,
    ! [V_p,V_a,T_a] :
      ( c_Polynomial_Osmult(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_p) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p))
      | ~ class_Rings_Ocomm__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_smult__minus__left]) ).

fof(f_511_2,plain,
    ! [U_1743,U_1742,U_1741] :
      ( c_Polynomial_Osmult(U_1741,c_Groups_Ouminus__class_Ouminus(U_1741,U_1742),U_1743) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1741),c_Polynomial_Osmult(U_1741,U_1742,U_1743))
      | ~ class_Rings_Ocomm__ring(U_1741) ),
    inference(variable_rename,[status(thm)],[f_511_1]) ).

fof(f_511_3,plain,
    ! [U_1741,U_1742,U_1743] :
      ( c_Polynomial_Osmult(U_1741,c_Groups_Ouminus__class_Ouminus(U_1741,U_1742),U_1743) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1741),c_Polynomial_Osmult(U_1741,U_1742,U_1743))
      | ~ class_Rings_Ocomm__ring(U_1741) ),
    inference(definitional_conversion,[status(esa)],[f_511_2]) ).

cnf(f_511_4,plain,
    ( c_Polynomial_Osmult(U_1741,c_Groups_Ouminus__class_Ouminus(U_1741,U_1742),U_1743) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1741),c_Polynomial_Osmult(U_1741,U_1742,U_1743))
    | ~ class_Rings_Ocomm__ring(U_1741) ),
    inference(clausify,[status(thm)],[f_511_3]) ).

fof(f_512_1,plain,
    ! [V_p,V_a,T_a] :
      ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p))
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__pCons]) ).

fof(f_512_2,plain,
    ! [U_1746,U_1745,U_1744] :
      ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1744),c_Polynomial_OpCons(U_1744,U_1745,U_1746)) = c_Polynomial_OpCons(U_1744,c_Groups_Ouminus__class_Ouminus(U_1744,U_1745),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1744),U_1746))
      | ~ class_Groups_Oab__group__add(U_1744) ),
    inference(variable_rename,[status(thm)],[f_512_1]) ).

fof(f_512_3,plain,
    ! [U_1744,U_1745,U_1746] :
      ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1744),c_Polynomial_OpCons(U_1744,U_1745,U_1746)) = c_Polynomial_OpCons(U_1744,c_Groups_Ouminus__class_Ouminus(U_1744,U_1745),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1744),U_1746))
      | ~ class_Groups_Oab__group__add(U_1744) ),
    inference(definitional_conversion,[status(esa)],[f_512_2]) ).

cnf(f_512_4,plain,
    ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1744),c_Polynomial_OpCons(U_1744,U_1745,U_1746)) = c_Polynomial_OpCons(U_1744,c_Groups_Ouminus__class_Ouminus(U_1744,U_1745),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1744),U_1746))
    | ~ class_Groups_Oab__group__add(U_1744) ),
    inference(clausify,[status(thm)],[f_512_3]) ).

fof(f_513_1,plain,
    ! [V_p,V_a,T_b] :
      ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b,V_a,V_p)) = c_Polynomial_OpCons(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),V_p))
      | ~ class_Groups_Oab__group__add(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_minus__poly__code_I2_J]) ).

fof(f_513_2,plain,
    ! [U_1749,U_1748,U_1747] :
      ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1747),c_Polynomial_OpCons(U_1747,U_1748,U_1749)) = c_Polynomial_OpCons(U_1747,c_Groups_Ouminus__class_Ouminus(U_1747,U_1748),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1747),U_1749))
      | ~ class_Groups_Oab__group__add(U_1747) ),
    inference(variable_rename,[status(thm)],[f_513_1]) ).

fof(f_513_3,plain,
    ! [U_1747,U_1748,U_1749] :
      ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1747),c_Polynomial_OpCons(U_1747,U_1748,U_1749)) = c_Polynomial_OpCons(U_1747,c_Groups_Ouminus__class_Ouminus(U_1747,U_1748),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1747),U_1749))
      | ~ class_Groups_Oab__group__add(U_1747) ),
    inference(definitional_conversion,[status(esa)],[f_513_2]) ).

cnf(f_513_4,plain,
    ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1747),c_Polynomial_OpCons(U_1747,U_1748,U_1749)) = c_Polynomial_OpCons(U_1747,c_Groups_Ouminus__class_Ouminus(U_1747,U_1748),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1747),U_1749))
    | ~ class_Groups_Oab__group__add(U_1747) ),
    inference(clausify,[status(thm)],[f_513_3]) ).

fof(f_514_1,plain,
    ! [V_a,T_a] :
      ( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = V_a
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__minus]) ).

fof(f_514_2,plain,
    ! [U_1751,U_1750] :
      ( c_Groups_Ouminus__class_Ouminus(U_1750,c_Groups_Ouminus__class_Ouminus(U_1750,U_1751)) = U_1751
      | ~ class_Groups_Ogroup__add(U_1750) ),
    inference(variable_rename,[status(thm)],[f_514_1]) ).

fof(f_514_3,plain,
    ! [U_1751,U_1750] :
      ( c_Groups_Ouminus__class_Ouminus(U_1750,c_Groups_Ouminus__class_Ouminus(U_1750,U_1751)) = U_1751
      | ~ class_Groups_Ogroup__add(U_1750) ),
    inference(definitional_conversion,[status(esa)],[f_514_2]) ).

cnf(f_514_4,plain,
    ( c_Groups_Ouminus__class_Ouminus(U_1750,c_Groups_Ouminus__class_Ouminus(U_1750,U_1751)) = U_1751
    | ~ class_Groups_Ogroup__add(U_1750) ),
    inference(clausify,[status(thm)],[f_514_3]) ).

fof(f_515_1,plain,
    ! [V_b_2,V_ab_2,T_a] :
      ( ( ( V_ab_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
          | V_b_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2) )
        & ( V_b_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2)
          | V_ab_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) ) )
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_equation__minus__iff]) ).

fof(f_515_2,plain,
    ! [U_1754,U_1753,U_1752] :
      ( ( ( U_1753 = c_Groups_Ouminus__class_Ouminus(U_1752,U_1754)
          | U_1754 != c_Groups_Ouminus__class_Ouminus(U_1752,U_1753) )
        & ( U_1754 = c_Groups_Ouminus__class_Ouminus(U_1752,U_1753)
          | U_1753 != c_Groups_Ouminus__class_Ouminus(U_1752,U_1754) ) )
      | ~ class_Groups_Ogroup__add(U_1752) ),
    inference(variable_rename,[status(thm)],[f_515_1]) ).

fof(f_515_3,plain,
    ( ! [U_1752,U_1753,U_1754] :
        ( U_1753 = c_Groups_Ouminus__class_Ouminus(U_1752,U_1754)
        | U_1754 != c_Groups_Ouminus__class_Ouminus(U_1752,U_1753)
        | ~ sP153(U_1752,U_1753,U_1754) )
    & ! [U_1752,U_1753,U_1754] :
        ( U_1754 = c_Groups_Ouminus__class_Ouminus(U_1752,U_1753)
        | U_1753 != c_Groups_Ouminus__class_Ouminus(U_1752,U_1754)
        | ~ sP153(U_1752,U_1753,U_1754) )
    & ! [U_1752,U_1753,U_1754] :
        ( sP153(U_1752,U_1753,U_1754)
        | ~ class_Groups_Ogroup__add(U_1752) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP153])],[f_515_2]) ).

cnf(f_515_4,plain,
    ( sP153(U_1752,U_1753,U_1754)
    | ~ class_Groups_Ogroup__add(U_1752) ),
    inference(clausify,[status(thm)],[f_515_3]) ).

cnf(f_515_5,plain,
    ( U_1754 = c_Groups_Ouminus__class_Ouminus(U_1752,U_1753)
    | U_1753 != c_Groups_Ouminus__class_Ouminus(U_1752,U_1754)
    | ~ sP153(U_1752,U_1753,U_1754) ),
    inference(clausify,[status(thm)],[f_515_3]) ).

cnf(f_515_6,plain,
    ( U_1753 = c_Groups_Ouminus__class_Ouminus(U_1752,U_1754)
    | U_1754 != c_Groups_Ouminus__class_Ouminus(U_1752,U_1753)
    | ~ sP153(U_1752,U_1753,U_1754) ),
    inference(clausify,[status(thm)],[f_515_3]) ).

fof(f_516_1,plain,
    ! [V_b_2,V_ab_2,T_a] :
      ( ( ( c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2) = V_b_2
          | c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) != V_ab_2 )
        & ( c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) = V_ab_2
          | c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2) != V_b_2 ) )
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__equation__iff]) ).

fof(f_516_2,plain,
    ! [U_1757,U_1756,U_1755] :
      ( ( ( c_Groups_Ouminus__class_Ouminus(U_1755,U_1756) = U_1757
          | c_Groups_Ouminus__class_Ouminus(U_1755,U_1757) != U_1756 )
        & ( c_Groups_Ouminus__class_Ouminus(U_1755,U_1757) = U_1756
          | c_Groups_Ouminus__class_Ouminus(U_1755,U_1756) != U_1757 ) )
      | ~ class_Groups_Ogroup__add(U_1755) ),
    inference(variable_rename,[status(thm)],[f_516_1]) ).

fof(f_516_3,plain,
    ( ! [U_1757,U_1756,U_1755] :
        ( c_Groups_Ouminus__class_Ouminus(U_1755,U_1756) = U_1757
        | c_Groups_Ouminus__class_Ouminus(U_1755,U_1757) != U_1756
        | ~ sP154(U_1757,U_1756,U_1755) )
    & ! [U_1757,U_1756,U_1755] :
        ( c_Groups_Ouminus__class_Ouminus(U_1755,U_1757) = U_1756
        | c_Groups_Ouminus__class_Ouminus(U_1755,U_1756) != U_1757
        | ~ sP154(U_1757,U_1756,U_1755) )
    & ! [U_1757,U_1756,U_1755] :
        ( sP154(U_1757,U_1756,U_1755)
        | ~ class_Groups_Ogroup__add(U_1755) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP154])],[f_516_2]) ).

cnf(f_516_4,plain,
    ( sP154(U_1757,U_1756,U_1755)
    | ~ class_Groups_Ogroup__add(U_1755) ),
    inference(clausify,[status(thm)],[f_516_3]) ).

cnf(f_516_5,plain,
    ( c_Groups_Ouminus__class_Ouminus(U_1755,U_1757) = U_1756
    | c_Groups_Ouminus__class_Ouminus(U_1755,U_1756) != U_1757
    | ~ sP154(U_1757,U_1756,U_1755) ),
    inference(clausify,[status(thm)],[f_516_3]) ).

cnf(f_516_6,plain,
    ( c_Groups_Ouminus__class_Ouminus(U_1755,U_1756) = U_1757
    | c_Groups_Ouminus__class_Ouminus(U_1755,U_1757) != U_1756
    | ~ sP154(U_1757,U_1756,U_1755) ),
    inference(clausify,[status(thm)],[f_516_3]) ).

fof(f_517_1,plain,
    ! [V_b_2,V_ab_2,T_a] :
      ( ( ( c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
          | V_ab_2 != V_b_2 )
        & ( V_ab_2 = V_b_2
          | c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2) != c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) ) )
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal]) ).

fof(f_517_2,plain,
    ! [U_1760,U_1759,U_1758] :
      ( ( ( c_Groups_Ouminus__class_Ouminus(U_1758,U_1759) = c_Groups_Ouminus__class_Ouminus(U_1758,U_1760)
          | U_1759 != U_1760 )
        & ( U_1759 = U_1760
          | c_Groups_Ouminus__class_Ouminus(U_1758,U_1759) != c_Groups_Ouminus__class_Ouminus(U_1758,U_1760) ) )
      | ~ class_Groups_Ogroup__add(U_1758) ),
    inference(variable_rename,[status(thm)],[f_517_1]) ).

fof(f_517_3,plain,
    ( ! [U_1760,U_1759,U_1758] :
        ( c_Groups_Ouminus__class_Ouminus(U_1758,U_1759) = c_Groups_Ouminus__class_Ouminus(U_1758,U_1760)
        | U_1759 != U_1760
        | ~ sP155(U_1760,U_1759,U_1758) )
    & ! [U_1760,U_1759,U_1758] :
        ( U_1759 = U_1760
        | c_Groups_Ouminus__class_Ouminus(U_1758,U_1759) != c_Groups_Ouminus__class_Ouminus(U_1758,U_1760)
        | ~ sP155(U_1760,U_1759,U_1758) )
    & ! [U_1760,U_1759,U_1758] :
        ( sP155(U_1760,U_1759,U_1758)
        | ~ class_Groups_Ogroup__add(U_1758) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP155])],[f_517_2]) ).

cnf(f_517_4,plain,
    ( sP155(U_1760,U_1759,U_1758)
    | ~ class_Groups_Ogroup__add(U_1758) ),
    inference(clausify,[status(thm)],[f_517_3]) ).

cnf(f_517_5,plain,
    ( U_1759 = U_1760
    | c_Groups_Ouminus__class_Ouminus(U_1758,U_1759) != c_Groups_Ouminus__class_Ouminus(U_1758,U_1760)
    | ~ sP155(U_1760,U_1759,U_1758) ),
    inference(clausify,[status(thm)],[f_517_3]) ).

cnf(f_517_6,plain,
    ( c_Groups_Ouminus__class_Ouminus(U_1758,U_1759) = c_Groups_Ouminus__class_Ouminus(U_1758,U_1760)
    | U_1759 != U_1760
    | ~ sP155(U_1760,U_1759,U_1758) ),
    inference(clausify,[status(thm)],[f_517_3]) ).

fof(f_518_1,plain,
    ! [V_n,V_x,T_a] :
      ( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n)
      | ~ class_RealVector_Oreal__normed__div__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_norm__power]) ).

fof(f_518_2,plain,
    ! [U_1763,U_1762,U_1761] :
      ( c_RealVector_Onorm__class_Onorm(U_1761,hAPP(hAPP(c_Power_Opower__class_Opower(U_1761),U_1762),U_1763)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1761,U_1762)),U_1763)
      | ~ class_RealVector_Oreal__normed__div__algebra(U_1761) ),
    inference(variable_rename,[status(thm)],[f_518_1]) ).

fof(f_518_3,plain,
    ! [U_1762,U_1761,U_1763] :
      ( c_RealVector_Onorm__class_Onorm(U_1761,hAPP(hAPP(c_Power_Opower__class_Opower(U_1761),U_1762),U_1763)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1761,U_1762)),U_1763)
      | ~ class_RealVector_Oreal__normed__div__algebra(U_1761) ),
    inference(definitional_conversion,[status(esa)],[f_518_2]) ).

cnf(f_518_4,plain,
    ( c_RealVector_Onorm__class_Onorm(U_1761,hAPP(hAPP(c_Power_Opower__class_Opower(U_1761),U_1762),U_1763)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1761,U_1762)),U_1763)
    | ~ class_RealVector_Oreal__normed__div__algebra(U_1761) ),
    inference(clausify,[status(thm)],[f_518_3]) ).

fof(f_519_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
          | ( V_x_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
            & V_x_2 != V_y_2 ) )
        & ( V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
          | V_x_2 = V_y_2
          | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) )
      | ~ class_Rings_Oidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_realpow__two__disj]) ).

fof(f_519_2,plain,
    ! [U_1766,U_1765,U_1764] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1764),U_1765),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1764),U_1766),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
          | ( U_1765 != c_Groups_Ouminus__class_Ouminus(U_1764,U_1766)
            & U_1765 != U_1766 ) )
        & ( U_1765 = c_Groups_Ouminus__class_Ouminus(U_1764,U_1766)
          | U_1765 = U_1766
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_1764),U_1765),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(U_1764),U_1766),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) )
      | ~ class_Rings_Oidom(U_1764) ),
    inference(variable_rename,[status(thm)],[f_519_1]) ).

fof(f_519_3,plain,
    ( ! [U_1766,U_1765,U_1764] :
        ( U_1765 != c_Groups_Ouminus__class_Ouminus(U_1764,U_1766)
        | ~ sP156(U_1766,U_1765,U_1764) )
    & ! [U_1766,U_1765,U_1764] :
        ( U_1765 != U_1766
        | ~ sP156(U_1766,U_1765,U_1764) )
    & ! [U_1766,U_1765,U_1764] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1764),U_1765),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1764),U_1766),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | sP156(U_1766,U_1765,U_1764)
        | ~ sP157(U_1766,U_1765,U_1764) )
    & ! [U_1766,U_1765,U_1764] :
        ( U_1765 = c_Groups_Ouminus__class_Ouminus(U_1764,U_1766)
        | U_1765 = U_1766
        | hAPP(hAPP(c_Power_Opower__class_Opower(U_1764),U_1765),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(U_1764),U_1766),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | ~ sP157(U_1766,U_1765,U_1764) )
    & ! [U_1766,U_1765,U_1764] :
        ( sP157(U_1766,U_1765,U_1764)
        | ~ class_Rings_Oidom(U_1764) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP156,sP157])],[f_519_2]) ).

cnf(f_519_4,plain,
    ( sP157(U_1766,U_1765,U_1764)
    | ~ class_Rings_Oidom(U_1764) ),
    inference(clausify,[status(thm)],[f_519_3]) ).

cnf(f_519_5,plain,
    ( U_1765 = c_Groups_Ouminus__class_Ouminus(U_1764,U_1766)
    | U_1765 = U_1766
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_1764),U_1765),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(U_1764),U_1766),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ sP157(U_1766,U_1765,U_1764) ),
    inference(clausify,[status(thm)],[f_519_3]) ).

cnf(f_519_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1764),U_1765),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1764),U_1766),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | sP156(U_1766,U_1765,U_1764)
    | ~ sP157(U_1766,U_1765,U_1764) ),
    inference(clausify,[status(thm)],[f_519_3]) ).

cnf(f_519_7,plain,
    ( U_1765 != U_1766
    | ~ sP156(U_1766,U_1765,U_1764) ),
    inference(clausify,[status(thm)],[f_519_3]) ).

cnf(f_519_8,plain,
    ( U_1765 != c_Groups_Ouminus__class_Ouminus(U_1764,U_1766)
    | ~ sP156(U_1766,U_1765,U_1764) ),
    inference(clausify,[status(thm)],[f_519_3]) ).

fof(f_520_1,plain,
    ! [V_p,T_a] :
      ( c_Polynomial_Opos__poly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p))
      | c_Polynomial_Opos__poly(T_a,V_p)
      | V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_pos__poly__total]) ).

fof(f_520_2,plain,
    ! [U_1768,U_1767] :
      ( c_Polynomial_Opos__poly(U_1767,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1767),U_1768))
      | c_Polynomial_Opos__poly(U_1767,U_1768)
      | U_1768 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1767))
      | ~ class_Rings_Olinordered__idom(U_1767) ),
    inference(variable_rename,[status(thm)],[f_520_1]) ).

fof(f_520_3,plain,
    ! [U_1767,U_1768] :
      ( c_Polynomial_Opos__poly(U_1767,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1767),U_1768))
      | c_Polynomial_Opos__poly(U_1767,U_1768)
      | U_1768 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1767))
      | ~ class_Rings_Olinordered__idom(U_1767) ),
    inference(definitional_conversion,[status(esa)],[f_520_2]) ).

cnf(f_520_4,plain,
    ( c_Polynomial_Opos__poly(U_1767,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1767),U_1768))
    | c_Polynomial_Opos__poly(U_1767,U_1768)
    | U_1768 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1767))
    | ~ class_Rings_Olinordered__idom(U_1767) ),
    inference(clausify,[status(thm)],[f_520_3]) ).

fof(f_521_1,plain,
    ! [V_n,V_a,T_a] :
      ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n)) = c_Polynomial_Omonom(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_n)
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__monom]) ).

fof(f_521_2,plain,
    ! [U_1771,U_1770,U_1769] :
      ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1769),c_Polynomial_Omonom(U_1769,U_1770,U_1771)) = c_Polynomial_Omonom(U_1769,c_Groups_Ouminus__class_Ouminus(U_1769,U_1770),U_1771)
      | ~ class_Groups_Oab__group__add(U_1769) ),
    inference(variable_rename,[status(thm)],[f_521_1]) ).

fof(f_521_3,plain,
    ! [U_1770,U_1769,U_1771] :
      ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1769),c_Polynomial_Omonom(U_1769,U_1770,U_1771)) = c_Polynomial_Omonom(U_1769,c_Groups_Ouminus__class_Ouminus(U_1769,U_1770),U_1771)
      | ~ class_Groups_Oab__group__add(U_1769) ),
    inference(definitional_conversion,[status(esa)],[f_521_2]) ).

cnf(f_521_4,plain,
    ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1769),c_Polynomial_Omonom(U_1769,U_1770,U_1771)) = c_Polynomial_Omonom(U_1769,c_Groups_Ouminus__class_Ouminus(U_1769,U_1770),U_1771)
    | ~ class_Groups_Oab__group__add(U_1769) ),
    inference(clausify,[status(thm)],[f_521_3]) ).

fof(f_522_1,plain,
    ! [V_x,V_n,V_p,T_a] :
      ( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),V_p),V_n)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),V_n)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_poly__power]) ).

fof(f_522_2,plain,
    ! [U_1775,U_1774,U_1773,U_1772] :
      ( hAPP(c_Polynomial_Opoly(U_1772,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_1772)),U_1773),U_1774)),U_1775) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1772),hAPP(c_Polynomial_Opoly(U_1772,U_1773),U_1775)),U_1774)
      | ~ class_Rings_Ocomm__semiring__1(U_1772) ),
    inference(variable_rename,[status(thm)],[f_522_1]) ).

fof(f_522_3,plain,
    ! [U_1772,U_1773,U_1774,U_1775] :
      ( hAPP(c_Polynomial_Opoly(U_1772,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_1772)),U_1773),U_1774)),U_1775) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1772),hAPP(c_Polynomial_Opoly(U_1772,U_1773),U_1775)),U_1774)
      | ~ class_Rings_Ocomm__semiring__1(U_1772) ),
    inference(definitional_conversion,[status(esa)],[f_522_2]) ).

cnf(f_522_4,plain,
    ( hAPP(c_Polynomial_Opoly(U_1772,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_1772)),U_1773),U_1774)),U_1775) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1772),hAPP(c_Polynomial_Opoly(U_1772,U_1773),U_1775)),U_1774)
    | ~ class_Rings_Ocomm__semiring__1(U_1772) ),
    inference(clausify,[status(thm)],[f_522_3]) ).

fof(f_523_1,plain,
    ! [V_x,V_p,T_a] :
      ( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_x) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))
      | ~ class_Rings_Ocomm__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_poly__minus]) ).

fof(f_523_2,plain,
    ! [U_1778,U_1777,U_1776] :
      ( hAPP(c_Polynomial_Opoly(U_1776,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1776),U_1777)),U_1778) = c_Groups_Ouminus__class_Ouminus(U_1776,hAPP(c_Polynomial_Opoly(U_1776,U_1777),U_1778))
      | ~ class_Rings_Ocomm__ring(U_1776) ),
    inference(variable_rename,[status(thm)],[f_523_1]) ).

fof(f_523_3,plain,
    ! [U_1776,U_1777,U_1778] :
      ( hAPP(c_Polynomial_Opoly(U_1776,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1776),U_1777)),U_1778) = c_Groups_Ouminus__class_Ouminus(U_1776,hAPP(c_Polynomial_Opoly(U_1776,U_1777),U_1778))
      | ~ class_Rings_Ocomm__ring(U_1776) ),
    inference(definitional_conversion,[status(esa)],[f_523_2]) ).

cnf(f_523_4,plain,
    ( hAPP(c_Polynomial_Opoly(U_1776,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1776),U_1777)),U_1778) = c_Groups_Ouminus__class_Ouminus(U_1776,hAPP(c_Polynomial_Opoly(U_1776,U_1777),U_1778))
    | ~ class_Rings_Ocomm__ring(U_1776) ),
    inference(clausify,[status(thm)],[f_523_3]) ).

fof(f_524_1,plain,
    ! [V_q,V_x,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J]) ).

fof(f_524_2,plain,
    ! [U_1781,U_1780,U_1779] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1779),U_1780),c_Nat_OSuc(U_1781)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1779),U_1780),hAPP(hAPP(c_Power_Opower__class_Opower(U_1779),U_1780),U_1781))
      | ~ class_Rings_Ocomm__semiring__1(U_1779) ),
    inference(variable_rename,[status(thm)],[f_524_1]) ).

fof(f_524_3,plain,
    ! [U_1779,U_1780,U_1781] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1779),U_1780),c_Nat_OSuc(U_1781)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1779),U_1780),hAPP(hAPP(c_Power_Opower__class_Opower(U_1779),U_1780),U_1781))
      | ~ class_Rings_Ocomm__semiring__1(U_1779) ),
    inference(definitional_conversion,[status(esa)],[f_524_2]) ).

cnf(f_524_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1779),U_1780),c_Nat_OSuc(U_1781)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1779),U_1780),hAPP(hAPP(c_Power_Opower__class_Opower(U_1779),U_1780),U_1781))
    | ~ class_Rings_Ocomm__semiring__1(U_1779) ),
    inference(clausify,[status(thm)],[f_524_3]) ).

fof(f_525_1,plain,
    ! [V_q,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J]) ).

fof(f_525_2,plain,
    ! [U_1784,U_1783,U_1782] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1782),U_1783),hAPP(hAPP(c_Power_Opower__class_Opower(U_1782),U_1783),U_1784)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1782),U_1783),c_Nat_OSuc(U_1784))
      | ~ class_Rings_Ocomm__semiring__1(U_1782) ),
    inference(variable_rename,[status(thm)],[f_525_1]) ).

fof(f_525_3,plain,
    ! [U_1782,U_1783,U_1784] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1782),U_1783),hAPP(hAPP(c_Power_Opower__class_Opower(U_1782),U_1783),U_1784)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1782),U_1783),c_Nat_OSuc(U_1784))
      | ~ class_Rings_Ocomm__semiring__1(U_1782) ),
    inference(definitional_conversion,[status(esa)],[f_525_2]) ).

cnf(f_525_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1782),U_1783),hAPP(hAPP(c_Power_Opower__class_Opower(U_1782),U_1783),U_1784)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1782),U_1783),c_Nat_OSuc(U_1784))
    | ~ class_Rings_Ocomm__semiring__1(U_1782) ),
    inference(clausify,[status(thm)],[f_525_3]) ).

fof(f_526_1,plain,
    ! [V_q,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J]) ).

fof(f_526_2,plain,
    ! [U_1787,U_1786,U_1785] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1785),hAPP(hAPP(c_Power_Opower__class_Opower(U_1785),U_1786),U_1787)),U_1786) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1785),U_1786),c_Nat_OSuc(U_1787))
      | ~ class_Rings_Ocomm__semiring__1(U_1785) ),
    inference(variable_rename,[status(thm)],[f_526_1]) ).

fof(f_526_3,plain,
    ! [U_1785,U_1786,U_1787] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1785),hAPP(hAPP(c_Power_Opower__class_Opower(U_1785),U_1786),U_1787)),U_1786) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1785),U_1786),c_Nat_OSuc(U_1787))
      | ~ class_Rings_Ocomm__semiring__1(U_1785) ),
    inference(definitional_conversion,[status(esa)],[f_526_2]) ).

cnf(f_526_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1785),hAPP(hAPP(c_Power_Opower__class_Opower(U_1785),U_1786),U_1787)),U_1786) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1785),U_1786),c_Nat_OSuc(U_1787))
    | ~ class_Rings_Ocomm__semiring__1(U_1785) ),
    inference(clausify,[status(thm)],[f_526_3]) ).

fof(f_527_1,plain,
    ! [V_n,V_x,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x)),V_n))
      | ~ class_RealVector_Oreal__normed__algebra__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_norm__power__ineq]) ).

fof(f_527_2,plain,
    ! [U_1790,U_1789,U_1788] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1788,hAPP(hAPP(c_Power_Opower__class_Opower(U_1788),U_1789),U_1790)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1788,U_1789)),U_1790))
      | ~ class_RealVector_Oreal__normed__algebra__1(U_1788) ),
    inference(variable_rename,[status(thm)],[f_527_1]) ).

fof(f_527_3,plain,
    ! [U_1788,U_1789,U_1790] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1788,hAPP(hAPP(c_Power_Opower__class_Opower(U_1788),U_1789),U_1790)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1788,U_1789)),U_1790))
      | ~ class_RealVector_Oreal__normed__algebra__1(U_1788) ),
    inference(definitional_conversion,[status(esa)],[f_527_2]) ).

cnf(f_527_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1788,hAPP(hAPP(c_Power_Opower__class_Opower(U_1788),U_1789),U_1790)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1788,U_1789)),U_1790))
    | ~ class_RealVector_Oreal__normed__algebra__1(U_1788) ),
    inference(clausify,[status(thm)],[f_527_3]) ).

fof(f_528_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_real__0__less__add__iff]) ).

fof(f_528_2,plain,
    ! [U_1792,U_1791] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1791,U_1792))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1791),U_1792) )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1791),U_1792)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1791,U_1792)) ) ),
    inference(variable_rename,[status(thm)],[f_528_1]) ).

fof(f_528_3,plain,
    ( ! [U_1796,U_1794] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1794,U_1796))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1794),U_1796) )
    & ! [U_1795,U_1793] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1793),U_1795)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1793,U_1795)) ) ),
    inference(miniscope,[status(thm)],[f_528_2]) ).

fof(f_528_4,plain,
    ( ! [U_1796,U_1794] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1794,U_1796))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1794),U_1796) )
    & ! [U_1793,U_1795] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1793),U_1795)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1793,U_1795)) ) ),
    inference(definitional_conversion,[status(esa)],[f_528_3]) ).

cnf(f_528_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1793),U_1795)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1793,U_1795)) ),
    inference(clausify,[status(thm)],[f_528_4]) ).

cnf(f_528_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1794,U_1796))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1794),U_1796) ),
    inference(clausify,[status(thm)],[f_528_4]) ).

fof(f_529_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
    inference(fof_nnf,[status(thm)],[fact_real__add__less__0__iff]) ).

fof(f_529_2,plain,
    ! [U_1798,U_1797] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1797,U_1798),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1798,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1797)) )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1798,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1797))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1797,U_1798),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
    inference(variable_rename,[status(thm)],[f_529_1]) ).

fof(f_529_3,plain,
    ( ! [U_1802,U_1800] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1800,U_1802),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1802,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1800)) )
    & ! [U_1801,U_1799] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1801,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1799))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1799,U_1801),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
    inference(miniscope,[status(thm)],[f_529_2]) ).

fof(f_529_4,plain,
    ( ! [U_1802,U_1800] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1800,U_1802),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1802,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1800)) )
    & ! [U_1801,U_1799] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1801,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1799))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1799,U_1801),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
    inference(definitional_conversion,[status(esa)],[f_529_3]) ).

cnf(f_529_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1801,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1799))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1799,U_1801),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(clausify,[status(thm)],[f_529_4]) ).

cnf(f_529_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1800,U_1802),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1802,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1800)) ),
    inference(clausify,[status(thm)],[f_529_4]) ).

fof(f_530_1,plain,
    ! [V_ab_2,T_a] :
      ( ( ( c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2) = V_ab_2
          | V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a)
          | c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2) != V_ab_2 ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__equal__zero]) ).

fof(f_530_2,plain,
    ! [U_1804,U_1803] :
      ( ( ( c_Groups_Ouminus__class_Ouminus(U_1803,U_1804) = U_1804
          | U_1804 != c_Groups_Ozero__class_Ozero(U_1803) )
        & ( U_1804 = c_Groups_Ozero__class_Ozero(U_1803)
          | c_Groups_Ouminus__class_Ouminus(U_1803,U_1804) != U_1804 ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_1803) ),
    inference(variable_rename,[status(thm)],[f_530_1]) ).

fof(f_530_3,plain,
    ( ! [U_1803,U_1804] :
        ( c_Groups_Ouminus__class_Ouminus(U_1803,U_1804) = U_1804
        | U_1804 != c_Groups_Ozero__class_Ozero(U_1803)
        | ~ sP158(U_1803,U_1804) )
    & ! [U_1803,U_1804] :
        ( U_1804 = c_Groups_Ozero__class_Ozero(U_1803)
        | c_Groups_Ouminus__class_Ouminus(U_1803,U_1804) != U_1804
        | ~ sP158(U_1803,U_1804) )
    & ! [U_1803,U_1804] :
        ( sP158(U_1803,U_1804)
        | ~ class_Groups_Olinordered__ab__group__add(U_1803) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP158])],[f_530_2]) ).

cnf(f_530_4,plain,
    ( sP158(U_1803,U_1804)
    | ~ class_Groups_Olinordered__ab__group__add(U_1803) ),
    inference(clausify,[status(thm)],[f_530_3]) ).

cnf(f_530_5,plain,
    ( U_1804 = c_Groups_Ozero__class_Ozero(U_1803)
    | c_Groups_Ouminus__class_Ouminus(U_1803,U_1804) != U_1804
    | ~ sP158(U_1803,U_1804) ),
    inference(clausify,[status(thm)],[f_530_3]) ).

cnf(f_530_6,plain,
    ( c_Groups_Ouminus__class_Ouminus(U_1803,U_1804) = U_1804
    | U_1804 != c_Groups_Ozero__class_Ozero(U_1803)
    | ~ sP158(U_1803,U_1804) ),
    inference(clausify,[status(thm)],[f_530_3]) ).

fof(f_531_1,plain,
    ! [V_ab_2,T_a] :
      ( ( ( c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2) = c_Groups_Ozero__class_Ozero(T_a)
          | V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a)
          | c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal]) ).

fof(f_531_2,plain,
    ! [U_1806,U_1805] :
      ( ( ( c_Groups_Ouminus__class_Ouminus(U_1805,U_1806) = c_Groups_Ozero__class_Ozero(U_1805)
          | U_1806 != c_Groups_Ozero__class_Ozero(U_1805) )
        & ( U_1806 = c_Groups_Ozero__class_Ozero(U_1805)
          | c_Groups_Ouminus__class_Ouminus(U_1805,U_1806) != c_Groups_Ozero__class_Ozero(U_1805) ) )
      | ~ class_Groups_Ogroup__add(U_1805) ),
    inference(variable_rename,[status(thm)],[f_531_1]) ).

fof(f_531_3,plain,
    ( ! [U_1806,U_1805] :
        ( c_Groups_Ouminus__class_Ouminus(U_1805,U_1806) = c_Groups_Ozero__class_Ozero(U_1805)
        | U_1806 != c_Groups_Ozero__class_Ozero(U_1805)
        | ~ sP159(U_1806,U_1805) )
    & ! [U_1806,U_1805] :
        ( U_1806 = c_Groups_Ozero__class_Ozero(U_1805)
        | c_Groups_Ouminus__class_Ouminus(U_1805,U_1806) != c_Groups_Ozero__class_Ozero(U_1805)
        | ~ sP159(U_1806,U_1805) )
    & ! [U_1806,U_1805] :
        ( sP159(U_1806,U_1805)
        | ~ class_Groups_Ogroup__add(U_1805) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP159])],[f_531_2]) ).

cnf(f_531_4,plain,
    ( sP159(U_1806,U_1805)
    | ~ class_Groups_Ogroup__add(U_1805) ),
    inference(clausify,[status(thm)],[f_531_3]) ).

cnf(f_531_5,plain,
    ( U_1806 = c_Groups_Ozero__class_Ozero(U_1805)
    | c_Groups_Ouminus__class_Ouminus(U_1805,U_1806) != c_Groups_Ozero__class_Ozero(U_1805)
    | ~ sP159(U_1806,U_1805) ),
    inference(clausify,[status(thm)],[f_531_3]) ).

cnf(f_531_6,plain,
    ( c_Groups_Ouminus__class_Ouminus(U_1805,U_1806) = c_Groups_Ozero__class_Ozero(U_1805)
    | U_1806 != c_Groups_Ozero__class_Ozero(U_1805)
    | ~ sP159(U_1806,U_1805) ),
    inference(clausify,[status(thm)],[f_531_3]) ).

fof(f_532_1,plain,
    ! [V_ab_2,T_a] :
      ( ( ( V_ab_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2)
          | V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_ab_2 = c_Groups_Ozero__class_Ozero(T_a)
          | V_ab_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_equal__neg__zero]) ).

fof(f_532_2,plain,
    ! [U_1808,U_1807] :
      ( ( ( U_1808 = c_Groups_Ouminus__class_Ouminus(U_1807,U_1808)
          | U_1808 != c_Groups_Ozero__class_Ozero(U_1807) )
        & ( U_1808 = c_Groups_Ozero__class_Ozero(U_1807)
          | U_1808 != c_Groups_Ouminus__class_Ouminus(U_1807,U_1808) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_1807) ),
    inference(variable_rename,[status(thm)],[f_532_1]) ).

fof(f_532_3,plain,
    ( ! [U_1807,U_1808] :
        ( U_1808 = c_Groups_Ouminus__class_Ouminus(U_1807,U_1808)
        | U_1808 != c_Groups_Ozero__class_Ozero(U_1807)
        | ~ sP160(U_1807,U_1808) )
    & ! [U_1807,U_1808] :
        ( U_1808 = c_Groups_Ozero__class_Ozero(U_1807)
        | U_1808 != c_Groups_Ouminus__class_Ouminus(U_1807,U_1808)
        | ~ sP160(U_1807,U_1808) )
    & ! [U_1807,U_1808] :
        ( sP160(U_1807,U_1808)
        | ~ class_Groups_Olinordered__ab__group__add(U_1807) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP160])],[f_532_2]) ).

cnf(f_532_4,plain,
    ( sP160(U_1807,U_1808)
    | ~ class_Groups_Olinordered__ab__group__add(U_1807) ),
    inference(clausify,[status(thm)],[f_532_3]) ).

cnf(f_532_5,plain,
    ( U_1808 = c_Groups_Ozero__class_Ozero(U_1807)
    | U_1808 != c_Groups_Ouminus__class_Ouminus(U_1807,U_1808)
    | ~ sP160(U_1807,U_1808) ),
    inference(clausify,[status(thm)],[f_532_3]) ).

cnf(f_532_6,plain,
    ( U_1808 = c_Groups_Ouminus__class_Ouminus(U_1807,U_1808)
    | U_1808 != c_Groups_Ozero__class_Ozero(U_1807)
    | ~ sP160(U_1807,U_1808) ),
    inference(clausify,[status(thm)],[f_532_3]) ).

fof(f_533_1,plain,
    ! [V_ab_2,T_a] :
      ( ( ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2)
          | c_Groups_Ozero__class_Ozero(T_a) != V_ab_2 )
        & ( c_Groups_Ozero__class_Ozero(T_a) = V_ab_2
          | c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2) ) )
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__0__equal__iff__equal]) ).

fof(f_533_2,plain,
    ! [U_1810,U_1809] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_1809) = c_Groups_Ouminus__class_Ouminus(U_1809,U_1810)
          | c_Groups_Ozero__class_Ozero(U_1809) != U_1810 )
        & ( c_Groups_Ozero__class_Ozero(U_1809) = U_1810
          | c_Groups_Ozero__class_Ozero(U_1809) != c_Groups_Ouminus__class_Ouminus(U_1809,U_1810) ) )
      | ~ class_Groups_Ogroup__add(U_1809) ),
    inference(variable_rename,[status(thm)],[f_533_1]) ).

fof(f_533_3,plain,
    ( ! [U_1810,U_1809] :
        ( c_Groups_Ozero__class_Ozero(U_1809) = c_Groups_Ouminus__class_Ouminus(U_1809,U_1810)
        | c_Groups_Ozero__class_Ozero(U_1809) != U_1810
        | ~ sP161(U_1810,U_1809) )
    & ! [U_1810,U_1809] :
        ( c_Groups_Ozero__class_Ozero(U_1809) = U_1810
        | c_Groups_Ozero__class_Ozero(U_1809) != c_Groups_Ouminus__class_Ouminus(U_1809,U_1810)
        | ~ sP161(U_1810,U_1809) )
    & ! [U_1810,U_1809] :
        ( sP161(U_1810,U_1809)
        | ~ class_Groups_Ogroup__add(U_1809) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP161])],[f_533_2]) ).

cnf(f_533_4,plain,
    ( sP161(U_1810,U_1809)
    | ~ class_Groups_Ogroup__add(U_1809) ),
    inference(clausify,[status(thm)],[f_533_3]) ).

cnf(f_533_5,plain,
    ( c_Groups_Ozero__class_Ozero(U_1809) = U_1810
    | c_Groups_Ozero__class_Ozero(U_1809) != c_Groups_Ouminus__class_Ouminus(U_1809,U_1810)
    | ~ sP161(U_1810,U_1809) ),
    inference(clausify,[status(thm)],[f_533_3]) ).

cnf(f_533_6,plain,
    ( c_Groups_Ozero__class_Ozero(U_1809) = c_Groups_Ouminus__class_Ouminus(U_1809,U_1810)
    | c_Groups_Ozero__class_Ozero(U_1809) != U_1810
    | ~ sP161(U_1810,U_1809) ),
    inference(clausify,[status(thm)],[f_533_3]) ).

fof(f_534_1,plain,
    ! [T_a] :
      ( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__zero]) ).

fof(f_534_2,plain,
    ! [U_1811] :
      ( c_Groups_Ouminus__class_Ouminus(U_1811,c_Groups_Ozero__class_Ozero(U_1811)) = c_Groups_Ozero__class_Ozero(U_1811)
      | ~ class_Groups_Ogroup__add(U_1811) ),
    inference(variable_rename,[status(thm)],[f_534_1]) ).

fof(f_534_3,plain,
    ! [U_1811] :
      ( c_Groups_Ouminus__class_Ouminus(U_1811,c_Groups_Ozero__class_Ozero(U_1811)) = c_Groups_Ozero__class_Ozero(U_1811)
      | ~ class_Groups_Ogroup__add(U_1811) ),
    inference(definitional_conversion,[status(esa)],[f_534_2]) ).

cnf(f_534_4,plain,
    ( c_Groups_Ouminus__class_Ouminus(U_1811,c_Groups_Ozero__class_Ozero(U_1811)) = c_Groups_Ozero__class_Ozero(U_1811)
    | ~ class_Groups_Ogroup__add(U_1811) ),
    inference(clausify,[status(thm)],[f_534_3]) ).

fof(f_535_1,plain,
    ! [V_b_2,V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2)) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__minus__iff]) ).

fof(f_535_2,plain,
    ! [U_1814,U_1813,U_1812] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_1812,U_1813,c_Groups_Ouminus__class_Ouminus(U_1812,U_1814))
          | ~ c_Orderings_Oord__class_Oless__eq(U_1812,U_1814,c_Groups_Ouminus__class_Ouminus(U_1812,U_1813)) )
        & ( c_Orderings_Oord__class_Oless__eq(U_1812,U_1814,c_Groups_Ouminus__class_Ouminus(U_1812,U_1813))
          | ~ c_Orderings_Oord__class_Oless__eq(U_1812,U_1813,c_Groups_Ouminus__class_Ouminus(U_1812,U_1814)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_1812) ),
    inference(variable_rename,[status(thm)],[f_535_1]) ).

fof(f_535_3,plain,
    ( ! [U_1812,U_1813,U_1814] :
        ( c_Orderings_Oord__class_Oless__eq(U_1812,U_1813,c_Groups_Ouminus__class_Ouminus(U_1812,U_1814))
        | ~ c_Orderings_Oord__class_Oless__eq(U_1812,U_1814,c_Groups_Ouminus__class_Ouminus(U_1812,U_1813))
        | ~ sP162(U_1812,U_1813,U_1814) )
    & ! [U_1812,U_1813,U_1814] :
        ( c_Orderings_Oord__class_Oless__eq(U_1812,U_1814,c_Groups_Ouminus__class_Ouminus(U_1812,U_1813))
        | ~ c_Orderings_Oord__class_Oless__eq(U_1812,U_1813,c_Groups_Ouminus__class_Ouminus(U_1812,U_1814))
        | ~ sP162(U_1812,U_1813,U_1814) )
    & ! [U_1812,U_1813,U_1814] :
        ( sP162(U_1812,U_1813,U_1814)
        | ~ class_Groups_Oordered__ab__group__add(U_1812) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP162])],[f_535_2]) ).

cnf(f_535_4,plain,
    ( sP162(U_1812,U_1813,U_1814)
    | ~ class_Groups_Oordered__ab__group__add(U_1812) ),
    inference(clausify,[status(thm)],[f_535_3]) ).

cnf(f_535_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1812,U_1814,c_Groups_Ouminus__class_Ouminus(U_1812,U_1813))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1812,U_1813,c_Groups_Ouminus__class_Ouminus(U_1812,U_1814))
    | ~ sP162(U_1812,U_1813,U_1814) ),
    inference(clausify,[status(thm)],[f_535_3]) ).

cnf(f_535_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1812,U_1813,c_Groups_Ouminus__class_Ouminus(U_1812,U_1814))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1812,U_1814,c_Groups_Ouminus__class_Ouminus(U_1812,U_1813))
    | ~ sP162(U_1812,U_1813,U_1814) ),
    inference(clausify,[status(thm)],[f_535_3]) ).

fof(f_536_1,plain,
    ! [V_b_2,V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2),V_b_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_ab_2) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_ab_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2),V_b_2) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__le__iff]) ).

fof(f_536_2,plain,
    ! [U_1817,U_1816,U_1815] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_1815,c_Groups_Ouminus__class_Ouminus(U_1815,U_1816),U_1817)
          | ~ c_Orderings_Oord__class_Oless__eq(U_1815,c_Groups_Ouminus__class_Ouminus(U_1815,U_1817),U_1816) )
        & ( c_Orderings_Oord__class_Oless__eq(U_1815,c_Groups_Ouminus__class_Ouminus(U_1815,U_1817),U_1816)
          | ~ c_Orderings_Oord__class_Oless__eq(U_1815,c_Groups_Ouminus__class_Ouminus(U_1815,U_1816),U_1817) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_1815) ),
    inference(variable_rename,[status(thm)],[f_536_1]) ).

fof(f_536_3,plain,
    ( ! [U_1816,U_1817,U_1815] :
        ( c_Orderings_Oord__class_Oless__eq(U_1815,c_Groups_Ouminus__class_Ouminus(U_1815,U_1816),U_1817)
        | ~ c_Orderings_Oord__class_Oless__eq(U_1815,c_Groups_Ouminus__class_Ouminus(U_1815,U_1817),U_1816)
        | ~ sP163(U_1816,U_1817,U_1815) )
    & ! [U_1816,U_1817,U_1815] :
        ( c_Orderings_Oord__class_Oless__eq(U_1815,c_Groups_Ouminus__class_Ouminus(U_1815,U_1817),U_1816)
        | ~ c_Orderings_Oord__class_Oless__eq(U_1815,c_Groups_Ouminus__class_Ouminus(U_1815,U_1816),U_1817)
        | ~ sP163(U_1816,U_1817,U_1815) )
    & ! [U_1816,U_1817,U_1815] :
        ( sP163(U_1816,U_1817,U_1815)
        | ~ class_Groups_Oordered__ab__group__add(U_1815) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP163])],[f_536_2]) ).

cnf(f_536_4,plain,
    ( sP163(U_1816,U_1817,U_1815)
    | ~ class_Groups_Oordered__ab__group__add(U_1815) ),
    inference(clausify,[status(thm)],[f_536_3]) ).

cnf(f_536_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1815,c_Groups_Ouminus__class_Ouminus(U_1815,U_1817),U_1816)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1815,c_Groups_Ouminus__class_Ouminus(U_1815,U_1816),U_1817)
    | ~ sP163(U_1816,U_1817,U_1815) ),
    inference(clausify,[status(thm)],[f_536_3]) ).

cnf(f_536_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1815,c_Groups_Ouminus__class_Ouminus(U_1815,U_1816),U_1817)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1815,c_Groups_Ouminus__class_Ouminus(U_1815,U_1817),U_1816)
    | ~ sP163(U_1816,U_1817,U_1815) ),
    inference(clausify,[status(thm)],[f_536_3]) ).

fof(f_537_1,plain,
    ! [V_ab_2,V_b_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,V_b_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2)) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le]) ).

fof(f_537_2,plain,
    ! [U_1820,U_1819,U_1818] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_1818,c_Groups_Ouminus__class_Ouminus(U_1818,U_1819),c_Groups_Ouminus__class_Ouminus(U_1818,U_1820))
          | ~ c_Orderings_Oord__class_Oless__eq(U_1818,U_1820,U_1819) )
        & ( c_Orderings_Oord__class_Oless__eq(U_1818,U_1820,U_1819)
          | ~ c_Orderings_Oord__class_Oless__eq(U_1818,c_Groups_Ouminus__class_Ouminus(U_1818,U_1819),c_Groups_Ouminus__class_Ouminus(U_1818,U_1820)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_1818) ),
    inference(variable_rename,[status(thm)],[f_537_1]) ).

fof(f_537_3,plain,
    ( ! [U_1819,U_1820,U_1818] :
        ( c_Orderings_Oord__class_Oless__eq(U_1818,c_Groups_Ouminus__class_Ouminus(U_1818,U_1819),c_Groups_Ouminus__class_Ouminus(U_1818,U_1820))
        | ~ c_Orderings_Oord__class_Oless__eq(U_1818,U_1820,U_1819)
        | ~ sP164(U_1819,U_1820,U_1818) )
    & ! [U_1819,U_1820,U_1818] :
        ( c_Orderings_Oord__class_Oless__eq(U_1818,U_1820,U_1819)
        | ~ c_Orderings_Oord__class_Oless__eq(U_1818,c_Groups_Ouminus__class_Ouminus(U_1818,U_1819),c_Groups_Ouminus__class_Ouminus(U_1818,U_1820))
        | ~ sP164(U_1819,U_1820,U_1818) )
    & ! [U_1819,U_1820,U_1818] :
        ( sP164(U_1819,U_1820,U_1818)
        | ~ class_Groups_Oordered__ab__group__add(U_1818) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP164])],[f_537_2]) ).

cnf(f_537_4,plain,
    ( sP164(U_1819,U_1820,U_1818)
    | ~ class_Groups_Oordered__ab__group__add(U_1818) ),
    inference(clausify,[status(thm)],[f_537_3]) ).

cnf(f_537_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1818,U_1820,U_1819)
    | ~ c_Orderings_Oord__class_Oless__eq(U_1818,c_Groups_Ouminus__class_Ouminus(U_1818,U_1819),c_Groups_Ouminus__class_Ouminus(U_1818,U_1820))
    | ~ sP164(U_1819,U_1820,U_1818) ),
    inference(clausify,[status(thm)],[f_537_3]) ).

cnf(f_537_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1818,c_Groups_Ouminus__class_Ouminus(U_1818,U_1819),c_Groups_Ouminus__class_Ouminus(U_1818,U_1820))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1818,U_1820,U_1819)
    | ~ sP164(U_1819,U_1820,U_1818) ),
    inference(clausify,[status(thm)],[f_537_3]) ).

fof(f_538_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__imp__neg__le]) ).

fof(f_538_2,plain,
    ! [U_1823,U_1822,U_1821] :
      ( c_Orderings_Oord__class_Oless__eq(U_1821,c_Groups_Ouminus__class_Ouminus(U_1821,U_1823),c_Groups_Ouminus__class_Ouminus(U_1821,U_1822))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1821,U_1822,U_1823)
      | ~ class_Groups_Oordered__ab__group__add(U_1821) ),
    inference(variable_rename,[status(thm)],[f_538_1]) ).

fof(f_538_3,plain,
    ! [U_1822,U_1823,U_1821] :
      ( c_Orderings_Oord__class_Oless__eq(U_1821,c_Groups_Ouminus__class_Ouminus(U_1821,U_1823),c_Groups_Ouminus__class_Ouminus(U_1821,U_1822))
      | ~ c_Orderings_Oord__class_Oless__eq(U_1821,U_1822,U_1823)
      | ~ class_Groups_Oordered__ab__group__add(U_1821) ),
    inference(definitional_conversion,[status(esa)],[f_538_2]) ).

cnf(f_538_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_1821,c_Groups_Ouminus__class_Ouminus(U_1821,U_1823),c_Groups_Ouminus__class_Ouminus(U_1821,U_1822))
    | ~ c_Orderings_Oord__class_Oless__eq(U_1821,U_1822,U_1823)
    | ~ class_Groups_Oordered__ab__group__add(U_1821) ),
    inference(clausify,[status(thm)],[f_538_3]) ).

fof(f_539_1,plain,
    ! [V_b_2,V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
          | ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2)) )
        & ( c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2))
          | ~ c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__minus__iff]) ).

fof(f_539_2,plain,
    ! [U_1826,U_1825,U_1824] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1824,U_1825,c_Groups_Ouminus__class_Ouminus(U_1824,U_1826))
          | ~ c_Orderings_Oord__class_Oless(U_1824,U_1826,c_Groups_Ouminus__class_Ouminus(U_1824,U_1825)) )
        & ( c_Orderings_Oord__class_Oless(U_1824,U_1826,c_Groups_Ouminus__class_Ouminus(U_1824,U_1825))
          | ~ c_Orderings_Oord__class_Oless(U_1824,U_1825,c_Groups_Ouminus__class_Ouminus(U_1824,U_1826)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_1824) ),
    inference(variable_rename,[status(thm)],[f_539_1]) ).

fof(f_539_3,plain,
    ( ! [U_1824,U_1825,U_1826] :
        ( c_Orderings_Oord__class_Oless(U_1824,U_1825,c_Groups_Ouminus__class_Ouminus(U_1824,U_1826))
        | ~ c_Orderings_Oord__class_Oless(U_1824,U_1826,c_Groups_Ouminus__class_Ouminus(U_1824,U_1825))
        | ~ sP165(U_1824,U_1825,U_1826) )
    & ! [U_1824,U_1825,U_1826] :
        ( c_Orderings_Oord__class_Oless(U_1824,U_1826,c_Groups_Ouminus__class_Ouminus(U_1824,U_1825))
        | ~ c_Orderings_Oord__class_Oless(U_1824,U_1825,c_Groups_Ouminus__class_Ouminus(U_1824,U_1826))
        | ~ sP165(U_1824,U_1825,U_1826) )
    & ! [U_1824,U_1825,U_1826] :
        ( sP165(U_1824,U_1825,U_1826)
        | ~ class_Groups_Oordered__ab__group__add(U_1824) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP165])],[f_539_2]) ).

cnf(f_539_4,plain,
    ( sP165(U_1824,U_1825,U_1826)
    | ~ class_Groups_Oordered__ab__group__add(U_1824) ),
    inference(clausify,[status(thm)],[f_539_3]) ).

cnf(f_539_5,plain,
    ( c_Orderings_Oord__class_Oless(U_1824,U_1826,c_Groups_Ouminus__class_Ouminus(U_1824,U_1825))
    | ~ c_Orderings_Oord__class_Oless(U_1824,U_1825,c_Groups_Ouminus__class_Ouminus(U_1824,U_1826))
    | ~ sP165(U_1824,U_1825,U_1826) ),
    inference(clausify,[status(thm)],[f_539_3]) ).

cnf(f_539_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1824,U_1825,c_Groups_Ouminus__class_Ouminus(U_1824,U_1826))
    | ~ c_Orderings_Oord__class_Oless(U_1824,U_1826,c_Groups_Ouminus__class_Ouminus(U_1824,U_1825))
    | ~ sP165(U_1824,U_1825,U_1826) ),
    inference(clausify,[status(thm)],[f_539_3]) ).

fof(f_540_1,plain,
    ! [V_b_2,V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2),V_b_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_ab_2) )
        & ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_ab_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2),V_b_2) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__less__iff]) ).

fof(f_540_2,plain,
    ! [U_1829,U_1828,U_1827] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1827,c_Groups_Ouminus__class_Ouminus(U_1827,U_1828),U_1829)
          | ~ c_Orderings_Oord__class_Oless(U_1827,c_Groups_Ouminus__class_Ouminus(U_1827,U_1829),U_1828) )
        & ( c_Orderings_Oord__class_Oless(U_1827,c_Groups_Ouminus__class_Ouminus(U_1827,U_1829),U_1828)
          | ~ c_Orderings_Oord__class_Oless(U_1827,c_Groups_Ouminus__class_Ouminus(U_1827,U_1828),U_1829) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_1827) ),
    inference(variable_rename,[status(thm)],[f_540_1]) ).

fof(f_540_3,plain,
    ( ! [U_1828,U_1829,U_1827] :
        ( c_Orderings_Oord__class_Oless(U_1827,c_Groups_Ouminus__class_Ouminus(U_1827,U_1828),U_1829)
        | ~ c_Orderings_Oord__class_Oless(U_1827,c_Groups_Ouminus__class_Ouminus(U_1827,U_1829),U_1828)
        | ~ sP166(U_1828,U_1829,U_1827) )
    & ! [U_1828,U_1829,U_1827] :
        ( c_Orderings_Oord__class_Oless(U_1827,c_Groups_Ouminus__class_Ouminus(U_1827,U_1829),U_1828)
        | ~ c_Orderings_Oord__class_Oless(U_1827,c_Groups_Ouminus__class_Ouminus(U_1827,U_1828),U_1829)
        | ~ sP166(U_1828,U_1829,U_1827) )
    & ! [U_1828,U_1829,U_1827] :
        ( sP166(U_1828,U_1829,U_1827)
        | ~ class_Groups_Oordered__ab__group__add(U_1827) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP166])],[f_540_2]) ).

cnf(f_540_4,plain,
    ( sP166(U_1828,U_1829,U_1827)
    | ~ class_Groups_Oordered__ab__group__add(U_1827) ),
    inference(clausify,[status(thm)],[f_540_3]) ).

cnf(f_540_5,plain,
    ( c_Orderings_Oord__class_Oless(U_1827,c_Groups_Ouminus__class_Ouminus(U_1827,U_1829),U_1828)
    | ~ c_Orderings_Oord__class_Oless(U_1827,c_Groups_Ouminus__class_Ouminus(U_1827,U_1828),U_1829)
    | ~ sP166(U_1828,U_1829,U_1827) ),
    inference(clausify,[status(thm)],[f_540_3]) ).

cnf(f_540_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1827,c_Groups_Ouminus__class_Ouminus(U_1827,U_1828),U_1829)
    | ~ c_Orderings_Oord__class_Oless(U_1827,c_Groups_Ouminus__class_Ouminus(U_1827,U_1829),U_1828)
    | ~ sP166(U_1828,U_1829,U_1827) ),
    inference(clausify,[status(thm)],[f_540_3]) ).

fof(f_541_1,plain,
    ! [V_ab_2,V_b_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2))
          | ~ c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2) )
        & ( c_Orderings_Oord__class_Oless(T_a,V_ab_2,V_b_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2)) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less]) ).

fof(f_541_2,plain,
    ! [U_1832,U_1831,U_1830] :
      ( ( ( c_Orderings_Oord__class_Oless(U_1830,c_Groups_Ouminus__class_Ouminus(U_1830,U_1831),c_Groups_Ouminus__class_Ouminus(U_1830,U_1832))
          | ~ c_Orderings_Oord__class_Oless(U_1830,U_1832,U_1831) )
        & ( c_Orderings_Oord__class_Oless(U_1830,U_1832,U_1831)
          | ~ c_Orderings_Oord__class_Oless(U_1830,c_Groups_Ouminus__class_Ouminus(U_1830,U_1831),c_Groups_Ouminus__class_Ouminus(U_1830,U_1832)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_1830) ),
    inference(variable_rename,[status(thm)],[f_541_1]) ).

fof(f_541_3,plain,
    ( ! [U_1832,U_1831,U_1830] :
        ( c_Orderings_Oord__class_Oless(U_1830,c_Groups_Ouminus__class_Ouminus(U_1830,U_1831),c_Groups_Ouminus__class_Ouminus(U_1830,U_1832))
        | ~ c_Orderings_Oord__class_Oless(U_1830,U_1832,U_1831)
        | ~ sP167(U_1832,U_1831,U_1830) )
    & ! [U_1832,U_1831,U_1830] :
        ( c_Orderings_Oord__class_Oless(U_1830,U_1832,U_1831)
        | ~ c_Orderings_Oord__class_Oless(U_1830,c_Groups_Ouminus__class_Ouminus(U_1830,U_1831),c_Groups_Ouminus__class_Ouminus(U_1830,U_1832))
        | ~ sP167(U_1832,U_1831,U_1830) )
    & ! [U_1832,U_1831,U_1830] :
        ( sP167(U_1832,U_1831,U_1830)
        | ~ class_Groups_Oordered__ab__group__add(U_1830) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP167])],[f_541_2]) ).

cnf(f_541_4,plain,
    ( sP167(U_1832,U_1831,U_1830)
    | ~ class_Groups_Oordered__ab__group__add(U_1830) ),
    inference(clausify,[status(thm)],[f_541_3]) ).

cnf(f_541_5,plain,
    ( c_Orderings_Oord__class_Oless(U_1830,U_1832,U_1831)
    | ~ c_Orderings_Oord__class_Oless(U_1830,c_Groups_Ouminus__class_Ouminus(U_1830,U_1831),c_Groups_Ouminus__class_Ouminus(U_1830,U_1832))
    | ~ sP167(U_1832,U_1831,U_1830) ),
    inference(clausify,[status(thm)],[f_541_3]) ).

cnf(f_541_6,plain,
    ( c_Orderings_Oord__class_Oless(U_1830,c_Groups_Ouminus__class_Ouminus(U_1830,U_1831),c_Groups_Ouminus__class_Ouminus(U_1830,U_1832))
    | ~ c_Orderings_Oord__class_Oless(U_1830,U_1832,U_1831)
    | ~ sP167(U_1832,U_1831,U_1830) ),
    inference(clausify,[status(thm)],[f_541_3]) ).

fof(f_542_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))
      | ~ class_Rings_Oring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__mult__right]) ).

fof(f_542_2,plain,
    ! [U_1835,U_1834,U_1833] :
      ( c_Groups_Ouminus__class_Ouminus(U_1833,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1833),U_1834),U_1835)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1833),U_1834),c_Groups_Ouminus__class_Ouminus(U_1833,U_1835))
      | ~ class_Rings_Oring(U_1833) ),
    inference(variable_rename,[status(thm)],[f_542_1]) ).

fof(f_542_3,plain,
    ! [U_1834,U_1833,U_1835] :
      ( c_Groups_Ouminus__class_Ouminus(U_1833,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1833),U_1834),U_1835)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1833),U_1834),c_Groups_Ouminus__class_Ouminus(U_1833,U_1835))
      | ~ class_Rings_Oring(U_1833) ),
    inference(definitional_conversion,[status(esa)],[f_542_2]) ).

cnf(f_542_4,plain,
    ( c_Groups_Ouminus__class_Ouminus(U_1833,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1833),U_1834),U_1835)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1833),U_1834),c_Groups_Ouminus__class_Ouminus(U_1833,U_1835))
    | ~ class_Rings_Oring(U_1833) ),
    inference(clausify,[status(thm)],[f_542_3]) ).

fof(f_543_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b)
      | ~ class_Rings_Oring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__mult__left]) ).

fof(f_543_2,plain,
    ! [U_1838,U_1837,U_1836] :
      ( c_Groups_Ouminus__class_Ouminus(U_1836,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1836),U_1837),U_1838)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1836),c_Groups_Ouminus__class_Ouminus(U_1836,U_1837)),U_1838)
      | ~ class_Rings_Oring(U_1836) ),
    inference(variable_rename,[status(thm)],[f_543_1]) ).

fof(f_543_3,plain,
    ! [U_1836,U_1837,U_1838] :
      ( c_Groups_Ouminus__class_Ouminus(U_1836,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1836),U_1837),U_1838)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1836),c_Groups_Ouminus__class_Ouminus(U_1836,U_1837)),U_1838)
      | ~ class_Rings_Oring(U_1836) ),
    inference(definitional_conversion,[status(esa)],[f_543_2]) ).

cnf(f_543_4,plain,
    ( c_Groups_Ouminus__class_Ouminus(U_1836,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1836),U_1837),U_1838)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1836),c_Groups_Ouminus__class_Ouminus(U_1836,U_1837)),U_1838)
    | ~ class_Rings_Oring(U_1836) ),
    inference(clausify,[status(thm)],[f_543_3]) ).

fof(f_544_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))
      | ~ class_Rings_Oring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__mult__commute]) ).

fof(f_544_2,plain,
    ! [U_1841,U_1840,U_1839] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1839),c_Groups_Ouminus__class_Ouminus(U_1839,U_1840)),U_1841) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1839),U_1840),c_Groups_Ouminus__class_Ouminus(U_1839,U_1841))
      | ~ class_Rings_Oring(U_1839) ),
    inference(variable_rename,[status(thm)],[f_544_1]) ).

fof(f_544_3,plain,
    ! [U_1839,U_1840,U_1841] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1839),c_Groups_Ouminus__class_Ouminus(U_1839,U_1840)),U_1841) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1839),U_1840),c_Groups_Ouminus__class_Ouminus(U_1839,U_1841))
      | ~ class_Rings_Oring(U_1839) ),
    inference(definitional_conversion,[status(esa)],[f_544_2]) ).

cnf(f_544_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1839),c_Groups_Ouminus__class_Ouminus(U_1839,U_1840)),U_1841) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1839),U_1840),c_Groups_Ouminus__class_Ouminus(U_1839,U_1841))
    | ~ class_Rings_Oring(U_1839) ),
    inference(clausify,[status(thm)],[f_544_3]) ).

fof(f_545_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)
      | ~ class_Rings_Oring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__mult__minus]) ).

fof(f_545_2,plain,
    ! [U_1844,U_1843,U_1842] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1842),c_Groups_Ouminus__class_Ouminus(U_1842,U_1843)),c_Groups_Ouminus__class_Ouminus(U_1842,U_1844)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1842),U_1843),U_1844)
      | ~ class_Rings_Oring(U_1842) ),
    inference(variable_rename,[status(thm)],[f_545_1]) ).

fof(f_545_3,plain,
    ! [U_1842,U_1843,U_1844] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1842),c_Groups_Ouminus__class_Ouminus(U_1842,U_1843)),c_Groups_Ouminus__class_Ouminus(U_1842,U_1844)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1842),U_1843),U_1844)
      | ~ class_Rings_Oring(U_1842) ),
    inference(definitional_conversion,[status(esa)],[f_545_2]) ).

cnf(f_545_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1842),c_Groups_Ouminus__class_Ouminus(U_1842,U_1843)),c_Groups_Ouminus__class_Ouminus(U_1842,U_1844)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1842),U_1843),U_1844)
    | ~ class_Rings_Oring(U_1842) ),
    inference(clausify,[status(thm)],[f_545_3]) ).

fof(f_546_1,plain,
    ! [V_b_2,V_ab_2,T_a] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ab_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)
          | ( V_ab_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
            & V_ab_2 != V_b_2 ) )
        & ( V_ab_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
          | V_ab_2 = V_b_2
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ab_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2) ) )
      | ~ class_Rings_Oidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_square__eq__iff]) ).

fof(f_546_2,plain,
    ! [U_1847,U_1846,U_1845] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1845),U_1846),U_1846) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1845),U_1847),U_1847)
          | ( U_1846 != c_Groups_Ouminus__class_Ouminus(U_1845,U_1847)
            & U_1846 != U_1847 ) )
        & ( U_1846 = c_Groups_Ouminus__class_Ouminus(U_1845,U_1847)
          | U_1846 = U_1847
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1845),U_1846),U_1846) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1845),U_1847),U_1847) ) )
      | ~ class_Rings_Oidom(U_1845) ),
    inference(variable_rename,[status(thm)],[f_546_1]) ).

fof(f_546_3,plain,
    ( ! [U_1845,U_1846,U_1847] :
        ( U_1846 != c_Groups_Ouminus__class_Ouminus(U_1845,U_1847)
        | ~ sP168(U_1845,U_1846,U_1847) )
    & ! [U_1845,U_1846,U_1847] :
        ( U_1846 != U_1847
        | ~ sP168(U_1845,U_1846,U_1847) )
    & ! [U_1845,U_1846,U_1847] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1845),U_1846),U_1846) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1845),U_1847),U_1847)
        | sP168(U_1845,U_1846,U_1847)
        | ~ sP169(U_1845,U_1846,U_1847) )
    & ! [U_1845,U_1846,U_1847] :
        ( U_1846 = c_Groups_Ouminus__class_Ouminus(U_1845,U_1847)
        | U_1846 = U_1847
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1845),U_1846),U_1846) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1845),U_1847),U_1847)
        | ~ sP169(U_1845,U_1846,U_1847) )
    & ! [U_1845,U_1846,U_1847] :
        ( sP169(U_1845,U_1846,U_1847)
        | ~ class_Rings_Oidom(U_1845) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP168,sP169])],[f_546_2]) ).

cnf(f_546_4,plain,
    ( sP169(U_1845,U_1846,U_1847)
    | ~ class_Rings_Oidom(U_1845) ),
    inference(clausify,[status(thm)],[f_546_3]) ).

cnf(f_546_5,plain,
    ( U_1846 = c_Groups_Ouminus__class_Ouminus(U_1845,U_1847)
    | U_1846 = U_1847
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1845),U_1846),U_1846) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1845),U_1847),U_1847)
    | ~ sP169(U_1845,U_1846,U_1847) ),
    inference(clausify,[status(thm)],[f_546_3]) ).

cnf(f_546_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1845),U_1846),U_1846) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1845),U_1847),U_1847)
    | sP168(U_1845,U_1846,U_1847)
    | ~ sP169(U_1845,U_1846,U_1847) ),
    inference(clausify,[status(thm)],[f_546_3]) ).

cnf(f_546_7,plain,
    ( U_1846 != U_1847
    | ~ sP168(U_1845,U_1846,U_1847) ),
    inference(clausify,[status(thm)],[f_546_3]) ).

cnf(f_546_8,plain,
    ( U_1846 != c_Groups_Ouminus__class_Ouminus(U_1845,U_1847)
    | ~ sP168(U_1845,U_1846,U_1847) ),
    inference(clausify,[status(thm)],[f_546_3]) ).

fof(f_547_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult_Ominus__right]) ).

fof(f_547_2,plain,
    ! [U_1850,U_1849,U_1848] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1848),U_1849),c_Groups_Ouminus__class_Ouminus(U_1848,U_1850)) = c_Groups_Ouminus__class_Ouminus(U_1848,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1848),U_1849),U_1850))
      | ~ class_RealVector_Oreal__normed__algebra(U_1848) ),
    inference(variable_rename,[status(thm)],[f_547_1]) ).

fof(f_547_3,plain,
    ! [U_1849,U_1850,U_1848] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1848),U_1849),c_Groups_Ouminus__class_Ouminus(U_1848,U_1850)) = c_Groups_Ouminus__class_Ouminus(U_1848,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1848),U_1849),U_1850))
      | ~ class_RealVector_Oreal__normed__algebra(U_1848) ),
    inference(definitional_conversion,[status(esa)],[f_547_2]) ).

cnf(f_547_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1848),U_1849),c_Groups_Ouminus__class_Ouminus(U_1848,U_1850)) = c_Groups_Ouminus__class_Ouminus(U_1848,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1848),U_1849),U_1850))
    | ~ class_RealVector_Oreal__normed__algebra(U_1848) ),
    inference(clausify,[status(thm)],[f_547_3]) ).

fof(f_548_1,plain,
    ! [V_x,V_xa,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x))
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__right_Ominus]) ).

fof(f_548_2,plain,
    ! [U_1853,U_1852,U_1851] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1851),U_1852),c_Groups_Ouminus__class_Ouminus(U_1851,U_1853)) = c_Groups_Ouminus__class_Ouminus(U_1851,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1851),U_1852),U_1853))
      | ~ class_RealVector_Oreal__normed__algebra(U_1851) ),
    inference(variable_rename,[status(thm)],[f_548_1]) ).

fof(f_548_3,plain,
    ! [U_1851,U_1852,U_1853] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1851),U_1852),c_Groups_Ouminus__class_Ouminus(U_1851,U_1853)) = c_Groups_Ouminus__class_Ouminus(U_1851,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1851),U_1852),U_1853))
      | ~ class_RealVector_Oreal__normed__algebra(U_1851) ),
    inference(definitional_conversion,[status(esa)],[f_548_2]) ).

cnf(f_548_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1851),U_1852),c_Groups_Ouminus__class_Ouminus(U_1851,U_1853)) = c_Groups_Ouminus__class_Ouminus(U_1851,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1851),U_1852),U_1853))
    | ~ class_RealVector_Oreal__normed__algebra(U_1851) ),
    inference(clausify,[status(thm)],[f_548_3]) ).

fof(f_549_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult_Ominus__left]) ).

fof(f_549_2,plain,
    ! [U_1856,U_1855,U_1854] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1854),c_Groups_Ouminus__class_Ouminus(U_1854,U_1855)),U_1856) = c_Groups_Ouminus__class_Ouminus(U_1854,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1854),U_1855),U_1856))
      | ~ class_RealVector_Oreal__normed__algebra(U_1854) ),
    inference(variable_rename,[status(thm)],[f_549_1]) ).

fof(f_549_3,plain,
    ! [U_1854,U_1855,U_1856] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1854),c_Groups_Ouminus__class_Ouminus(U_1854,U_1855)),U_1856) = c_Groups_Ouminus__class_Ouminus(U_1854,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1854),U_1855),U_1856))
      | ~ class_RealVector_Oreal__normed__algebra(U_1854) ),
    inference(definitional_conversion,[status(esa)],[f_549_2]) ).

cnf(f_549_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1854),c_Groups_Ouminus__class_Ouminus(U_1854,U_1855)),U_1856) = c_Groups_Ouminus__class_Ouminus(U_1854,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1854),U_1855),U_1856))
    | ~ class_RealVector_Oreal__normed__algebra(U_1854) ),
    inference(clausify,[status(thm)],[f_549_3]) ).

fof(f_550_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_x)),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__left_Ominus]) ).

fof(f_550_2,plain,
    ! [U_1859,U_1858,U_1857] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1857),c_Groups_Ouminus__class_Ouminus(U_1857,U_1858)),U_1859) = c_Groups_Ouminus__class_Ouminus(U_1857,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1857),U_1858),U_1859))
      | ~ class_RealVector_Oreal__normed__algebra(U_1857) ),
    inference(variable_rename,[status(thm)],[f_550_1]) ).

fof(f_550_3,plain,
    ! [U_1857,U_1858,U_1859] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1857),c_Groups_Ouminus__class_Ouminus(U_1857,U_1858)),U_1859) = c_Groups_Ouminus__class_Ouminus(U_1857,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1857),U_1858),U_1859))
      | ~ class_RealVector_Oreal__normed__algebra(U_1857) ),
    inference(definitional_conversion,[status(esa)],[f_550_2]) ).

cnf(f_550_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1857),c_Groups_Ouminus__class_Ouminus(U_1857,U_1858)),U_1859) = c_Groups_Ouminus__class_Ouminus(U_1857,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1857),U_1858),U_1859))
    | ~ class_RealVector_Oreal__normed__algebra(U_1857) ),
    inference(clausify,[status(thm)],[f_550_3]) ).

fof(f_551_1,plain,
    ! [V_q,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_q))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J]) ).

fof(f_551_2,plain,
    ! [U_1863,U_1862,U_1861,U_1860] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1860),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1860),U_1861),U_1862)),U_1863) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1860),hAPP(hAPP(c_Power_Opower__class_Opower(U_1860),U_1861),U_1863)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1860),U_1862),U_1863))
      | ~ class_Rings_Ocomm__semiring__1(U_1860) ),
    inference(variable_rename,[status(thm)],[f_551_1]) ).

fof(f_551_3,plain,
    ! [U_1860,U_1861,U_1862,U_1863] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1860),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1860),U_1861),U_1862)),U_1863) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1860),hAPP(hAPP(c_Power_Opower__class_Opower(U_1860),U_1861),U_1863)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1860),U_1862),U_1863))
      | ~ class_Rings_Ocomm__semiring__1(U_1860) ),
    inference(definitional_conversion,[status(esa)],[f_551_2]) ).

cnf(f_551_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1860),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1860),U_1861),U_1862)),U_1863) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1860),hAPP(hAPP(c_Power_Opower__class_Opower(U_1860),U_1861),U_1863)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1860),U_1862),U_1863))
    | ~ class_Rings_Ocomm__semiring__1(U_1860) ),
    inference(clausify,[status(thm)],[f_551_3]) ).

fof(f_552_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__add__distrib]) ).

fof(f_552_2,plain,
    ! [U_1866,U_1865,U_1864] :
      ( c_Groups_Ouminus__class_Ouminus(U_1864,c_Groups_Oplus__class_Oplus(U_1864,U_1865,U_1866)) = c_Groups_Oplus__class_Oplus(U_1864,c_Groups_Ouminus__class_Ouminus(U_1864,U_1865),c_Groups_Ouminus__class_Ouminus(U_1864,U_1866))
      | ~ class_Groups_Oab__group__add(U_1864) ),
    inference(variable_rename,[status(thm)],[f_552_1]) ).

fof(f_552_3,plain,
    ! [U_1864,U_1865,U_1866] :
      ( c_Groups_Ouminus__class_Ouminus(U_1864,c_Groups_Oplus__class_Oplus(U_1864,U_1865,U_1866)) = c_Groups_Oplus__class_Oplus(U_1864,c_Groups_Ouminus__class_Ouminus(U_1864,U_1865),c_Groups_Ouminus__class_Ouminus(U_1864,U_1866))
      | ~ class_Groups_Oab__group__add(U_1864) ),
    inference(definitional_conversion,[status(esa)],[f_552_2]) ).

cnf(f_552_4,plain,
    ( c_Groups_Ouminus__class_Ouminus(U_1864,c_Groups_Oplus__class_Oplus(U_1864,U_1865,U_1866)) = c_Groups_Oplus__class_Oplus(U_1864,c_Groups_Ouminus__class_Ouminus(U_1864,U_1865),c_Groups_Ouminus__class_Ouminus(U_1864,U_1866))
    | ~ class_Groups_Oab__group__add(U_1864) ),
    inference(clausify,[status(thm)],[f_552_3]) ).

fof(f_553_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a))
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__add]) ).

fof(f_553_2,plain,
    ! [U_1869,U_1868,U_1867] :
      ( c_Groups_Ouminus__class_Ouminus(U_1867,c_Groups_Oplus__class_Oplus(U_1867,U_1868,U_1869)) = c_Groups_Oplus__class_Oplus(U_1867,c_Groups_Ouminus__class_Ouminus(U_1867,U_1869),c_Groups_Ouminus__class_Ouminus(U_1867,U_1868))
      | ~ class_Groups_Ogroup__add(U_1867) ),
    inference(variable_rename,[status(thm)],[f_553_1]) ).

fof(f_553_3,plain,
    ! [U_1867,U_1868,U_1869] :
      ( c_Groups_Ouminus__class_Ouminus(U_1867,c_Groups_Oplus__class_Oplus(U_1867,U_1868,U_1869)) = c_Groups_Oplus__class_Oplus(U_1867,c_Groups_Ouminus__class_Ouminus(U_1867,U_1869),c_Groups_Ouminus__class_Ouminus(U_1867,U_1868))
      | ~ class_Groups_Ogroup__add(U_1867) ),
    inference(definitional_conversion,[status(esa)],[f_553_2]) ).

cnf(f_553_4,plain,
    ( c_Groups_Ouminus__class_Ouminus(U_1867,c_Groups_Oplus__class_Oplus(U_1867,U_1868,U_1869)) = c_Groups_Oplus__class_Oplus(U_1867,c_Groups_Ouminus__class_Ouminus(U_1867,U_1869),c_Groups_Ouminus__class_Ouminus(U_1867,U_1868))
    | ~ class_Groups_Ogroup__add(U_1867) ),
    inference(clausify,[status(thm)],[f_553_3]) ).

fof(f_554_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)) = V_b
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__minus__cancel]) ).

fof(f_554_2,plain,
    ! [U_1872,U_1871,U_1870] :
      ( c_Groups_Oplus__class_Oplus(U_1870,U_1871,c_Groups_Oplus__class_Oplus(U_1870,c_Groups_Ouminus__class_Ouminus(U_1870,U_1871),U_1872)) = U_1872
      | ~ class_Groups_Ogroup__add(U_1870) ),
    inference(variable_rename,[status(thm)],[f_554_1]) ).

fof(f_554_3,plain,
    ! [U_1871,U_1870,U_1872] :
      ( c_Groups_Oplus__class_Oplus(U_1870,U_1871,c_Groups_Oplus__class_Oplus(U_1870,c_Groups_Ouminus__class_Ouminus(U_1870,U_1871),U_1872)) = U_1872
      | ~ class_Groups_Ogroup__add(U_1870) ),
    inference(definitional_conversion,[status(esa)],[f_554_2]) ).

cnf(f_554_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_1870,U_1871,c_Groups_Oplus__class_Oplus(U_1870,c_Groups_Ouminus__class_Ouminus(U_1870,U_1871),U_1872)) = U_1872
    | ~ class_Groups_Ogroup__add(U_1870) ),
    inference(clausify,[status(thm)],[f_554_3]) ).

fof(f_555_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = V_b
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__add__cancel]) ).

fof(f_555_2,plain,
    ! [U_1875,U_1874,U_1873] :
      ( c_Groups_Oplus__class_Oplus(U_1873,c_Groups_Ouminus__class_Ouminus(U_1873,U_1874),c_Groups_Oplus__class_Oplus(U_1873,U_1874,U_1875)) = U_1875
      | ~ class_Groups_Ogroup__add(U_1873) ),
    inference(variable_rename,[status(thm)],[f_555_1]) ).

fof(f_555_3,plain,
    ! [U_1873,U_1874,U_1875] :
      ( c_Groups_Oplus__class_Oplus(U_1873,c_Groups_Ouminus__class_Ouminus(U_1873,U_1874),c_Groups_Oplus__class_Oplus(U_1873,U_1874,U_1875)) = U_1875
      | ~ class_Groups_Ogroup__add(U_1873) ),
    inference(definitional_conversion,[status(esa)],[f_555_2]) ).

cnf(f_555_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_1873,c_Groups_Ouminus__class_Ouminus(U_1873,U_1874),c_Groups_Oplus__class_Oplus(U_1873,U_1874,U_1875)) = U_1875
    | ~ class_Groups_Ogroup__add(U_1873) ),
    inference(clausify,[status(thm)],[f_555_3]) ).

fof(f_556_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__diff__eq]) ).

fof(f_556_2,plain,
    ! [U_1878,U_1877,U_1876] :
      ( c_Groups_Ouminus__class_Ouminus(U_1876,c_Groups_Ominus__class_Ominus(U_1876,U_1877,U_1878)) = c_Groups_Ominus__class_Ominus(U_1876,U_1878,U_1877)
      | ~ class_Groups_Oab__group__add(U_1876) ),
    inference(variable_rename,[status(thm)],[f_556_1]) ).

fof(f_556_3,plain,
    ! [U_1876,U_1877,U_1878] :
      ( c_Groups_Ouminus__class_Ouminus(U_1876,c_Groups_Ominus__class_Ominus(U_1876,U_1877,U_1878)) = c_Groups_Ominus__class_Ominus(U_1876,U_1878,U_1877)
      | ~ class_Groups_Oab__group__add(U_1876) ),
    inference(definitional_conversion,[status(esa)],[f_556_2]) ).

cnf(f_556_4,plain,
    ( c_Groups_Ouminus__class_Ouminus(U_1876,c_Groups_Ominus__class_Ominus(U_1876,U_1877,U_1878)) = c_Groups_Ominus__class_Ominus(U_1876,U_1878,U_1877)
    | ~ class_Groups_Oab__group__add(U_1876) ),
    inference(clausify,[status(thm)],[f_556_3]) ).

fof(f_557_1,plain,
    ! [V_g_2,V_f_2,T_a,T_b] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)
          | c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) )
        & ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2)
            & c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) )
          | ~ c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2) ) )
      | ~ class_Orderings_Oord(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_less__fun__def]) ).

fof(f_557_2,plain,
    ! [U_1882,U_1881,U_1880,U_1879] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_fun(U_1880,U_1879),U_1881,U_1882)
          | c_Orderings_Oord__class_Oless__eq(tc_fun(U_1880,U_1879),U_1882,U_1881)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1880,U_1879),U_1881,U_1882) )
        & ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1880,U_1879),U_1882,U_1881)
            & c_Orderings_Oord__class_Oless__eq(tc_fun(U_1880,U_1879),U_1881,U_1882) )
          | ~ c_Orderings_Oord__class_Oless(tc_fun(U_1880,U_1879),U_1881,U_1882) ) )
      | ~ class_Orderings_Oord(U_1879) ),
    inference(variable_rename,[status(thm)],[f_557_1]) ).

fof(f_557_3,plain,
    ( ! [U_1879,U_1880,U_1881,U_1882] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1880,U_1879),U_1882,U_1881)
        | ~ sP170(U_1879,U_1880,U_1881,U_1882) )
    & ! [U_1879,U_1880,U_1881,U_1882] :
        ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_1880,U_1879),U_1881,U_1882)
        | ~ sP170(U_1879,U_1880,U_1881,U_1882) )
    & ! [U_1879,U_1880,U_1881,U_1882] :
        ( c_Orderings_Oord__class_Oless(tc_fun(U_1880,U_1879),U_1881,U_1882)
        | c_Orderings_Oord__class_Oless__eq(tc_fun(U_1880,U_1879),U_1882,U_1881)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1880,U_1879),U_1881,U_1882)
        | ~ sP171(U_1879,U_1880,U_1881,U_1882) )
    & ! [U_1879,U_1880,U_1881,U_1882] :
        ( sP170(U_1879,U_1880,U_1881,U_1882)
        | ~ c_Orderings_Oord__class_Oless(tc_fun(U_1880,U_1879),U_1881,U_1882)
        | ~ sP171(U_1879,U_1880,U_1881,U_1882) )
    & ! [U_1879,U_1880,U_1881,U_1882] :
        ( sP171(U_1879,U_1880,U_1881,U_1882)
        | ~ class_Orderings_Oord(U_1879) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP170,sP171])],[f_557_2]) ).

cnf(f_557_4,plain,
    ( sP171(U_1879,U_1880,U_1881,U_1882)
    | ~ class_Orderings_Oord(U_1879) ),
    inference(clausify,[status(thm)],[f_557_3]) ).

cnf(f_557_5,plain,
    ( sP170(U_1879,U_1880,U_1881,U_1882)
    | ~ c_Orderings_Oord__class_Oless(tc_fun(U_1880,U_1879),U_1881,U_1882)
    | ~ sP171(U_1879,U_1880,U_1881,U_1882) ),
    inference(clausify,[status(thm)],[f_557_3]) ).

cnf(f_557_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_fun(U_1880,U_1879),U_1881,U_1882)
    | c_Orderings_Oord__class_Oless__eq(tc_fun(U_1880,U_1879),U_1882,U_1881)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1880,U_1879),U_1881,U_1882)
    | ~ sP171(U_1879,U_1880,U_1881,U_1882) ),
    inference(clausify,[status(thm)],[f_557_3]) ).

cnf(f_557_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_1880,U_1879),U_1881,U_1882)
    | ~ sP170(U_1879,U_1880,U_1881,U_1882) ),
    inference(clausify,[status(thm)],[f_557_3]) ).

cnf(f_557_8,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_1880,U_1879),U_1882,U_1881)
    | ~ sP170(U_1879,U_1880,U_1881,U_1882) ),
    inference(clausify,[status(thm)],[f_557_3]) ).

fof(f_558_1,plain,
    ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)),
    inference(fof_nnf,[status(thm)],[fact_zpower__zadd__distrib]) ).

fof(f_558_2,plain,
    ! [U_1885,U_1884,U_1883] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1883),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1884,U_1885)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1883),U_1884)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1883),U_1885)),
    inference(variable_rename,[status(thm)],[f_558_1]) ).

fof(f_558_3,plain,
    ! [U_1884,U_1885,U_1883] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1883),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1884,U_1885)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1883),U_1884)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1883),U_1885)),
    inference(definitional_conversion,[status(esa)],[f_558_2]) ).

cnf(f_558_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1883),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1884,U_1885)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1883),U_1884)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1883),U_1885)),
    inference(clausify,[status(thm)],[f_558_3]) ).

fof(f_559_1,plain,
    ! [V_x,T_a] :
      ( c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_RealVector_Onorm__class_Onorm(T_a,V_x)
      | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_norm__minus__cancel]) ).

fof(f_559_2,plain,
    ! [U_1887,U_1886] :
      ( c_RealVector_Onorm__class_Onorm(U_1886,c_Groups_Ouminus__class_Ouminus(U_1886,U_1887)) = c_RealVector_Onorm__class_Onorm(U_1886,U_1887)
      | ~ class_RealVector_Oreal__normed__vector(U_1886) ),
    inference(variable_rename,[status(thm)],[f_559_1]) ).

fof(f_559_3,plain,
    ! [U_1887,U_1886] :
      ( c_RealVector_Onorm__class_Onorm(U_1886,c_Groups_Ouminus__class_Ouminus(U_1886,U_1887)) = c_RealVector_Onorm__class_Onorm(U_1886,U_1887)
      | ~ class_RealVector_Oreal__normed__vector(U_1886) ),
    inference(definitional_conversion,[status(esa)],[f_559_2]) ).

cnf(f_559_4,plain,
    ( c_RealVector_Onorm__class_Onorm(U_1886,c_Groups_Ouminus__class_Ouminus(U_1886,U_1887)) = c_RealVector_Onorm__class_Onorm(U_1886,U_1887)
    | ~ class_RealVector_Oreal__normed__vector(U_1886) ),
    inference(clausify,[status(thm)],[f_559_3]) ).

fof(f_560_1,plain,
    ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m),
    inference(fof_nnf,[status(thm)],[fact_Zero__not__Suc]) ).

fof(f_560_2,plain,
    ! [U_1888] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1888),
    inference(variable_rename,[status(thm)],[f_560_1]) ).

fof(f_560_3,plain,
    ! [U_1888] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1888),
    inference(definitional_conversion,[status(esa)],[f_560_2]) ).

cnf(f_560_4,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1888),
    inference(clausify,[status(thm)],[f_560_3]) ).

fof(f_561_1,plain,
    ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_nat_H),
    inference(fof_nnf,[status(thm)],[fact_nat_Osimps_I2_J]) ).

fof(f_561_2,plain,
    ! [U_1889] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1889),
    inference(variable_rename,[status(thm)],[f_561_1]) ).

fof(f_561_3,plain,
    ! [U_1889] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1889),
    inference(definitional_conversion,[status(esa)],[f_561_2]) ).

cnf(f_561_4,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1889),
    inference(clausify,[status(thm)],[f_561_3]) ).

fof(f_562_1,plain,
    ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_Suc__not__Zero]) ).

fof(f_562_2,plain,
    ! [U_1890] : c_Nat_OSuc(U_1890) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_562_1]) ).

fof(f_562_3,plain,
    ! [U_1890] : c_Nat_OSuc(U_1890) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_562_2]) ).

cnf(f_562_4,plain,
    c_Nat_OSuc(U_1890) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_562_3]) ).

fof(f_563_1,plain,
    ! [V_nat_H_1] : c_Nat_OSuc(V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_nat_Osimps_I3_J]) ).

fof(f_563_2,plain,
    ! [U_1891] : c_Nat_OSuc(U_1891) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_563_1]) ).

fof(f_563_3,plain,
    ! [U_1891] : c_Nat_OSuc(U_1891) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_563_2]) ).

cnf(f_563_4,plain,
    c_Nat_OSuc(U_1891) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_563_3]) ).

fof(f_564_1,plain,
    ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(V_m),
    inference(fof_nnf,[status(thm)],[fact_Zero__neq__Suc]) ).

fof(f_564_2,plain,
    ! [U_1892] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1892),
    inference(variable_rename,[status(thm)],[f_564_1]) ).

fof(f_564_3,plain,
    ! [U_1892] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1892),
    inference(definitional_conversion,[status(esa)],[f_564_2]) ).

cnf(f_564_4,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1892),
    inference(clausify,[status(thm)],[f_564_3]) ).

fof(f_565_1,plain,
    ! [V_m] : c_Nat_OSuc(V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_Suc__neq__Zero]) ).

fof(f_565_2,plain,
    ! [U_1893] : c_Nat_OSuc(U_1893) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_565_1]) ).

fof(f_565_3,plain,
    ! [U_1893] : c_Nat_OSuc(U_1893) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_565_2]) ).

cnf(f_565_4,plain,
    c_Nat_OSuc(U_1893) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_565_3]) ).

fof(f_566_1,plain,
    ! [V_q,V_p,V_x,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J]) ).

fof(f_566_2,plain,
    ! [U_1897,U_1896,U_1895,U_1894] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1894),hAPP(hAPP(c_Power_Opower__class_Opower(U_1894),U_1895),U_1896)),U_1897) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1894),U_1895),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1896),U_1897))
      | ~ class_Rings_Ocomm__semiring__1(U_1894) ),
    inference(variable_rename,[status(thm)],[f_566_1]) ).

fof(f_566_3,plain,
    ! [U_1897,U_1894,U_1895,U_1896] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1894),hAPP(hAPP(c_Power_Opower__class_Opower(U_1894),U_1895),U_1896)),U_1897) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1894),U_1895),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1896),U_1897))
      | ~ class_Rings_Ocomm__semiring__1(U_1894) ),
    inference(definitional_conversion,[status(esa)],[f_566_2]) ).

cnf(f_566_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1894),hAPP(hAPP(c_Power_Opower__class_Opower(U_1894),U_1895),U_1896)),U_1897) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1894),U_1895),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1896),U_1897))
    | ~ class_Rings_Ocomm__semiring__1(U_1894) ),
    inference(clausify,[status(thm)],[f_566_3]) ).

fof(f_567_1,plain,
    ! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)),
    inference(fof_nnf,[status(thm)],[fact_zpower__zpower]) ).

fof(f_567_2,plain,
    ! [U_1900,U_1899,U_1898] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1898),U_1899)),U_1900) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1898),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1899),U_1900)),
    inference(variable_rename,[status(thm)],[f_567_1]) ).

fof(f_567_3,plain,
    ! [U_1898,U_1899,U_1900] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1898),U_1899)),U_1900) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1898),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1899),U_1900)),
    inference(definitional_conversion,[status(esa)],[f_567_2]) ).

cnf(f_567_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1898),U_1899)),U_1900) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1898),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1899),U_1900)),
    inference(clausify,[status(thm)],[f_567_3]) ).

fof(f_568_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J]) ).

fof(f_568_2,plain,
    ! [U_1902,U_1901] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1901),U_1902),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1902
      | ~ class_Rings_Ocomm__semiring__1(U_1901) ),
    inference(variable_rename,[status(thm)],[f_568_1]) ).

fof(f_568_3,plain,
    ! [U_1901,U_1902] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1901),U_1902),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1902
      | ~ class_Rings_Ocomm__semiring__1(U_1901) ),
    inference(definitional_conversion,[status(esa)],[f_568_2]) ).

cnf(f_568_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1901),U_1902),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1902
    | ~ class_Rings_Ocomm__semiring__1(U_1901) ),
    inference(clausify,[status(thm)],[f_568_3]) ).

fof(f_569_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_not__less__eq]) ).

fof(f_569_2,plain,
    ! [U_1904,U_1903] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1903,U_1904)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1904,c_Nat_OSuc(U_1903)) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1904,c_Nat_OSuc(U_1903))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1903,U_1904) ) ),
    inference(variable_rename,[status(thm)],[f_569_1]) ).

fof(f_569_3,plain,
    ( ! [U_1908,U_1906] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1906,U_1908)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1908,c_Nat_OSuc(U_1906)) )
    & ! [U_1907,U_1905] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1907,c_Nat_OSuc(U_1905))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1905,U_1907) ) ),
    inference(miniscope,[status(thm)],[f_569_2]) ).

fof(f_569_4,plain,
    ( ! [U_1906,U_1908] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1906,U_1908)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1908,c_Nat_OSuc(U_1906)) )
    & ! [U_1905,U_1907] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1907,c_Nat_OSuc(U_1905))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1905,U_1907) ) ),
    inference(definitional_conversion,[status(esa)],[f_569_3]) ).

cnf(f_569_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1907,c_Nat_OSuc(U_1905))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1905,U_1907) ),
    inference(clausify,[status(thm)],[f_569_4]) ).

cnf(f_569_6,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1906,U_1908)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1908,c_Nat_OSuc(U_1906)) ),
    inference(clausify,[status(thm)],[f_569_4]) ).

fof(f_570_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
        | ( V_m_2 != V_n_2
          & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) )
      & ( V_m_2 = V_n_2
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__Suc__eq]) ).

fof(f_570_2,plain,
    ! [U_1910,U_1909] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1909,c_Nat_OSuc(U_1910))
        | ( U_1909 != U_1910
          & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1909,U_1910) ) )
      & ( U_1909 = U_1910
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1909,U_1910)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1909,c_Nat_OSuc(U_1910)) ) ),
    inference(variable_rename,[status(thm)],[f_570_1]) ).

fof(f_570_3,plain,
    ( ! [U_1914,U_1912] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1912,c_Nat_OSuc(U_1914))
        | ( U_1912 != U_1914
          & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1912,U_1914) ) )
    & ! [U_1913,U_1911] :
        ( U_1911 = U_1913
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1911,U_1913)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1911,c_Nat_OSuc(U_1913)) ) ),
    inference(miniscope,[status(thm)],[f_570_2]) ).

fof(f_570_4,plain,
    ( ! [U_1912,U_1914] :
        ( U_1912 != U_1914
        | ~ sP172(U_1912,U_1914) )
    & ! [U_1912,U_1914] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1912,U_1914)
        | ~ sP172(U_1912,U_1914) )
    & ! [U_1912,U_1914] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1912,c_Nat_OSuc(U_1914))
        | sP172(U_1912,U_1914) )
    & ! [U_1911,U_1913] :
        ( U_1911 = U_1913
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1911,U_1913)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1911,c_Nat_OSuc(U_1913)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP172])],[f_570_3]) ).

cnf(f_570_5,plain,
    ( U_1911 = U_1913
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1911,U_1913)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1911,c_Nat_OSuc(U_1913)) ),
    inference(clausify,[status(thm)],[f_570_4]) ).

cnf(f_570_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1912,c_Nat_OSuc(U_1914))
    | sP172(U_1912,U_1914) ),
    inference(clausify,[status(thm)],[f_570_4]) ).

cnf(f_570_7,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1912,U_1914)
    | ~ sP172(U_1912,U_1914) ),
    inference(clausify,[status(thm)],[f_570_4]) ).

cnf(f_570_8,plain,
    ( U_1912 != U_1914
    | ~ sP172(U_1912,U_1914) ),
    inference(clausify,[status(thm)],[f_570_4]) ).

fof(f_571_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_n_2))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__less__eq]) ).

fof(f_571_2,plain,
    ! [U_1916,U_1915] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1915),c_Nat_OSuc(U_1916))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1915,U_1916) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1915,U_1916)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1915),c_Nat_OSuc(U_1916)) ) ),
    inference(variable_rename,[status(thm)],[f_571_1]) ).

fof(f_571_3,plain,
    ( ! [U_1920,U_1918] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1918),c_Nat_OSuc(U_1920))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1918,U_1920) )
    & ! [U_1919,U_1917] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1917,U_1919)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1917),c_Nat_OSuc(U_1919)) ) ),
    inference(miniscope,[status(thm)],[f_571_2]) ).

fof(f_571_4,plain,
    ( ! [U_1920,U_1918] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1918),c_Nat_OSuc(U_1920))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1918,U_1920) )
    & ! [U_1917,U_1919] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1917,U_1919)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1917),c_Nat_OSuc(U_1919)) ) ),
    inference(definitional_conversion,[status(esa)],[f_571_3]) ).

cnf(f_571_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1917,U_1919)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1917),c_Nat_OSuc(U_1919)) ),
    inference(clausify,[status(thm)],[f_571_4]) ).

cnf(f_571_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1918),c_Nat_OSuc(U_1920))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1918,U_1920) ),
    inference(clausify,[status(thm)],[f_571_4]) ).

fof(f_572_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))
          | V_n_2 != V_m_2 )
        & ( V_n_2 = V_m_2
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)) ) )
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) ),
    inference(fof_nnf,[status(thm)],[fact_not__less__less__Suc__eq]) ).

fof(f_572_2,plain,
    ! [U_1922,U_1921] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1921,c_Nat_OSuc(U_1922))
          | U_1921 != U_1922 )
        & ( U_1921 = U_1922
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1921,c_Nat_OSuc(U_1922)) ) )
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1921,U_1922) ),
    inference(variable_rename,[status(thm)],[f_572_1]) ).

fof(f_572_3,plain,
    ( ! [U_1921,U_1922] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1921,c_Nat_OSuc(U_1922))
        | U_1921 != U_1922
        | ~ sP173(U_1921,U_1922) )
    & ! [U_1921,U_1922] :
        ( U_1921 = U_1922
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1921,c_Nat_OSuc(U_1922))
        | ~ sP173(U_1921,U_1922) )
    & ! [U_1921,U_1922] :
        ( sP173(U_1921,U_1922)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1921,U_1922) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP173])],[f_572_2]) ).

cnf(f_572_4,plain,
    ( sP173(U_1921,U_1922)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1921,U_1922) ),
    inference(clausify,[status(thm)],[f_572_3]) ).

cnf(f_572_5,plain,
    ( U_1921 = U_1922
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1921,c_Nat_OSuc(U_1922))
    | ~ sP173(U_1921,U_1922) ),
    inference(clausify,[status(thm)],[f_572_3]) ).

cnf(f_572_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1921,c_Nat_OSuc(U_1922))
    | U_1921 != U_1922
    | ~ sP173(U_1921,U_1922) ),
    inference(clausify,[status(thm)],[f_572_3]) ).

fof(f_573_1,plain,
    ! [V_m,V_n] :
      ( V_m = V_n
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m) ),
    inference(fof_nnf,[status(thm)],[fact_less__antisym]) ).

fof(f_573_2,plain,
    ! [U_1924,U_1923] :
      ( U_1924 = U_1923
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1923,c_Nat_OSuc(U_1924))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1923,U_1924) ),
    inference(variable_rename,[status(thm)],[f_573_1]) ).

fof(f_573_3,plain,
    ! [U_1923,U_1924] :
      ( U_1924 = U_1923
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1923,c_Nat_OSuc(U_1924))
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1923,U_1924) ),
    inference(definitional_conversion,[status(esa)],[f_573_2]) ).

cnf(f_573_4,plain,
    ( U_1924 = U_1923
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1923,c_Nat_OSuc(U_1924))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1923,U_1924) ),
    inference(clausify,[status(thm)],[f_573_3]) ).

fof(f_574_1,plain,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
    inference(fof_nnf,[status(thm)],[fact_less__SucI]) ).

fof(f_574_2,plain,
    ! [U_1926,U_1925] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1925,c_Nat_OSuc(U_1926))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1925,U_1926) ),
    inference(variable_rename,[status(thm)],[f_574_1]) ).

fof(f_574_3,plain,
    ! [U_1925,U_1926] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1925,c_Nat_OSuc(U_1926))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1925,U_1926) ),
    inference(definitional_conversion,[status(esa)],[f_574_2]) ).

cnf(f_574_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1925,c_Nat_OSuc(U_1926))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1925,U_1926) ),
    inference(clausify,[status(thm)],[f_574_3]) ).

fof(f_575_1,plain,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
      | c_Nat_OSuc(V_m) = V_n
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__lessI]) ).

fof(f_575_2,plain,
    ! [U_1928,U_1927] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1927),U_1928)
      | c_Nat_OSuc(U_1927) = U_1928
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1927,U_1928) ),
    inference(variable_rename,[status(thm)],[f_575_1]) ).

fof(f_575_3,plain,
    ! [U_1927,U_1928] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1927),U_1928)
      | c_Nat_OSuc(U_1927) = U_1928
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1927,U_1928) ),
    inference(definitional_conversion,[status(esa)],[f_575_2]) ).

cnf(f_575_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1927),U_1928)
    | c_Nat_OSuc(U_1927) = U_1928
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1927,U_1928) ),
    inference(clausify,[status(thm)],[f_575_3]) ).

fof(f_576_1,plain,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_less__trans__Suc]) ).

fof(f_576_2,plain,
    ! [U_1931,U_1930,U_1929] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1929),U_1931)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1930,U_1931)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1929,U_1930) ),
    inference(variable_rename,[status(thm)],[f_576_1]) ).

fof(f_576_3,plain,
    ! [U_1930,U_1929,U_1931] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1929),U_1931)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1930,U_1931)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1929,U_1930) ),
    inference(definitional_conversion,[status(esa)],[f_576_2]) ).

cnf(f_576_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1929),U_1931)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1930,U_1931)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1929,U_1930) ),
    inference(clausify,[status(thm)],[f_576_3]) ).

fof(f_577_1,plain,
    ! [V_n,V_m] :
      ( V_m = V_n
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_less__SucE]) ).

fof(f_577_2,plain,
    ! [U_1933,U_1932] :
      ( U_1932 = U_1933
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1932,U_1933)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1932,c_Nat_OSuc(U_1933)) ),
    inference(variable_rename,[status(thm)],[f_577_1]) ).

fof(f_577_3,plain,
    ! [U_1932,U_1933] :
      ( U_1932 = U_1933
      | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1932,U_1933)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1932,c_Nat_OSuc(U_1933)) ),
    inference(definitional_conversion,[status(esa)],[f_577_2]) ).

cnf(f_577_4,plain,
    ( U_1932 = U_1933
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1932,U_1933)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1932,c_Nat_OSuc(U_1933)) ),
    inference(clausify,[status(thm)],[f_577_3]) ).

fof(f_578_1,plain,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__lessD]) ).

fof(f_578_2,plain,
    ! [U_1935,U_1934] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1934,U_1935)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1934),U_1935) ),
    inference(variable_rename,[status(thm)],[f_578_1]) ).

fof(f_578_3,plain,
    ! [U_1935,U_1934] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1934,U_1935)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1934),U_1935) ),
    inference(definitional_conversion,[status(esa)],[f_578_2]) ).

cnf(f_578_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1934,U_1935)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1934),U_1935) ),
    inference(clausify,[status(thm)],[f_578_3]) ).

fof(f_579_1,plain,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD]) ).

fof(f_579_2,plain,
    ! [U_1937,U_1936] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1936,U_1937)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1936),c_Nat_OSuc(U_1937)) ),
    inference(variable_rename,[status(thm)],[f_579_1]) ).

fof(f_579_3,plain,
    ! [U_1936,U_1937] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1936,U_1937)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1936),c_Nat_OSuc(U_1937)) ),
    inference(definitional_conversion,[status(esa)],[f_579_2]) ).

cnf(f_579_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1936,U_1937)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_1936),c_Nat_OSuc(U_1937)) ),
    inference(clausify,[status(thm)],[f_579_3]) ).

fof(f_580_1,plain,
    ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
    inference(fof_nnf,[status(thm)],[fact_add__Suc__right]) ).

fof(f_580_2,plain,
    ! [U_1939,U_1938] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1938,c_Nat_OSuc(U_1939)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1938,U_1939)),
    inference(variable_rename,[status(thm)],[f_580_1]) ).

fof(f_580_3,plain,
    ! [U_1938,U_1939] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1938,c_Nat_OSuc(U_1939)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1938,U_1939)),
    inference(definitional_conversion,[status(esa)],[f_580_2]) ).

cnf(f_580_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1938,c_Nat_OSuc(U_1939)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1938,U_1939)),
    inference(clausify,[status(thm)],[f_580_3]) ).

fof(f_581_1,plain,
    ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)),
    inference(fof_nnf,[status(thm)],[fact_add__Suc]) ).

fof(f_581_2,plain,
    ! [U_1941,U_1940] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_1940),U_1941) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1940,U_1941)),
    inference(variable_rename,[status(thm)],[f_581_1]) ).

fof(f_581_3,plain,
    ! [U_1940,U_1941] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_1940),U_1941) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1940,U_1941)),
    inference(definitional_conversion,[status(esa)],[f_581_2]) ).

cnf(f_581_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_1940),U_1941) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1940,U_1941)),
    inference(clausify,[status(thm)],[f_581_3]) ).

fof(f_582_1,plain,
    ! [V_n,V_m] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)),
    inference(fof_nnf,[status(thm)],[fact_add__Suc__shift]) ).

fof(f_582_2,plain,
    ! [U_1943,U_1942] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_1942),U_1943) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1942,c_Nat_OSuc(U_1943)),
    inference(variable_rename,[status(thm)],[f_582_1]) ).

fof(f_582_3,plain,
    ! [U_1942,U_1943] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_1942),U_1943) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1942,c_Nat_OSuc(U_1943)),
    inference(definitional_conversion,[status(esa)],[f_582_2]) ).

cnf(f_582_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_1942),U_1943) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1942,c_Nat_OSuc(U_1943)),
    inference(clausify,[status(thm)],[f_582_3]) ).

fof(f_583_1,plain,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__leD]) ).

fof(f_583_2,plain,
    ! [U_1945,U_1944] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1944,U_1945)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1944),U_1945) ),
    inference(variable_rename,[status(thm)],[f_583_1]) ).

fof(f_583_3,plain,
    ! [U_1944,U_1945] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1944,U_1945)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1944),U_1945) ),
    inference(definitional_conversion,[status(esa)],[f_583_2]) ).

cnf(f_583_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1944,U_1945)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1944),U_1945) ),
    inference(clausify,[status(thm)],[f_583_3]) ).

fof(f_584_1,plain,
    ! [V_n,V_m] :
      ( V_m = c_Nat_OSuc(V_n)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_le__SucE]) ).

fof(f_584_2,plain,
    ! [U_1947,U_1946] :
      ( U_1946 = c_Nat_OSuc(U_1947)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1946,U_1947)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1946,c_Nat_OSuc(U_1947)) ),
    inference(variable_rename,[status(thm)],[f_584_1]) ).

fof(f_584_3,plain,
    ! [U_1947,U_1946] :
      ( U_1946 = c_Nat_OSuc(U_1947)
      | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1946,U_1947)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1946,c_Nat_OSuc(U_1947)) ),
    inference(definitional_conversion,[status(esa)],[f_584_2]) ).

cnf(f_584_4,plain,
    ( U_1946 = c_Nat_OSuc(U_1947)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1946,U_1947)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1946,c_Nat_OSuc(U_1947)) ),
    inference(clausify,[status(thm)],[f_584_3]) ).

fof(f_585_1,plain,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
    inference(fof_nnf,[status(thm)],[fact_le__SucI]) ).

fof(f_585_2,plain,
    ! [U_1949,U_1948] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1948,c_Nat_OSuc(U_1949))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1948,U_1949) ),
    inference(variable_rename,[status(thm)],[f_585_1]) ).

fof(f_585_3,plain,
    ! [U_1949,U_1948] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1948,c_Nat_OSuc(U_1949))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1948,U_1949) ),
    inference(definitional_conversion,[status(esa)],[f_585_2]) ).

cnf(f_585_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1948,c_Nat_OSuc(U_1949))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1948,U_1949) ),
    inference(clausify,[status(thm)],[f_585_3]) ).

fof(f_586_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__le__mono]) ).

fof(f_586_2,plain,
    ! [U_1951,U_1950] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1950),c_Nat_OSuc(U_1951))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1950,U_1951) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1950,U_1951)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1950),c_Nat_OSuc(U_1951)) ) ),
    inference(variable_rename,[status(thm)],[f_586_1]) ).

fof(f_586_3,plain,
    ( ! [U_1955,U_1953] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1953),c_Nat_OSuc(U_1955))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1953,U_1955) )
    & ! [U_1954,U_1952] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1952,U_1954)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1952),c_Nat_OSuc(U_1954)) ) ),
    inference(miniscope,[status(thm)],[f_586_2]) ).

fof(f_586_4,plain,
    ( ! [U_1953,U_1955] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1953),c_Nat_OSuc(U_1955))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1953,U_1955) )
    & ! [U_1954,U_1952] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1952,U_1954)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1952),c_Nat_OSuc(U_1954)) ) ),
    inference(definitional_conversion,[status(esa)],[f_586_3]) ).

cnf(f_586_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1952,U_1954)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1952),c_Nat_OSuc(U_1954)) ),
    inference(clausify,[status(thm)],[f_586_4]) ).

cnf(f_586_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1953),c_Nat_OSuc(U_1955))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1953,U_1955) ),
    inference(clausify,[status(thm)],[f_586_4]) ).

fof(f_587_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
        | ( V_m_2 != c_Nat_OSuc(V_n_2)
          & ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) )
      & ( V_m_2 = c_Nat_OSuc(V_n_2)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__Suc__eq]) ).

fof(f_587_2,plain,
    ! [U_1957,U_1956] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1956,c_Nat_OSuc(U_1957))
        | ( U_1956 != c_Nat_OSuc(U_1957)
          & ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1956,U_1957) ) )
      & ( U_1956 = c_Nat_OSuc(U_1957)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1956,U_1957)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1956,c_Nat_OSuc(U_1957)) ) ),
    inference(variable_rename,[status(thm)],[f_587_1]) ).

fof(f_587_3,plain,
    ( ! [U_1961,U_1959] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1959,c_Nat_OSuc(U_1961))
        | ( U_1959 != c_Nat_OSuc(U_1961)
          & ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1959,U_1961) ) )
    & ! [U_1960,U_1958] :
        ( U_1958 = c_Nat_OSuc(U_1960)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1958,U_1960)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1958,c_Nat_OSuc(U_1960)) ) ),
    inference(miniscope,[status(thm)],[f_587_2]) ).

fof(f_587_4,plain,
    ( ! [U_1961,U_1959] :
        ( U_1959 != c_Nat_OSuc(U_1961)
        | ~ sP174(U_1961,U_1959) )
    & ! [U_1961,U_1959] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1959,U_1961)
        | ~ sP174(U_1961,U_1959) )
    & ! [U_1961,U_1959] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1959,c_Nat_OSuc(U_1961))
        | sP174(U_1961,U_1959) )
    & ! [U_1960,U_1958] :
        ( U_1958 = c_Nat_OSuc(U_1960)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1958,U_1960)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1958,c_Nat_OSuc(U_1960)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP174])],[f_587_3]) ).

cnf(f_587_5,plain,
    ( U_1958 = c_Nat_OSuc(U_1960)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1958,U_1960)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1958,c_Nat_OSuc(U_1960)) ),
    inference(clausify,[status(thm)],[f_587_4]) ).

cnf(f_587_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1959,c_Nat_OSuc(U_1961))
    | sP174(U_1961,U_1959) ),
    inference(clausify,[status(thm)],[f_587_4]) ).

cnf(f_587_7,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1959,U_1961)
    | ~ sP174(U_1961,U_1959) ),
    inference(clausify,[status(thm)],[f_587_4]) ).

cnf(f_587_8,plain,
    ( U_1959 != c_Nat_OSuc(U_1961)
    | ~ sP174(U_1961,U_1959) ),
    inference(clausify,[status(thm)],[f_587_4]) ).

fof(f_588_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_not__less__eq__eq]) ).

fof(f_588_2,plain,
    ! [U_1963,U_1962] :
      ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1962,U_1963)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1963),U_1962) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1963),U_1962)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1962,U_1963) ) ),
    inference(variable_rename,[status(thm)],[f_588_1]) ).

fof(f_588_3,plain,
    ( ! [U_1967,U_1965] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1965,U_1967)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1967),U_1965) )
    & ! [U_1966,U_1964] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1966),U_1964)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1964,U_1966) ) ),
    inference(miniscope,[status(thm)],[f_588_2]) ).

fof(f_588_4,plain,
    ( ! [U_1967,U_1965] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1965,U_1967)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1967),U_1965) )
    & ! [U_1964,U_1966] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1966),U_1964)
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1964,U_1966) ) ),
    inference(definitional_conversion,[status(esa)],[f_588_3]) ).

cnf(f_588_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1966),U_1964)
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1964,U_1966) ),
    inference(clausify,[status(thm)],[f_588_4]) ).

cnf(f_588_6,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1965,U_1967)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1967),U_1965) ),
    inference(clausify,[status(thm)],[f_588_4]) ).

fof(f_589_1,plain,
    ! [V_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n),
    inference(fof_nnf,[status(thm)],[fact_Suc__n__not__le__n]) ).

fof(f_589_2,plain,
    ! [U_1968] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1968),U_1968),
    inference(variable_rename,[status(thm)],[f_589_1]) ).

fof(f_589_3,plain,
    ! [U_1968] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1968),U_1968),
    inference(definitional_conversion,[status(esa)],[f_589_2]) ).

cnf(f_589_4,plain,
    ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1968),U_1968),
    inference(clausify,[status(thm)],[f_589_3]) ).

fof(f_590_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)
        | V_m_2 != V_n_2 )
      & ( V_m_2 = V_n_2
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__mult__cancel1]) ).

fof(f_590_2,plain,
    ! [U_1971,U_1970,U_1969] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1969)),U_1970) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1969)),U_1971)
        | U_1970 != U_1971 )
      & ( U_1970 = U_1971
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1969)),U_1970) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1969)),U_1971) ) ),
    inference(variable_rename,[status(thm)],[f_590_1]) ).

fof(f_590_3,plain,
    ( ! [U_1977,U_1975] :
        ( ! [U_1973] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1973)),U_1975) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1973)),U_1977)
        | U_1975 != U_1977 )
    & ! [U_1976,U_1974] :
        ( ! [U_1972] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1972)),U_1974) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1972)),U_1976)
        | U_1974 = U_1976 ) ),
    inference(miniscope,[status(thm)],[f_590_2]) ).

fof(f_590_4,plain,
    ( ! [U_1977,U_1975,U_1973] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1973)),U_1975) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1973)),U_1977)
        | U_1975 != U_1977 )
    & ! [U_1976,U_1974,U_1972] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1972)),U_1974) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1972)),U_1976)
        | U_1974 = U_1976 ) ),
    inference(definitional_conversion,[status(esa)],[f_590_3]) ).

cnf(f_590_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1972)),U_1974) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1972)),U_1976)
    | U_1974 = U_1976 ),
    inference(clausify,[status(thm)],[f_590_4]) ).

cnf(f_590_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1973)),U_1975) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1973)),U_1977)
    | U_1975 != U_1977 ),
    inference(clausify,[status(thm)],[f_590_4]) ).

fof(f_591_1,plain,
    ! [T_a] :
      ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__poly__code_I1_J]) ).

fof(f_591_2,plain,
    ! [U_1978] :
      ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1978),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1978))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1978))
      | ~ class_Groups_Oab__group__add(U_1978) ),
    inference(variable_rename,[status(thm)],[f_591_1]) ).

fof(f_591_3,plain,
    ! [U_1978] :
      ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1978),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1978))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1978))
      | ~ class_Groups_Oab__group__add(U_1978) ),
    inference(definitional_conversion,[status(esa)],[f_591_2]) ).

cnf(f_591_4,plain,
    ( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1978),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1978))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1978))
    | ~ class_Groups_Oab__group__add(U_1978) ),
    inference(clausify,[status(thm)],[f_591_3]) ).

fof(f_592_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
        | V_x_2 = V_y_2
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) )
      & ( ( V_x_2 != V_y_2
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) )
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_real__less__def]) ).

fof(f_592_2,plain,
    ! [U_1980,U_1979] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1979,U_1980)
        | U_1979 = U_1980
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1979,U_1980) )
      & ( ( U_1979 != U_1980
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1979,U_1980) )
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1979,U_1980) ) ),
    inference(variable_rename,[status(thm)],[f_592_1]) ).

fof(f_592_3,plain,
    ( ! [U_1984,U_1982] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1982,U_1984)
        | U_1982 = U_1984
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1982,U_1984) )
    & ! [U_1983,U_1981] :
        ( ( U_1981 != U_1983
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1981,U_1983) )
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1981,U_1983) ) ),
    inference(miniscope,[status(thm)],[f_592_2]) ).

fof(f_592_4,plain,
    ( ! [U_1981,U_1983] :
        ( U_1981 != U_1983
        | ~ sP175(U_1981,U_1983) )
    & ! [U_1981,U_1983] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1981,U_1983)
        | ~ sP175(U_1981,U_1983) )
    & ! [U_1984,U_1982] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1982,U_1984)
        | U_1982 = U_1984
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1982,U_1984) )
    & ! [U_1981,U_1983] :
        ( sP175(U_1981,U_1983)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1981,U_1983) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP175])],[f_592_3]) ).

cnf(f_592_5,plain,
    ( sP175(U_1981,U_1983)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1981,U_1983) ),
    inference(clausify,[status(thm)],[f_592_4]) ).

cnf(f_592_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1982,U_1984)
    | U_1982 = U_1984
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1982,U_1984) ),
    inference(clausify,[status(thm)],[f_592_4]) ).

cnf(f_592_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1981,U_1983)
    | ~ sP175(U_1981,U_1983) ),
    inference(clausify,[status(thm)],[f_592_4]) ).

cnf(f_592_8,plain,
    ( U_1981 != U_1983
    | ~ sP175(U_1981,U_1983) ),
    inference(clausify,[status(thm)],[f_592_4]) ).

fof(f_593_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
        | ( V_x_2 != V_y_2
          & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) )
      & ( V_x_2 = V_y_2
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__eq__real__def]) ).

fof(f_593_2,plain,
    ! [U_1986,U_1985] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1985,U_1986)
        | ( U_1985 != U_1986
          & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1985,U_1986) ) )
      & ( U_1985 = U_1986
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1985,U_1986)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1985,U_1986) ) ),
    inference(variable_rename,[status(thm)],[f_593_1]) ).

fof(f_593_3,plain,
    ( ! [U_1990,U_1988] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1988,U_1990)
        | ( U_1988 != U_1990
          & ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1988,U_1990) ) )
    & ! [U_1989,U_1987] :
        ( U_1987 = U_1989
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1987,U_1989)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1987,U_1989) ) ),
    inference(miniscope,[status(thm)],[f_593_2]) ).

fof(f_593_4,plain,
    ( ! [U_1990,U_1988] :
        ( U_1988 != U_1990
        | ~ sP176(U_1990,U_1988) )
    & ! [U_1990,U_1988] :
        ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1988,U_1990)
        | ~ sP176(U_1990,U_1988) )
    & ! [U_1990,U_1988] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1988,U_1990)
        | sP176(U_1990,U_1988) )
    & ! [U_1989,U_1987] :
        ( U_1987 = U_1989
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1987,U_1989)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1987,U_1989) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP176])],[f_593_3]) ).

cnf(f_593_5,plain,
    ( U_1987 = U_1989
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1987,U_1989)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1987,U_1989) ),
    inference(clausify,[status(thm)],[f_593_4]) ).

cnf(f_593_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1988,U_1990)
    | sP176(U_1990,U_1988) ),
    inference(clausify,[status(thm)],[f_593_4]) ).

cnf(f_593_7,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1988,U_1990)
    | ~ sP176(U_1990,U_1988) ),
    inference(clausify,[status(thm)],[f_593_4]) ).

cnf(f_593_8,plain,
    ( U_1988 != U_1990
    | ~ sP176(U_1990,U_1988) ),
    inference(clausify,[status(thm)],[f_593_4]) ).

fof(f_594_1,plain,
    ! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),
    inference(fof_nnf,[status(thm)],[fact_diff__Suc__Suc]) ).

fof(f_594_2,plain,
    ! [U_1992,U_1991] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1991),c_Nat_OSuc(U_1992)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1991,U_1992),
    inference(variable_rename,[status(thm)],[f_594_1]) ).

fof(f_594_3,plain,
    ! [U_1992,U_1991] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1991),c_Nat_OSuc(U_1992)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1991,U_1992),
    inference(definitional_conversion,[status(esa)],[f_594_2]) ).

cnf(f_594_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1991),c_Nat_OSuc(U_1992)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1991,U_1992),
    inference(clausify,[status(thm)],[f_594_3]) ).

fof(f_595_1,plain,
    ! [V_k,V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n),c_Nat_OSuc(V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k),
    inference(fof_nnf,[status(thm)],[fact_Suc__diff__diff]) ).

fof(f_595_2,plain,
    ! [U_1995,U_1994,U_1993] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1993),U_1994),c_Nat_OSuc(U_1995)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1993,U_1994),U_1995),
    inference(variable_rename,[status(thm)],[f_595_1]) ).

fof(f_595_3,plain,
    ! [U_1994,U_1993,U_1995] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1993),U_1994),c_Nat_OSuc(U_1995)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1993,U_1994),U_1995),
    inference(definitional_conversion,[status(esa)],[f_595_2]) ).

cnf(f_595_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1993),U_1994),c_Nat_OSuc(U_1995)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1993,U_1994),U_1995),
    inference(clausify,[status(thm)],[f_595_3]) ).

fof(f_596_1,plain,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[fact_real__zero__not__eq__one]) ).

fof(f_596_2,plain,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_596_1]) ).

cnf(f_596_3,plain,
    c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_596_2]) ).

fof(f_597_1,plain,
    ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),V_z) = V_z,
    inference(fof_nnf,[status(thm)],[fact_real__mult__1]) ).

fof(f_597_2,plain,
    ! [U_1996] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_1996) = U_1996,
    inference(variable_rename,[status(thm)],[f_597_1]) ).

fof(f_597_3,plain,
    ! [U_1996] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_1996) = U_1996,
    inference(definitional_conversion,[status(esa)],[f_597_2]) ).

cnf(f_597_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_1996) = U_1996,
    inference(clausify,[status(thm)],[f_597_3]) ).

fof(f_598_1,plain,
    ! [V_p,V_a,T_a] :
      ( c_Polynomial_Osmult(T_a,V_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p))
      | ~ class_Rings_Ocomm__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_smult__minus__right]) ).

fof(f_598_2,plain,
    ! [U_1999,U_1998,U_1997] :
      ( c_Polynomial_Osmult(U_1997,U_1998,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1997),U_1999)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1997),c_Polynomial_Osmult(U_1997,U_1998,U_1999))
      | ~ class_Rings_Ocomm__ring(U_1997) ),
    inference(variable_rename,[status(thm)],[f_598_1]) ).

fof(f_598_3,plain,
    ! [U_1997,U_1998,U_1999] :
      ( c_Polynomial_Osmult(U_1997,U_1998,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1997),U_1999)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1997),c_Polynomial_Osmult(U_1997,U_1998,U_1999))
      | ~ class_Rings_Ocomm__ring(U_1997) ),
    inference(definitional_conversion,[status(esa)],[f_598_2]) ).

cnf(f_598_4,plain,
    ( c_Polynomial_Osmult(U_1997,U_1998,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1997),U_1999)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1997),c_Polynomial_Osmult(U_1997,U_1998,U_1999))
    | ~ class_Rings_Ocomm__ring(U_1997) ),
    inference(clausify,[status(thm)],[f_598_3]) ).

fof(f_599_1,plain,
    ! [V_x_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_x_2))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq__one]) ).

fof(f_599_2,plain,
    ! [U_2000] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_2000))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2000) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2000)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_2000)) ) ),
    inference(variable_rename,[status(thm)],[f_599_1]) ).

fof(f_599_3,plain,
    ( ! [U_2002] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_2002))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2002) )
    & ! [U_2001] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2001)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_2001)) ) ),
    inference(miniscope,[status(thm)],[f_599_2]) ).

fof(f_599_4,plain,
    ( ! [U_2002] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_2002))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2002) )
    & ! [U_2001] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2001)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_2001)) ) ),
    inference(definitional_conversion,[status(esa)],[f_599_3]) ).

cnf(f_599_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2001)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_2001)) ),
    inference(clausify,[status(thm)],[f_599_4]) ).

cnf(f_599_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_2002))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2002) ),
    inference(clausify,[status(thm)],[f_599_4]) ).

fof(f_600_1,plain,
    ! [V_n,V_r,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_r),c_Nat_OSuc(V_n)),V_r)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_r,c_Groups_Oone__class_Oone(T_a))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_realpow__Suc__le__self]) ).

fof(f_600_2,plain,
    ! [U_2005,U_2004,U_2003] :
      ( c_Orderings_Oord__class_Oless__eq(U_2003,hAPP(hAPP(c_Power_Opower__class_Opower(U_2003),U_2004),c_Nat_OSuc(U_2005)),U_2004)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2003,U_2004,c_Groups_Oone__class_Oone(U_2003))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2003,c_Groups_Ozero__class_Ozero(U_2003),U_2004)
      | ~ class_Rings_Olinordered__semidom(U_2003) ),
    inference(variable_rename,[status(thm)],[f_600_1]) ).

fof(f_600_3,plain,
    ! [U_2003,U_2004,U_2005] :
      ( c_Orderings_Oord__class_Oless__eq(U_2003,hAPP(hAPP(c_Power_Opower__class_Opower(U_2003),U_2004),c_Nat_OSuc(U_2005)),U_2004)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2003,U_2004,c_Groups_Oone__class_Oone(U_2003))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2003,c_Groups_Ozero__class_Ozero(U_2003),U_2004)
      | ~ class_Rings_Olinordered__semidom(U_2003) ),
    inference(definitional_conversion,[status(esa)],[f_600_2]) ).

cnf(f_600_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2003,hAPP(hAPP(c_Power_Opower__class_Opower(U_2003),U_2004),c_Nat_OSuc(U_2005)),U_2004)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2003,U_2004,c_Groups_Oone__class_Oone(U_2003))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2003,c_Groups_Ozero__class_Ozero(U_2003),U_2004)
    | ~ class_Rings_Olinordered__semidom(U_2003) ),
    inference(clausify,[status(thm)],[f_600_3]) ).

fof(f_601_1,plain,
    ! [V_y,V_x] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_x,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,V_y)),
    inference(fof_nnf,[status(thm)],[fact_complex__diff__def]) ).

fof(f_601_2,plain,
    ! [U_2007,U_2006] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2006,U_2007) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_2006,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,U_2007)),
    inference(variable_rename,[status(thm)],[f_601_1]) ).

fof(f_601_3,plain,
    ! [U_2007,U_2006] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2006,U_2007) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_2006,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,U_2007)),
    inference(definitional_conversion,[status(esa)],[f_601_2]) ).

cnf(f_601_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2006,U_2007) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_2006,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,U_2007)),
    inference(clausify,[status(thm)],[f_601_3]) ).

fof(f_602_1,plain,
    c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_natfloor__zero]) ).

fof(f_602_2,plain,
    c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_602_1]) ).

cnf(f_602_3,plain,
    c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_602_2]) ).

fof(f_603_1,plain,
    ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),
    inference(fof_nnf,[status(thm)],[fact_zero__le__natfloor]) ).

fof(f_603_2,plain,
    ! [U_2008] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(U_2008)),
    inference(variable_rename,[status(thm)],[f_603_1]) ).

fof(f_603_3,plain,
    ! [U_2008] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(U_2008)),
    inference(definitional_conversion,[status(esa)],[f_603_2]) ).

cnf(f_603_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(U_2008)),
    inference(clausify,[status(thm)],[f_603_3]) ).

fof(f_604_1,plain,
    ! [V_y,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y) ),
    inference(fof_nnf,[status(thm)],[fact_natfloor__mono]) ).

fof(f_604_2,plain,
    ! [U_2010,U_2009] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(U_2009),c_RComplete_Onatfloor(U_2010))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2009,U_2010) ),
    inference(variable_rename,[status(thm)],[f_604_1]) ).

fof(f_604_3,plain,
    ! [U_2009,U_2010] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(U_2009),c_RComplete_Onatfloor(U_2010))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2009,U_2010) ),
    inference(definitional_conversion,[status(esa)],[f_604_2]) ).

cnf(f_604_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(U_2009),c_RComplete_Onatfloor(U_2010))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2009,U_2010) ),
    inference(clausify,[status(thm)],[f_604_3]) ).

fof(f_605_1,plain,
    ! [V_y,V_x,T_a] :
      ( c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y))
      | ~ class_Rings_Ocomm__ring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_realpow__two__diff]) ).

fof(f_605_2,plain,
    ! [U_2013,U_2012,U_2011] :
      ( c_Groups_Ominus__class_Ominus(U_2011,hAPP(hAPP(c_Power_Opower__class_Opower(U_2011),U_2012),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2011),U_2013),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2011),c_Groups_Ominus__class_Ominus(U_2011,U_2012,U_2013)),c_Groups_Oplus__class_Oplus(U_2011,U_2012,U_2013))
      | ~ class_Rings_Ocomm__ring__1(U_2011) ),
    inference(variable_rename,[status(thm)],[f_605_1]) ).

fof(f_605_3,plain,
    ! [U_2011,U_2012,U_2013] :
      ( c_Groups_Ominus__class_Ominus(U_2011,hAPP(hAPP(c_Power_Opower__class_Opower(U_2011),U_2012),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2011),U_2013),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2011),c_Groups_Ominus__class_Ominus(U_2011,U_2012,U_2013)),c_Groups_Oplus__class_Oplus(U_2011,U_2012,U_2013))
      | ~ class_Rings_Ocomm__ring__1(U_2011) ),
    inference(definitional_conversion,[status(esa)],[f_605_2]) ).

cnf(f_605_4,plain,
    ( c_Groups_Ominus__class_Ominus(U_2011,hAPP(hAPP(c_Power_Opower__class_Opower(U_2011),U_2012),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2011),U_2013),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2011),c_Groups_Ominus__class_Ominus(U_2011,U_2012,U_2013)),c_Groups_Oplus__class_Oplus(U_2011,U_2012,U_2013))
    | ~ class_Rings_Ocomm__ring__1(U_2011) ),
    inference(clausify,[status(thm)],[f_605_3]) ).

fof(f_606_1,plain,
    ! [V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2),V_ab_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2),V_ab_2) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff]) ).

fof(f_606_2,plain,
    ! [U_2015,U_2014] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_2014,c_Groups_Ouminus__class_Ouminus(U_2014,U_2015),U_2015)
          | ~ c_Orderings_Oord__class_Oless__eq(U_2014,c_Groups_Ozero__class_Ozero(U_2014),U_2015) )
        & ( c_Orderings_Oord__class_Oless__eq(U_2014,c_Groups_Ozero__class_Ozero(U_2014),U_2015)
          | ~ c_Orderings_Oord__class_Oless__eq(U_2014,c_Groups_Ouminus__class_Ouminus(U_2014,U_2015),U_2015) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_2014) ),
    inference(variable_rename,[status(thm)],[f_606_1]) ).

fof(f_606_3,plain,
    ( ! [U_2014,U_2015] :
        ( c_Orderings_Oord__class_Oless__eq(U_2014,c_Groups_Ouminus__class_Ouminus(U_2014,U_2015),U_2015)
        | ~ c_Orderings_Oord__class_Oless__eq(U_2014,c_Groups_Ozero__class_Ozero(U_2014),U_2015)
        | ~ sP177(U_2014,U_2015) )
    & ! [U_2014,U_2015] :
        ( c_Orderings_Oord__class_Oless__eq(U_2014,c_Groups_Ozero__class_Ozero(U_2014),U_2015)
        | ~ c_Orderings_Oord__class_Oless__eq(U_2014,c_Groups_Ouminus__class_Ouminus(U_2014,U_2015),U_2015)
        | ~ sP177(U_2014,U_2015) )
    & ! [U_2014,U_2015] :
        ( sP177(U_2014,U_2015)
        | ~ class_Groups_Olinordered__ab__group__add(U_2014) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP177])],[f_606_2]) ).

cnf(f_606_4,plain,
    ( sP177(U_2014,U_2015)
    | ~ class_Groups_Olinordered__ab__group__add(U_2014) ),
    inference(clausify,[status(thm)],[f_606_3]) ).

cnf(f_606_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2014,c_Groups_Ozero__class_Ozero(U_2014),U_2015)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2014,c_Groups_Ouminus__class_Ouminus(U_2014,U_2015),U_2015)
    | ~ sP177(U_2014,U_2015) ),
    inference(clausify,[status(thm)],[f_606_3]) ).

cnf(f_606_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2014,c_Groups_Ouminus__class_Ouminus(U_2014,U_2015),U_2015)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2014,c_Groups_Ozero__class_Ozero(U_2014),U_2015)
    | ~ sP177(U_2014,U_2015) ),
    inference(clausify,[status(thm)],[f_606_3]) ).

fof(f_607_1,plain,
    ! [V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2),c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__le__0__iff__le]) ).

fof(f_607_2,plain,
    ! [U_2017,U_2016] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_2016,c_Groups_Ouminus__class_Ouminus(U_2016,U_2017),c_Groups_Ozero__class_Ozero(U_2016))
          | ~ c_Orderings_Oord__class_Oless__eq(U_2016,c_Groups_Ozero__class_Ozero(U_2016),U_2017) )
        & ( c_Orderings_Oord__class_Oless__eq(U_2016,c_Groups_Ozero__class_Ozero(U_2016),U_2017)
          | ~ c_Orderings_Oord__class_Oless__eq(U_2016,c_Groups_Ouminus__class_Ouminus(U_2016,U_2017),c_Groups_Ozero__class_Ozero(U_2016)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_2016) ),
    inference(variable_rename,[status(thm)],[f_607_1]) ).

fof(f_607_3,plain,
    ( ! [U_2017,U_2016] :
        ( c_Orderings_Oord__class_Oless__eq(U_2016,c_Groups_Ouminus__class_Ouminus(U_2016,U_2017),c_Groups_Ozero__class_Ozero(U_2016))
        | ~ c_Orderings_Oord__class_Oless__eq(U_2016,c_Groups_Ozero__class_Ozero(U_2016),U_2017)
        | ~ sP178(U_2017,U_2016) )
    & ! [U_2017,U_2016] :
        ( c_Orderings_Oord__class_Oless__eq(U_2016,c_Groups_Ozero__class_Ozero(U_2016),U_2017)
        | ~ c_Orderings_Oord__class_Oless__eq(U_2016,c_Groups_Ouminus__class_Ouminus(U_2016,U_2017),c_Groups_Ozero__class_Ozero(U_2016))
        | ~ sP178(U_2017,U_2016) )
    & ! [U_2017,U_2016] :
        ( sP178(U_2017,U_2016)
        | ~ class_Groups_Oordered__ab__group__add(U_2016) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP178])],[f_607_2]) ).

cnf(f_607_4,plain,
    ( sP178(U_2017,U_2016)
    | ~ class_Groups_Oordered__ab__group__add(U_2016) ),
    inference(clausify,[status(thm)],[f_607_3]) ).

cnf(f_607_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2016,c_Groups_Ozero__class_Ozero(U_2016),U_2017)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2016,c_Groups_Ouminus__class_Ouminus(U_2016,U_2017),c_Groups_Ozero__class_Ozero(U_2016))
    | ~ sP178(U_2017,U_2016) ),
    inference(clausify,[status(thm)],[f_607_3]) ).

cnf(f_607_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2016,c_Groups_Ouminus__class_Ouminus(U_2016,U_2017),c_Groups_Ozero__class_Ozero(U_2016))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2016,c_Groups_Ozero__class_Ozero(U_2016),U_2017)
    | ~ sP178(U_2017,U_2016) ),
    inference(clausify,[status(thm)],[f_607_3]) ).

fof(f_608_1,plain,
    ! [V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__minus__self__iff]) ).

fof(f_608_2,plain,
    ! [U_2019,U_2018] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_2018,U_2019,c_Groups_Ouminus__class_Ouminus(U_2018,U_2019))
          | ~ c_Orderings_Oord__class_Oless__eq(U_2018,U_2019,c_Groups_Ozero__class_Ozero(U_2018)) )
        & ( c_Orderings_Oord__class_Oless__eq(U_2018,U_2019,c_Groups_Ozero__class_Ozero(U_2018))
          | ~ c_Orderings_Oord__class_Oless__eq(U_2018,U_2019,c_Groups_Ouminus__class_Ouminus(U_2018,U_2019)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_2018) ),
    inference(variable_rename,[status(thm)],[f_608_1]) ).

fof(f_608_3,plain,
    ( ! [U_2019,U_2018] :
        ( c_Orderings_Oord__class_Oless__eq(U_2018,U_2019,c_Groups_Ouminus__class_Ouminus(U_2018,U_2019))
        | ~ c_Orderings_Oord__class_Oless__eq(U_2018,U_2019,c_Groups_Ozero__class_Ozero(U_2018))
        | ~ sP179(U_2019,U_2018) )
    & ! [U_2019,U_2018] :
        ( c_Orderings_Oord__class_Oless__eq(U_2018,U_2019,c_Groups_Ozero__class_Ozero(U_2018))
        | ~ c_Orderings_Oord__class_Oless__eq(U_2018,U_2019,c_Groups_Ouminus__class_Ouminus(U_2018,U_2019))
        | ~ sP179(U_2019,U_2018) )
    & ! [U_2019,U_2018] :
        ( sP179(U_2019,U_2018)
        | ~ class_Groups_Olinordered__ab__group__add(U_2018) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP179])],[f_608_2]) ).

cnf(f_608_4,plain,
    ( sP179(U_2019,U_2018)
    | ~ class_Groups_Olinordered__ab__group__add(U_2018) ),
    inference(clausify,[status(thm)],[f_608_3]) ).

cnf(f_608_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2018,U_2019,c_Groups_Ozero__class_Ozero(U_2018))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2018,U_2019,c_Groups_Ouminus__class_Ouminus(U_2018,U_2019))
    | ~ sP179(U_2019,U_2018) ),
    inference(clausify,[status(thm)],[f_608_3]) ).

cnf(f_608_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2018,U_2019,c_Groups_Ouminus__class_Ouminus(U_2018,U_2019))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2018,U_2019,c_Groups_Ozero__class_Ozero(U_2018))
    | ~ sP179(U_2019,U_2018) ),
    inference(clausify,[status(thm)],[f_608_3]) ).

fof(f_609_1,plain,
    ! [V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) )
        & ( c_Orderings_Oord__class_Oless__eq(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2)) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le]) ).

fof(f_609_2,plain,
    ! [U_2021,U_2020] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_2020,c_Groups_Ozero__class_Ozero(U_2020),c_Groups_Ouminus__class_Ouminus(U_2020,U_2021))
          | ~ c_Orderings_Oord__class_Oless__eq(U_2020,U_2021,c_Groups_Ozero__class_Ozero(U_2020)) )
        & ( c_Orderings_Oord__class_Oless__eq(U_2020,U_2021,c_Groups_Ozero__class_Ozero(U_2020))
          | ~ c_Orderings_Oord__class_Oless__eq(U_2020,c_Groups_Ozero__class_Ozero(U_2020),c_Groups_Ouminus__class_Ouminus(U_2020,U_2021)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_2020) ),
    inference(variable_rename,[status(thm)],[f_609_1]) ).

fof(f_609_3,plain,
    ( ! [U_2021,U_2020] :
        ( c_Orderings_Oord__class_Oless__eq(U_2020,c_Groups_Ozero__class_Ozero(U_2020),c_Groups_Ouminus__class_Ouminus(U_2020,U_2021))
        | ~ c_Orderings_Oord__class_Oless__eq(U_2020,U_2021,c_Groups_Ozero__class_Ozero(U_2020))
        | ~ sP180(U_2021,U_2020) )
    & ! [U_2021,U_2020] :
        ( c_Orderings_Oord__class_Oless__eq(U_2020,U_2021,c_Groups_Ozero__class_Ozero(U_2020))
        | ~ c_Orderings_Oord__class_Oless__eq(U_2020,c_Groups_Ozero__class_Ozero(U_2020),c_Groups_Ouminus__class_Ouminus(U_2020,U_2021))
        | ~ sP180(U_2021,U_2020) )
    & ! [U_2021,U_2020] :
        ( sP180(U_2021,U_2020)
        | ~ class_Groups_Oordered__ab__group__add(U_2020) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP180])],[f_609_2]) ).

cnf(f_609_4,plain,
    ( sP180(U_2021,U_2020)
    | ~ class_Groups_Oordered__ab__group__add(U_2020) ),
    inference(clausify,[status(thm)],[f_609_3]) ).

cnf(f_609_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2020,U_2021,c_Groups_Ozero__class_Ozero(U_2020))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2020,c_Groups_Ozero__class_Ozero(U_2020),c_Groups_Ouminus__class_Ouminus(U_2020,U_2021))
    | ~ sP180(U_2021,U_2020) ),
    inference(clausify,[status(thm)],[f_609_3]) ).

cnf(f_609_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2020,c_Groups_Ozero__class_Ozero(U_2020),c_Groups_Ouminus__class_Ouminus(U_2020,U_2021))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2020,U_2021,c_Groups_Ozero__class_Ozero(U_2020))
    | ~ sP180(U_2021,U_2020) ),
    inference(clausify,[status(thm)],[f_609_3]) ).

fof(f_610_1,plain,
    ! [V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2))
          | ~ c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) )
        & ( c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2)) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less]) ).

fof(f_610_2,plain,
    ! [U_2023,U_2022] :
      ( ( ( c_Orderings_Oord__class_Oless(U_2022,c_Groups_Ozero__class_Ozero(U_2022),c_Groups_Ouminus__class_Ouminus(U_2022,U_2023))
          | ~ c_Orderings_Oord__class_Oless(U_2022,U_2023,c_Groups_Ozero__class_Ozero(U_2022)) )
        & ( c_Orderings_Oord__class_Oless(U_2022,U_2023,c_Groups_Ozero__class_Ozero(U_2022))
          | ~ c_Orderings_Oord__class_Oless(U_2022,c_Groups_Ozero__class_Ozero(U_2022),c_Groups_Ouminus__class_Ouminus(U_2022,U_2023)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_2022) ),
    inference(variable_rename,[status(thm)],[f_610_1]) ).

fof(f_610_3,plain,
    ( ! [U_2023,U_2022] :
        ( c_Orderings_Oord__class_Oless(U_2022,c_Groups_Ozero__class_Ozero(U_2022),c_Groups_Ouminus__class_Ouminus(U_2022,U_2023))
        | ~ c_Orderings_Oord__class_Oless(U_2022,U_2023,c_Groups_Ozero__class_Ozero(U_2022))
        | ~ sP181(U_2023,U_2022) )
    & ! [U_2023,U_2022] :
        ( c_Orderings_Oord__class_Oless(U_2022,U_2023,c_Groups_Ozero__class_Ozero(U_2022))
        | ~ c_Orderings_Oord__class_Oless(U_2022,c_Groups_Ozero__class_Ozero(U_2022),c_Groups_Ouminus__class_Ouminus(U_2022,U_2023))
        | ~ sP181(U_2023,U_2022) )
    & ! [U_2023,U_2022] :
        ( sP181(U_2023,U_2022)
        | ~ class_Groups_Oordered__ab__group__add(U_2022) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP181])],[f_610_2]) ).

cnf(f_610_4,plain,
    ( sP181(U_2023,U_2022)
    | ~ class_Groups_Oordered__ab__group__add(U_2022) ),
    inference(clausify,[status(thm)],[f_610_3]) ).

cnf(f_610_5,plain,
    ( c_Orderings_Oord__class_Oless(U_2022,U_2023,c_Groups_Ozero__class_Ozero(U_2022))
    | ~ c_Orderings_Oord__class_Oless(U_2022,c_Groups_Ozero__class_Ozero(U_2022),c_Groups_Ouminus__class_Ouminus(U_2022,U_2023))
    | ~ sP181(U_2023,U_2022) ),
    inference(clausify,[status(thm)],[f_610_3]) ).

cnf(f_610_6,plain,
    ( c_Orderings_Oord__class_Oless(U_2022,c_Groups_Ozero__class_Ozero(U_2022),c_Groups_Ouminus__class_Ouminus(U_2022,U_2023))
    | ~ c_Orderings_Oord__class_Oless(U_2022,U_2023,c_Groups_Ozero__class_Ozero(U_2022))
    | ~ sP181(U_2023,U_2022) ),
    inference(clausify,[status(thm)],[f_610_3]) ).

fof(f_611_1,plain,
    ! [V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2),c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) )
        & ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
      | ~ class_Groups_Oordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less]) ).

fof(f_611_2,plain,
    ! [U_2025,U_2024] :
      ( ( ( c_Orderings_Oord__class_Oless(U_2024,c_Groups_Ouminus__class_Ouminus(U_2024,U_2025),c_Groups_Ozero__class_Ozero(U_2024))
          | ~ c_Orderings_Oord__class_Oless(U_2024,c_Groups_Ozero__class_Ozero(U_2024),U_2025) )
        & ( c_Orderings_Oord__class_Oless(U_2024,c_Groups_Ozero__class_Ozero(U_2024),U_2025)
          | ~ c_Orderings_Oord__class_Oless(U_2024,c_Groups_Ouminus__class_Ouminus(U_2024,U_2025),c_Groups_Ozero__class_Ozero(U_2024)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_2024) ),
    inference(variable_rename,[status(thm)],[f_611_1]) ).

fof(f_611_3,plain,
    ( ! [U_2025,U_2024] :
        ( c_Orderings_Oord__class_Oless(U_2024,c_Groups_Ouminus__class_Ouminus(U_2024,U_2025),c_Groups_Ozero__class_Ozero(U_2024))
        | ~ c_Orderings_Oord__class_Oless(U_2024,c_Groups_Ozero__class_Ozero(U_2024),U_2025)
        | ~ sP182(U_2025,U_2024) )
    & ! [U_2025,U_2024] :
        ( c_Orderings_Oord__class_Oless(U_2024,c_Groups_Ozero__class_Ozero(U_2024),U_2025)
        | ~ c_Orderings_Oord__class_Oless(U_2024,c_Groups_Ouminus__class_Ouminus(U_2024,U_2025),c_Groups_Ozero__class_Ozero(U_2024))
        | ~ sP182(U_2025,U_2024) )
    & ! [U_2025,U_2024] :
        ( sP182(U_2025,U_2024)
        | ~ class_Groups_Oordered__ab__group__add(U_2024) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP182])],[f_611_2]) ).

cnf(f_611_4,plain,
    ( sP182(U_2025,U_2024)
    | ~ class_Groups_Oordered__ab__group__add(U_2024) ),
    inference(clausify,[status(thm)],[f_611_3]) ).

cnf(f_611_5,plain,
    ( c_Orderings_Oord__class_Oless(U_2024,c_Groups_Ozero__class_Ozero(U_2024),U_2025)
    | ~ c_Orderings_Oord__class_Oless(U_2024,c_Groups_Ouminus__class_Ouminus(U_2024,U_2025),c_Groups_Ozero__class_Ozero(U_2024))
    | ~ sP182(U_2025,U_2024) ),
    inference(clausify,[status(thm)],[f_611_3]) ).

cnf(f_611_6,plain,
    ( c_Orderings_Oord__class_Oless(U_2024,c_Groups_Ouminus__class_Ouminus(U_2024,U_2025),c_Groups_Ozero__class_Ozero(U_2024))
    | ~ c_Orderings_Oord__class_Oless(U_2024,c_Groups_Ozero__class_Ozero(U_2024),U_2025)
    | ~ sP182(U_2025,U_2024) ),
    inference(clausify,[status(thm)],[f_611_3]) ).

fof(f_612_1,plain,
    ! [V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2),V_ab_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2) )
        & ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ab_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2),V_ab_2) ) )
      | ~ class_Groups_Olinordered__ab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg]) ).

fof(f_612_2,plain,
    ! [U_2027,U_2026] :
      ( ( ( c_Orderings_Oord__class_Oless(U_2026,c_Groups_Ouminus__class_Ouminus(U_2026,U_2027),U_2027)
          | ~ c_Orderings_Oord__class_Oless(U_2026,c_Groups_Ozero__class_Ozero(U_2026),U_2027) )
        & ( c_Orderings_Oord__class_Oless(U_2026,c_Groups_Ozero__class_Ozero(U_2026),U_2027)
          | ~ c_Orderings_Oord__class_Oless(U_2026,c_Groups_Ouminus__class_Ouminus(U_2026,U_2027),U_2027) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_2026) ),
    inference(variable_rename,[status(thm)],[f_612_1]) ).

fof(f_612_3,plain,
    ( ! [U_2027,U_2026] :
        ( c_Orderings_Oord__class_Oless(U_2026,c_Groups_Ouminus__class_Ouminus(U_2026,U_2027),U_2027)
        | ~ c_Orderings_Oord__class_Oless(U_2026,c_Groups_Ozero__class_Ozero(U_2026),U_2027)
        | ~ sP183(U_2027,U_2026) )
    & ! [U_2027,U_2026] :
        ( c_Orderings_Oord__class_Oless(U_2026,c_Groups_Ozero__class_Ozero(U_2026),U_2027)
        | ~ c_Orderings_Oord__class_Oless(U_2026,c_Groups_Ouminus__class_Ouminus(U_2026,U_2027),U_2027)
        | ~ sP183(U_2027,U_2026) )
    & ! [U_2027,U_2026] :
        ( sP183(U_2027,U_2026)
        | ~ class_Groups_Olinordered__ab__group__add(U_2026) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP183])],[f_612_2]) ).

cnf(f_612_4,plain,
    ( sP183(U_2027,U_2026)
    | ~ class_Groups_Olinordered__ab__group__add(U_2026) ),
    inference(clausify,[status(thm)],[f_612_3]) ).

cnf(f_612_5,plain,
    ( c_Orderings_Oord__class_Oless(U_2026,c_Groups_Ozero__class_Ozero(U_2026),U_2027)
    | ~ c_Orderings_Oord__class_Oless(U_2026,c_Groups_Ouminus__class_Ouminus(U_2026,U_2027),U_2027)
    | ~ sP183(U_2027,U_2026) ),
    inference(clausify,[status(thm)],[f_612_3]) ).

cnf(f_612_6,plain,
    ( c_Orderings_Oord__class_Oless(U_2026,c_Groups_Ouminus__class_Ouminus(U_2026,U_2027),U_2027)
    | ~ c_Orderings_Oord__class_Oless(U_2026,c_Groups_Ozero__class_Ozero(U_2026),U_2027)
    | ~ sP183(U_2027,U_2026) ),
    inference(clausify,[status(thm)],[f_612_3]) ).

fof(f_613_1,plain,
    ! [V_ab_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2))
          | ~ c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a)) )
        & ( c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ozero__class_Ozero(T_a))
          | ~ c_Orderings_Oord__class_Oless(T_a,V_ab_2,c_Groups_Ouminus__class_Ouminus(T_a,V_ab_2)) ) )
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff]) ).

fof(f_613_2,plain,
    ! [U_2029,U_2028] :
      ( ( ( c_Orderings_Oord__class_Oless(U_2028,U_2029,c_Groups_Ouminus__class_Ouminus(U_2028,U_2029))
          | ~ c_Orderings_Oord__class_Oless(U_2028,U_2029,c_Groups_Ozero__class_Ozero(U_2028)) )
        & ( c_Orderings_Oord__class_Oless(U_2028,U_2029,c_Groups_Ozero__class_Ozero(U_2028))
          | ~ c_Orderings_Oord__class_Oless(U_2028,U_2029,c_Groups_Ouminus__class_Ouminus(U_2028,U_2029)) ) )
      | ~ class_Rings_Olinordered__idom(U_2028) ),
    inference(variable_rename,[status(thm)],[f_613_1]) ).

fof(f_613_3,plain,
    ( ! [U_2029,U_2028] :
        ( c_Orderings_Oord__class_Oless(U_2028,U_2029,c_Groups_Ouminus__class_Ouminus(U_2028,U_2029))
        | ~ c_Orderings_Oord__class_Oless(U_2028,U_2029,c_Groups_Ozero__class_Ozero(U_2028))
        | ~ sP184(U_2029,U_2028) )
    & ! [U_2029,U_2028] :
        ( c_Orderings_Oord__class_Oless(U_2028,U_2029,c_Groups_Ozero__class_Ozero(U_2028))
        | ~ c_Orderings_Oord__class_Oless(U_2028,U_2029,c_Groups_Ouminus__class_Ouminus(U_2028,U_2029))
        | ~ sP184(U_2029,U_2028) )
    & ! [U_2029,U_2028] :
        ( sP184(U_2029,U_2028)
        | ~ class_Rings_Olinordered__idom(U_2028) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP184])],[f_613_2]) ).

cnf(f_613_4,plain,
    ( sP184(U_2029,U_2028)
    | ~ class_Rings_Olinordered__idom(U_2028) ),
    inference(clausify,[status(thm)],[f_613_3]) ).

cnf(f_613_5,plain,
    ( c_Orderings_Oord__class_Oless(U_2028,U_2029,c_Groups_Ozero__class_Ozero(U_2028))
    | ~ c_Orderings_Oord__class_Oless(U_2028,U_2029,c_Groups_Ouminus__class_Ouminus(U_2028,U_2029))
    | ~ sP184(U_2029,U_2028) ),
    inference(clausify,[status(thm)],[f_613_3]) ).

cnf(f_613_6,plain,
    ( c_Orderings_Oord__class_Oless(U_2028,U_2029,c_Groups_Ouminus__class_Ouminus(U_2028,U_2029))
    | ~ c_Orderings_Oord__class_Oless(U_2028,U_2029,c_Groups_Ozero__class_Ozero(U_2028))
    | ~ sP184(U_2029,U_2028) ),
    inference(clausify,[status(thm)],[f_613_3]) ).

fof(f_614_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Groups_Ouminus__class_Ouminus(T_a,V_a) = V_b
      | c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) != c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__unique]) ).

fof(f_614_2,plain,
    ! [U_2032,U_2031,U_2030] :
      ( c_Groups_Ouminus__class_Ouminus(U_2030,U_2031) = U_2032
      | c_Groups_Oplus__class_Oplus(U_2030,U_2031,U_2032) != c_Groups_Ozero__class_Ozero(U_2030)
      | ~ class_Groups_Ogroup__add(U_2030) ),
    inference(variable_rename,[status(thm)],[f_614_1]) ).

fof(f_614_3,plain,
    ! [U_2032,U_2031,U_2030] :
      ( c_Groups_Ouminus__class_Ouminus(U_2030,U_2031) = U_2032
      | c_Groups_Oplus__class_Oplus(U_2030,U_2031,U_2032) != c_Groups_Ozero__class_Ozero(U_2030)
      | ~ class_Groups_Ogroup__add(U_2030) ),
    inference(definitional_conversion,[status(esa)],[f_614_2]) ).

cnf(f_614_4,plain,
    ( c_Groups_Ouminus__class_Ouminus(U_2030,U_2031) = U_2032
    | c_Groups_Oplus__class_Oplus(U_2030,U_2031,U_2032) != c_Groups_Ozero__class_Ozero(U_2030)
    | ~ class_Groups_Ogroup__add(U_2030) ),
    inference(clausify,[status(thm)],[f_614_3]) ).

fof(f_615_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
          | V_y_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) )
        & ( V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_x_2)
          | c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_add__eq__0__iff]) ).

fof(f_615_2,plain,
    ! [U_2035,U_2034,U_2033] :
      ( ( ( c_Groups_Oplus__class_Oplus(U_2033,U_2034,U_2035) = c_Groups_Ozero__class_Ozero(U_2033)
          | U_2035 != c_Groups_Ouminus__class_Ouminus(U_2033,U_2034) )
        & ( U_2035 = c_Groups_Ouminus__class_Ouminus(U_2033,U_2034)
          | c_Groups_Oplus__class_Oplus(U_2033,U_2034,U_2035) != c_Groups_Ozero__class_Ozero(U_2033) ) )
      | ~ class_Groups_Ogroup__add(U_2033) ),
    inference(variable_rename,[status(thm)],[f_615_1]) ).

fof(f_615_3,plain,
    ( ! [U_2033,U_2034,U_2035] :
        ( c_Groups_Oplus__class_Oplus(U_2033,U_2034,U_2035) = c_Groups_Ozero__class_Ozero(U_2033)
        | U_2035 != c_Groups_Ouminus__class_Ouminus(U_2033,U_2034)
        | ~ sP185(U_2033,U_2034,U_2035) )
    & ! [U_2033,U_2034,U_2035] :
        ( U_2035 = c_Groups_Ouminus__class_Ouminus(U_2033,U_2034)
        | c_Groups_Oplus__class_Oplus(U_2033,U_2034,U_2035) != c_Groups_Ozero__class_Ozero(U_2033)
        | ~ sP185(U_2033,U_2034,U_2035) )
    & ! [U_2033,U_2034,U_2035] :
        ( sP185(U_2033,U_2034,U_2035)
        | ~ class_Groups_Ogroup__add(U_2033) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP185])],[f_615_2]) ).

cnf(f_615_4,plain,
    ( sP185(U_2033,U_2034,U_2035)
    | ~ class_Groups_Ogroup__add(U_2033) ),
    inference(clausify,[status(thm)],[f_615_3]) ).

cnf(f_615_5,plain,
    ( U_2035 = c_Groups_Ouminus__class_Ouminus(U_2033,U_2034)
    | c_Groups_Oplus__class_Oplus(U_2033,U_2034,U_2035) != c_Groups_Ozero__class_Ozero(U_2033)
    | ~ sP185(U_2033,U_2034,U_2035) ),
    inference(clausify,[status(thm)],[f_615_3]) ).

cnf(f_615_6,plain,
    ( c_Groups_Oplus__class_Oplus(U_2033,U_2034,U_2035) = c_Groups_Ozero__class_Ozero(U_2033)
    | U_2035 != c_Groups_Ouminus__class_Ouminus(U_2033,U_2034)
    | ~ sP185(U_2033,U_2034,U_2035) ),
    inference(clausify,[status(thm)],[f_615_3]) ).

fof(f_616_1,plain,
    ! [V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ab__left__minus]) ).

fof(f_616_2,plain,
    ! [U_2037,U_2036] :
      ( c_Groups_Oplus__class_Oplus(U_2036,c_Groups_Ouminus__class_Ouminus(U_2036,U_2037),U_2037) = c_Groups_Ozero__class_Ozero(U_2036)
      | ~ class_Groups_Oab__group__add(U_2036) ),
    inference(variable_rename,[status(thm)],[f_616_1]) ).

fof(f_616_3,plain,
    ! [U_2037,U_2036] :
      ( c_Groups_Oplus__class_Oplus(U_2036,c_Groups_Ouminus__class_Ouminus(U_2036,U_2037),U_2037) = c_Groups_Ozero__class_Ozero(U_2036)
      | ~ class_Groups_Oab__group__add(U_2036) ),
    inference(definitional_conversion,[status(esa)],[f_616_2]) ).

cnf(f_616_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_2036,c_Groups_Ouminus__class_Ouminus(U_2036,U_2037),U_2037) = c_Groups_Ozero__class_Ozero(U_2036)
    | ~ class_Groups_Oab__group__add(U_2036) ),
    inference(clausify,[status(thm)],[f_616_3]) ).

fof(f_617_1,plain,
    ! [V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_left__minus]) ).

fof(f_617_2,plain,
    ! [U_2039,U_2038] :
      ( c_Groups_Oplus__class_Oplus(U_2038,c_Groups_Ouminus__class_Ouminus(U_2038,U_2039),U_2039) = c_Groups_Ozero__class_Ozero(U_2038)
      | ~ class_Groups_Ogroup__add(U_2038) ),
    inference(variable_rename,[status(thm)],[f_617_1]) ).

fof(f_617_3,plain,
    ! [U_2038,U_2039] :
      ( c_Groups_Oplus__class_Oplus(U_2038,c_Groups_Ouminus__class_Ouminus(U_2038,U_2039),U_2039) = c_Groups_Ozero__class_Ozero(U_2038)
      | ~ class_Groups_Ogroup__add(U_2038) ),
    inference(definitional_conversion,[status(esa)],[f_617_2]) ).

cnf(f_617_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_2038,c_Groups_Ouminus__class_Ouminus(U_2038,U_2039),U_2039) = c_Groups_Ozero__class_Ozero(U_2038)
    | ~ class_Groups_Ogroup__add(U_2038) ),
    inference(clausify,[status(thm)],[f_617_3]) ).

fof(f_618_1,plain,
    ! [V_b_2,V_ab_2,T_a] :
      ( ( ( V_ab_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
          | c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_b_2) != c_Groups_Ozero__class_Ozero(T_a) )
        & ( c_Groups_Oplus__class_Oplus(T_a,V_ab_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
          | V_ab_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) ) )
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0]) ).

fof(f_618_2,plain,
    ! [U_2042,U_2041,U_2040] :
      ( ( ( U_2041 = c_Groups_Ouminus__class_Ouminus(U_2040,U_2042)
          | c_Groups_Oplus__class_Oplus(U_2040,U_2041,U_2042) != c_Groups_Ozero__class_Ozero(U_2040) )
        & ( c_Groups_Oplus__class_Oplus(U_2040,U_2041,U_2042) = c_Groups_Ozero__class_Ozero(U_2040)
          | U_2041 != c_Groups_Ouminus__class_Ouminus(U_2040,U_2042) ) )
      | ~ class_Groups_Ogroup__add(U_2040) ),
    inference(variable_rename,[status(thm)],[f_618_1]) ).

fof(f_618_3,plain,
    ( ! [U_2040,U_2041,U_2042] :
        ( U_2041 = c_Groups_Ouminus__class_Ouminus(U_2040,U_2042)
        | c_Groups_Oplus__class_Oplus(U_2040,U_2041,U_2042) != c_Groups_Ozero__class_Ozero(U_2040)
        | ~ sP186(U_2040,U_2041,U_2042) )
    & ! [U_2040,U_2041,U_2042] :
        ( c_Groups_Oplus__class_Oplus(U_2040,U_2041,U_2042) = c_Groups_Ozero__class_Ozero(U_2040)
        | U_2041 != c_Groups_Ouminus__class_Ouminus(U_2040,U_2042)
        | ~ sP186(U_2040,U_2041,U_2042) )
    & ! [U_2040,U_2041,U_2042] :
        ( sP186(U_2040,U_2041,U_2042)
        | ~ class_Groups_Ogroup__add(U_2040) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP186])],[f_618_2]) ).

cnf(f_618_4,plain,
    ( sP186(U_2040,U_2041,U_2042)
    | ~ class_Groups_Ogroup__add(U_2040) ),
    inference(clausify,[status(thm)],[f_618_3]) ).

cnf(f_618_5,plain,
    ( c_Groups_Oplus__class_Oplus(U_2040,U_2041,U_2042) = c_Groups_Ozero__class_Ozero(U_2040)
    | U_2041 != c_Groups_Ouminus__class_Ouminus(U_2040,U_2042)
    | ~ sP186(U_2040,U_2041,U_2042) ),
    inference(clausify,[status(thm)],[f_618_3]) ).

cnf(f_618_6,plain,
    ( U_2041 = c_Groups_Ouminus__class_Ouminus(U_2040,U_2042)
    | c_Groups_Oplus__class_Oplus(U_2040,U_2041,U_2042) != c_Groups_Ozero__class_Ozero(U_2040)
    | ~ sP186(U_2040,U_2041,U_2042) ),
    inference(clausify,[status(thm)],[f_618_3]) ).

fof(f_619_1,plain,
    ! [V_a,T_a] :
      ( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_right__minus]) ).

fof(f_619_2,plain,
    ! [U_2044,U_2043] :
      ( c_Groups_Oplus__class_Oplus(U_2043,U_2044,c_Groups_Ouminus__class_Ouminus(U_2043,U_2044)) = c_Groups_Ozero__class_Ozero(U_2043)
      | ~ class_Groups_Ogroup__add(U_2043) ),
    inference(variable_rename,[status(thm)],[f_619_1]) ).

fof(f_619_3,plain,
    ! [U_2044,U_2043] :
      ( c_Groups_Oplus__class_Oplus(U_2043,U_2044,c_Groups_Ouminus__class_Ouminus(U_2043,U_2044)) = c_Groups_Ozero__class_Ozero(U_2043)
      | ~ class_Groups_Ogroup__add(U_2043) ),
    inference(definitional_conversion,[status(esa)],[f_619_2]) ).

cnf(f_619_4,plain,
    ( c_Groups_Oplus__class_Oplus(U_2043,U_2044,c_Groups_Ouminus__class_Ouminus(U_2043,U_2044)) = c_Groups_Ozero__class_Ozero(U_2043)
    | ~ class_Groups_Ogroup__add(U_2043) ),
    inference(clausify,[status(thm)],[f_619_3]) ).

fof(f_620_1,plain,
    ! [V_a,T_a] :
      ( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a)
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__0]) ).

fof(f_620_2,plain,
    ! [U_2046,U_2045] :
      ( c_Groups_Ominus__class_Ominus(U_2045,c_Groups_Ozero__class_Ozero(U_2045),U_2046) = c_Groups_Ouminus__class_Ouminus(U_2045,U_2046)
      | ~ class_Groups_Ogroup__add(U_2045) ),
    inference(variable_rename,[status(thm)],[f_620_1]) ).

fof(f_620_3,plain,
    ! [U_2045,U_2046] :
      ( c_Groups_Ominus__class_Ominus(U_2045,c_Groups_Ozero__class_Ozero(U_2045),U_2046) = c_Groups_Ouminus__class_Ouminus(U_2045,U_2046)
      | ~ class_Groups_Ogroup__add(U_2045) ),
    inference(definitional_conversion,[status(esa)],[f_620_2]) ).

cnf(f_620_4,plain,
    ( c_Groups_Ominus__class_Ominus(U_2045,c_Groups_Ozero__class_Ozero(U_2045),U_2046) = c_Groups_Ouminus__class_Ouminus(U_2045,U_2046)
    | ~ class_Groups_Ogroup__add(U_2045) ),
    inference(clausify,[status(thm)],[f_620_3]) ).

fof(f_621_1,plain,
    ! [V_x_2,T_a] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a)
          | ( V_x_2 != c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
            & V_x_2 != c_Groups_Oone__class_Oone(T_a) ) )
        & ( V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
          | V_x_2 = c_Groups_Oone__class_Oone(T_a)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) != c_Groups_Oone__class_Oone(T_a) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_square__eq__1__iff]) ).

fof(f_621_2,plain,
    ! [U_2048,U_2047] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2047),U_2048),U_2048) = c_Groups_Oone__class_Oone(U_2047)
          | ( U_2048 != c_Groups_Ouminus__class_Ouminus(U_2047,c_Groups_Oone__class_Oone(U_2047))
            & U_2048 != c_Groups_Oone__class_Oone(U_2047) ) )
        & ( U_2048 = c_Groups_Ouminus__class_Ouminus(U_2047,c_Groups_Oone__class_Oone(U_2047))
          | U_2048 = c_Groups_Oone__class_Oone(U_2047)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2047),U_2048),U_2048) != c_Groups_Oone__class_Oone(U_2047) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(U_2047) ),
    inference(variable_rename,[status(thm)],[f_621_1]) ).

fof(f_621_3,plain,
    ( ! [U_2047,U_2048] :
        ( U_2048 != c_Groups_Ouminus__class_Ouminus(U_2047,c_Groups_Oone__class_Oone(U_2047))
        | ~ sP187(U_2047,U_2048) )
    & ! [U_2047,U_2048] :
        ( U_2048 != c_Groups_Oone__class_Oone(U_2047)
        | ~ sP187(U_2047,U_2048) )
    & ! [U_2047,U_2048] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2047),U_2048),U_2048) = c_Groups_Oone__class_Oone(U_2047)
        | sP187(U_2047,U_2048)
        | ~ sP188(U_2047,U_2048) )
    & ! [U_2047,U_2048] :
        ( U_2048 = c_Groups_Ouminus__class_Ouminus(U_2047,c_Groups_Oone__class_Oone(U_2047))
        | U_2048 = c_Groups_Oone__class_Oone(U_2047)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2047),U_2048),U_2048) != c_Groups_Oone__class_Oone(U_2047)
        | ~ sP188(U_2047,U_2048) )
    & ! [U_2047,U_2048] :
        ( sP188(U_2047,U_2048)
        | ~ class_Rings_Oring__1__no__zero__divisors(U_2047) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP187,sP188])],[f_621_2]) ).

cnf(f_621_4,plain,
    ( sP188(U_2047,U_2048)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_2047) ),
    inference(clausify,[status(thm)],[f_621_3]) ).

cnf(f_621_5,plain,
    ( U_2048 = c_Groups_Ouminus__class_Ouminus(U_2047,c_Groups_Oone__class_Oone(U_2047))
    | U_2048 = c_Groups_Oone__class_Oone(U_2047)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2047),U_2048),U_2048) != c_Groups_Oone__class_Oone(U_2047)
    | ~ sP188(U_2047,U_2048) ),
    inference(clausify,[status(thm)],[f_621_3]) ).

cnf(f_621_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2047),U_2048),U_2048) = c_Groups_Oone__class_Oone(U_2047)
    | sP187(U_2047,U_2048)
    | ~ sP188(U_2047,U_2048) ),
    inference(clausify,[status(thm)],[f_621_3]) ).

cnf(f_621_7,plain,
    ( U_2048 != c_Groups_Oone__class_Oone(U_2047)
    | ~ sP187(U_2047,U_2048) ),
    inference(clausify,[status(thm)],[f_621_3]) ).

cnf(f_621_8,plain,
    ( U_2048 != c_Groups_Ouminus__class_Ouminus(U_2047,c_Groups_Oone__class_Oone(U_2047))
    | ~ sP187(U_2047,U_2048) ),
    inference(clausify,[status(thm)],[f_621_3]) ).

fof(f_622_1,plain,
    ! [V_x,T_a] :
      ( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x)
      | ~ class_Rings_Ocomm__ring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J]) ).

fof(f_622_2,plain,
    ! [U_2050,U_2049] :
      ( c_Groups_Ouminus__class_Ouminus(U_2049,U_2050) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2049),c_Groups_Ouminus__class_Ouminus(U_2049,c_Groups_Oone__class_Oone(U_2049))),U_2050)
      | ~ class_Rings_Ocomm__ring__1(U_2049) ),
    inference(variable_rename,[status(thm)],[f_622_1]) ).

fof(f_622_3,plain,
    ! [U_2049,U_2050] :
      ( c_Groups_Ouminus__class_Ouminus(U_2049,U_2050) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2049),c_Groups_Ouminus__class_Ouminus(U_2049,c_Groups_Oone__class_Oone(U_2049))),U_2050)
      | ~ class_Rings_Ocomm__ring__1(U_2049) ),
    inference(definitional_conversion,[status(esa)],[f_622_2]) ).

cnf(f_622_4,plain,
    ( c_Groups_Ouminus__class_Ouminus(U_2049,U_2050) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2049),c_Groups_Ouminus__class_Ouminus(U_2049,c_Groups_Oone__class_Oone(U_2049))),U_2050)
    | ~ class_Rings_Ocomm__ring__1(U_2049) ),
    inference(clausify,[status(thm)],[f_622_3]) ).

fof(f_623_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__def]) ).

fof(f_623_2,plain,
    ! [U_2053,U_2052,U_2051] :
      ( c_Groups_Ominus__class_Ominus(U_2051,U_2052,U_2053) = c_Groups_Oplus__class_Oplus(U_2051,U_2052,c_Groups_Ouminus__class_Ouminus(U_2051,U_2053))
      | ~ class_Groups_Ogroup__add(U_2051) ),
    inference(variable_rename,[status(thm)],[f_623_1]) ).

fof(f_623_3,plain,
    ! [U_2053,U_2052,U_2051] :
      ( c_Groups_Ominus__class_Ominus(U_2051,U_2052,U_2053) = c_Groups_Oplus__class_Oplus(U_2051,U_2052,c_Groups_Ouminus__class_Ouminus(U_2051,U_2053))
      | ~ class_Groups_Ogroup__add(U_2051) ),
    inference(definitional_conversion,[status(esa)],[f_623_2]) ).

cnf(f_623_4,plain,
    ( c_Groups_Ominus__class_Ominus(U_2051,U_2052,U_2053) = c_Groups_Oplus__class_Oplus(U_2051,U_2052,c_Groups_Ouminus__class_Ouminus(U_2051,U_2053))
    | ~ class_Groups_Ogroup__add(U_2051) ),
    inference(clausify,[status(thm)],[f_623_3]) ).

fof(f_624_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_ab__diff__minus]) ).

fof(f_624_2,plain,
    ! [U_2056,U_2055,U_2054] :
      ( c_Groups_Ominus__class_Ominus(U_2054,U_2055,U_2056) = c_Groups_Oplus__class_Oplus(U_2054,U_2055,c_Groups_Ouminus__class_Ouminus(U_2054,U_2056))
      | ~ class_Groups_Oab__group__add(U_2054) ),
    inference(variable_rename,[status(thm)],[f_624_1]) ).

fof(f_624_3,plain,
    ! [U_2054,U_2055,U_2056] :
      ( c_Groups_Ominus__class_Ominus(U_2054,U_2055,U_2056) = c_Groups_Oplus__class_Oplus(U_2054,U_2055,c_Groups_Ouminus__class_Ouminus(U_2054,U_2056))
      | ~ class_Groups_Oab__group__add(U_2054) ),
    inference(definitional_conversion,[status(esa)],[f_624_2]) ).

cnf(f_624_4,plain,
    ( c_Groups_Ominus__class_Ominus(U_2054,U_2055,U_2056) = c_Groups_Oplus__class_Oplus(U_2054,U_2055,c_Groups_Ouminus__class_Ouminus(U_2054,U_2056))
    | ~ class_Groups_Oab__group__add(U_2054) ),
    inference(clausify,[status(thm)],[f_624_3]) ).

fof(f_625_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)
      | ~ class_Groups_Ogroup__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__minus__eq__add]) ).

fof(f_625_2,plain,
    ! [U_2059,U_2058,U_2057] :
      ( c_Groups_Ominus__class_Ominus(U_2057,U_2058,c_Groups_Ouminus__class_Ouminus(U_2057,U_2059)) = c_Groups_Oplus__class_Oplus(U_2057,U_2058,U_2059)
      | ~ class_Groups_Ogroup__add(U_2057) ),
    inference(variable_rename,[status(thm)],[f_625_1]) ).

fof(f_625_3,plain,
    ! [U_2057,U_2058,U_2059] :
      ( c_Groups_Ominus__class_Ominus(U_2057,U_2058,c_Groups_Ouminus__class_Ouminus(U_2057,U_2059)) = c_Groups_Oplus__class_Oplus(U_2057,U_2058,U_2059)
      | ~ class_Groups_Ogroup__add(U_2057) ),
    inference(definitional_conversion,[status(esa)],[f_625_2]) ).

cnf(f_625_4,plain,
    ( c_Groups_Ominus__class_Ominus(U_2057,U_2058,c_Groups_Ouminus__class_Ouminus(U_2057,U_2059)) = c_Groups_Oplus__class_Oplus(U_2057,U_2058,U_2059)
    | ~ class_Groups_Ogroup__add(U_2057) ),
    inference(clausify,[status(thm)],[f_625_3]) ).

fof(f_626_1,plain,
    ! [V_y,V_x,T_a] :
      ( c_Groups_Ominus__class_Ominus(T_a,V_x,V_y) = c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y))
      | ~ class_Rings_Ocomm__ring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J]) ).

fof(f_626_2,plain,
    ! [U_2062,U_2061,U_2060] :
      ( c_Groups_Ominus__class_Ominus(U_2060,U_2061,U_2062) = c_Groups_Oplus__class_Oplus(U_2060,U_2061,c_Groups_Ouminus__class_Ouminus(U_2060,U_2062))
      | ~ class_Rings_Ocomm__ring__1(U_2060) ),
    inference(variable_rename,[status(thm)],[f_626_1]) ).

fof(f_626_3,plain,
    ! [U_2060,U_2061,U_2062] :
      ( c_Groups_Ominus__class_Ominus(U_2060,U_2061,U_2062) = c_Groups_Oplus__class_Oplus(U_2060,U_2061,c_Groups_Ouminus__class_Ouminus(U_2060,U_2062))
      | ~ class_Rings_Ocomm__ring__1(U_2060) ),
    inference(definitional_conversion,[status(esa)],[f_626_2]) ).

cnf(f_626_4,plain,
    ( c_Groups_Ominus__class_Ominus(U_2060,U_2061,U_2062) = c_Groups_Oplus__class_Oplus(U_2060,U_2061,c_Groups_Ouminus__class_Ouminus(U_2060,U_2062))
    | ~ class_Rings_Ocomm__ring__1(U_2060) ),
    inference(clausify,[status(thm)],[f_626_3]) ).

fof(f_627_1,plain,
    ! [V_x,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J]) ).

fof(f_627_2,plain,
    ! [U_2064,U_2063] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2063),U_2064),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2063)
      | ~ class_Rings_Ocomm__semiring__1(U_2063) ),
    inference(variable_rename,[status(thm)],[f_627_1]) ).

fof(f_627_3,plain,
    ! [U_2063,U_2064] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2063),U_2064),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2063)
      | ~ class_Rings_Ocomm__semiring__1(U_2063) ),
    inference(definitional_conversion,[status(esa)],[f_627_2]) ).

cnf(f_627_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2063),U_2064),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2063)
    | ~ class_Rings_Ocomm__semiring__1(U_2063) ),
    inference(clausify,[status(thm)],[f_627_3]) ).

fof(f_628_1,plain,
    ! [V_q,V_p,V_x,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J]) ).

fof(f_628_2,plain,
    ! [U_2068,U_2067,U_2066,U_2065] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2065),hAPP(hAPP(c_Power_Opower__class_Opower(U_2065),U_2066),U_2067)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2065),U_2066),U_2068)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2065),U_2066),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2067,U_2068))
      | ~ class_Rings_Ocomm__semiring__1(U_2065) ),
    inference(variable_rename,[status(thm)],[f_628_1]) ).

fof(f_628_3,plain,
    ! [U_2065,U_2066,U_2067,U_2068] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2065),hAPP(hAPP(c_Power_Opower__class_Opower(U_2065),U_2066),U_2067)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2065),U_2066),U_2068)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2065),U_2066),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2067,U_2068))
      | ~ class_Rings_Ocomm__semiring__1(U_2065) ),
    inference(definitional_conversion,[status(esa)],[f_628_2]) ).

cnf(f_628_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2065),hAPP(hAPP(c_Power_Opower__class_Opower(U_2065),U_2066),U_2067)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2065),U_2066),U_2068)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2065),U_2066),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2067,U_2068))
    | ~ class_Rings_Ocomm__semiring__1(U_2065) ),
    inference(clausify,[status(thm)],[f_628_3]) ).

fof(f_629_1,plain,
    ! [V_x,V_u] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_u),V_u)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)),
    inference(fof_nnf,[status(thm)],[fact_real__minus__mult__self__le]) ).

fof(f_629_2,plain,
    ! [U_2070,U_2069] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2069),U_2069)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2070),U_2070)),
    inference(variable_rename,[status(thm)],[f_629_1]) ).

fof(f_629_3,plain,
    ! [U_2069,U_2070] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2069),U_2069)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2070),U_2070)),
    inference(definitional_conversion,[status(esa)],[f_629_2]) ).

cnf(f_629_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2069),U_2069)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2070),U_2070)),
    inference(clausify,[status(thm)],[f_629_3]) ).

fof(f_630_1,plain,
    ! [T_a] :
      ( ~ c_Polynomial_Opos__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_not__pos__poly__0]) ).

fof(f_630_2,plain,
    ! [U_2071] :
      ( ~ c_Polynomial_Opos__poly(U_2071,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2071)))
      | ~ class_Rings_Olinordered__idom(U_2071) ),
    inference(variable_rename,[status(thm)],[f_630_1]) ).

fof(f_630_3,plain,
    ! [U_2071] :
      ( ~ c_Polynomial_Opos__poly(U_2071,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2071)))
      | ~ class_Rings_Olinordered__idom(U_2071) ),
    inference(definitional_conversion,[status(esa)],[f_630_2]) ).

cnf(f_630_4,plain,
    ( ~ c_Polynomial_Opos__poly(U_2071,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2071)))
    | ~ class_Rings_Olinordered__idom(U_2071) ),
    inference(clausify,[status(thm)],[f_630_3]) ).

fof(f_631_1,plain,
    ! [V_n_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
        | ! [B_m] : V_n_2 != c_Nat_OSuc(B_m) )
      & ( ? [B_m] : V_n_2 = c_Nat_OSuc(B_m)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_gr0__conv__Suc]) ).

fof(f_631_2,plain,
    ! [U_2074] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2074)
        | ! [U_2073] : U_2074 != c_Nat_OSuc(U_2073) )
      & ( ? [U_2072] : U_2074 = c_Nat_OSuc(U_2072)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2074) ) ),
    inference(variable_rename,[status(thm)],[f_631_1]) ).

fof(f_631_3,plain,
    ( ! [U_2076] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2076)
        | ! [U_2073] : U_2076 != c_Nat_OSuc(U_2073) )
    & ! [U_2075] :
        ( ? [U_2072] : U_2075 = c_Nat_OSuc(U_2072)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2075) ) ),
    inference(miniscope,[status(thm)],[f_631_2]) ).

fof(f_631_4,plain,
    ( ! [U_2076] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2076)
        | ! [U_2073] : U_2076 != c_Nat_OSuc(U_2073) )
    & ! [U_2075] :
        ( U_2075 = c_Nat_OSuc(sK16(U_2075))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2075) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_2072,sK16(U_2075))],[f_631_3]) ).

fof(f_631_5,plain,
    ( ! [U_2073,U_2076] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2076)
        | U_2076 != c_Nat_OSuc(U_2073) )
    & ! [U_2075] :
        ( U_2075 = c_Nat_OSuc(sK16(U_2075))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2075) ) ),
    inference(definitional_conversion,[status(esa)],[f_631_4]) ).

cnf(f_631_6,plain,
    ( U_2075 = c_Nat_OSuc(sK16(U_2075))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2075) ),
    inference(clausify,[status(thm)],[f_631_5]) ).

cnf(f_631_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2076)
    | U_2076 != c_Nat_OSuc(U_2073) ),
    inference(clausify,[status(thm)],[f_631_5]) ).

fof(f_632_1,plain,
    ! [V_n_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__Suc0]) ).

fof(f_632_2,plain,
    ! [U_2077] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2077,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_2077 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_2077 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2077,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(variable_rename,[status(thm)],[f_632_1]) ).

fof(f_632_3,plain,
    ( ! [U_2079] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2079,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_2079 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2078] :
        ( U_2078 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2078,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(miniscope,[status(thm)],[f_632_2]) ).

fof(f_632_4,plain,
    ( ! [U_2079] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2079,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_2079 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2078] :
        ( U_2078 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2078,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(definitional_conversion,[status(esa)],[f_632_3]) ).

cnf(f_632_5,plain,
    ( U_2078 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2078,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_632_4]) ).

cnf(f_632_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2079,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_2079 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_632_4]) ).

fof(f_633_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
        | ( ! [B_j] :
              ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2)
              | V_m_2 != c_Nat_OSuc(B_j) )
          & V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ? [B_j] :
            ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2)
            & V_m_2 = c_Nat_OSuc(B_j) )
        | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__0__disj]) ).

fof(f_633_2,plain,
    ! [U_2083,U_2082] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2082,c_Nat_OSuc(U_2083))
        | ( ! [U_2081] :
              ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2081,U_2083)
              | U_2082 != c_Nat_OSuc(U_2081) )
          & U_2082 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ? [U_2080] :
            ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2080,U_2083)
            & U_2082 = c_Nat_OSuc(U_2080) )
        | U_2082 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2082,c_Nat_OSuc(U_2083)) ) ),
    inference(variable_rename,[status(thm)],[f_633_1]) ).

fof(f_633_3,plain,
    ( ! [U_2087,U_2085] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2085,c_Nat_OSuc(U_2087))
        | ( ! [U_2081] :
              ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2081,U_2087)
              | U_2085 != c_Nat_OSuc(U_2081) )
          & U_2085 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_2086,U_2084] :
        ( ? [U_2080] :
            ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2080,U_2086)
            & U_2084 = c_Nat_OSuc(U_2080) )
        | U_2084 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2084,c_Nat_OSuc(U_2086)) ) ),
    inference(miniscope,[status(thm)],[f_633_2]) ).

fof(f_633_4,plain,
    ( ! [U_2087,U_2085] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2085,c_Nat_OSuc(U_2087))
        | ( ! [U_2081] :
              ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2081,U_2087)
              | U_2085 != c_Nat_OSuc(U_2081) )
          & U_2085 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_2086,U_2084] :
        ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK17(U_2086,U_2084),U_2086)
          & U_2084 = c_Nat_OSuc(sK17(U_2086,U_2084)) )
        | U_2084 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2084,c_Nat_OSuc(U_2086)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_2080,sK17(U_2086,U_2084))],[f_633_3]) ).

fof(f_633_5,plain,
    ( ! [U_2081,U_2085,U_2087] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2081,U_2087)
        | U_2085 != c_Nat_OSuc(U_2081)
        | ~ sP190(U_2081,U_2085,U_2087) )
    & ! [U_2081,U_2085,U_2087] :
        ( U_2085 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP190(U_2081,U_2085,U_2087) )
    & ! [U_2084,U_2086] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK17(U_2086,U_2084),U_2086)
        | ~ sP189(U_2084,U_2086) )
    & ! [U_2084,U_2086] :
        ( U_2084 = c_Nat_OSuc(sK17(U_2086,U_2084))
        | ~ sP189(U_2084,U_2086) )
    & ! [U_2081,U_2085,U_2087] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2085,c_Nat_OSuc(U_2087))
        | sP190(U_2081,U_2085,U_2087) )
    & ! [U_2084,U_2086] :
        ( sP189(U_2084,U_2086)
        | U_2084 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2084,c_Nat_OSuc(U_2086)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP189,sP190])],[f_633_4]) ).

cnf(f_633_6,plain,
    ( sP189(U_2084,U_2086)
    | U_2084 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2084,c_Nat_OSuc(U_2086)) ),
    inference(clausify,[status(thm)],[f_633_5]) ).

cnf(f_633_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2085,c_Nat_OSuc(U_2087))
    | sP190(U_2081,U_2085,U_2087) ),
    inference(clausify,[status(thm)],[f_633_5]) ).

cnf(f_633_8,plain,
    ( U_2084 = c_Nat_OSuc(sK17(U_2086,U_2084))
    | ~ sP189(U_2084,U_2086) ),
    inference(clausify,[status(thm)],[f_633_5]) ).

cnf(f_633_9,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK17(U_2086,U_2084),U_2086)
    | ~ sP189(U_2084,U_2086) ),
    inference(clausify,[status(thm)],[f_633_5]) ).

cnf(f_633_10,plain,
    ( U_2085 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP190(U_2081,U_2085,U_2087) ),
    inference(clausify,[status(thm)],[f_633_5]) ).

cnf(f_633_11,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2081,U_2087)
    | U_2085 != c_Nat_OSuc(U_2081)
    | ~ sP190(U_2081,U_2085,U_2087) ),
    inference(clausify,[status(thm)],[f_633_5]) ).

fof(f_634_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)
        | ( ( V_n_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | V_m_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
      & ( ( V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_one__is__add]) ).

fof(f_634_2,plain,
    ! [U_2089,U_2088] :
      ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2088,U_2089)
        | ( ( U_2089 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_2088 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_2089 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_2088 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
      & ( ( U_2089 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_2088 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_2089 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2088 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2088,U_2089) ) ),
    inference(variable_rename,[status(thm)],[f_634_1]) ).

fof(f_634_3,plain,
    ( ! [U_2093,U_2091] :
        ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2091,U_2093)
        | ( ( U_2093 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_2091 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_2093 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_2091 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
    & ! [U_2092,U_2090] :
        ( ( U_2092 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_2090 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_2092 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2090 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2090,U_2092) ) ),
    inference(miniscope,[status(thm)],[f_634_2]) ).

fof(f_634_4,plain,
    ( ! [U_2091,U_2093] :
        ( U_2093 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2091 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP193(U_2091,U_2093) )
    & ! [U_2091,U_2093] :
        ( U_2093 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2091 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP193(U_2091,U_2093) )
    & ! [U_2092,U_2090] :
        ( U_2092 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP192(U_2092,U_2090) )
    & ! [U_2092,U_2090] :
        ( U_2090 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP192(U_2092,U_2090) )
    & ! [U_2092,U_2090] :
        ( U_2092 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP191(U_2092,U_2090) )
    & ! [U_2092,U_2090] :
        ( U_2090 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP191(U_2092,U_2090) )
    & ! [U_2091,U_2093] :
        ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2091,U_2093)
        | sP193(U_2091,U_2093) )
    & ! [U_2092,U_2090] :
        ( sP192(U_2092,U_2090)
        | sP191(U_2092,U_2090)
        | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2090,U_2092) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP191,sP192,sP193])],[f_634_3]) ).

cnf(f_634_5,plain,
    ( sP192(U_2092,U_2090)
    | sP191(U_2092,U_2090)
    | c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2090,U_2092) ),
    inference(clausify,[status(thm)],[f_634_4]) ).

cnf(f_634_6,plain,
    ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2091,U_2093)
    | sP193(U_2091,U_2093) ),
    inference(clausify,[status(thm)],[f_634_4]) ).

cnf(f_634_7,plain,
    ( U_2090 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP191(U_2092,U_2090) ),
    inference(clausify,[status(thm)],[f_634_4]) ).

cnf(f_634_8,plain,
    ( U_2092 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP191(U_2092,U_2090) ),
    inference(clausify,[status(thm)],[f_634_4]) ).

cnf(f_634_9,plain,
    ( U_2090 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP192(U_2092,U_2090) ),
    inference(clausify,[status(thm)],[f_634_4]) ).

cnf(f_634_10,plain,
    ( U_2092 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP192(U_2092,U_2090) ),
    inference(clausify,[status(thm)],[f_634_4]) ).

cnf(f_634_11,plain,
    ( U_2093 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2091 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP193(U_2091,U_2093) ),
    inference(clausify,[status(thm)],[f_634_4]) ).

cnf(f_634_12,plain,
    ( U_2093 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_2091 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP193(U_2091,U_2093) ),
    inference(clausify,[status(thm)],[f_634_4]) ).

fof(f_635_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( ( V_n_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | V_m_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
      & ( ( V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(fof_nnf,[status(thm)],[fact_add__is__1]) ).

fof(f_635_2,plain,
    ! [U_2095,U_2094] :
      ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2094,U_2095) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( ( U_2095 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_2094 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_2095 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_2094 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
      & ( ( U_2095 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_2094 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_2095 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2094 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2094,U_2095) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_635_1]) ).

fof(f_635_3,plain,
    ( ! [U_2099,U_2097] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2097,U_2099) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( ( U_2099 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_2097 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_2099 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_2097 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
    & ! [U_2098,U_2096] :
        ( ( U_2098 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_2096 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_2098 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2096 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2096,U_2098) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_635_2]) ).

fof(f_635_4,plain,
    ( ! [U_2097,U_2099] :
        ( U_2099 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2097 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP196(U_2097,U_2099) )
    & ! [U_2097,U_2099] :
        ( U_2099 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2097 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP196(U_2097,U_2099) )
    & ! [U_2098,U_2096] :
        ( U_2098 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP195(U_2098,U_2096) )
    & ! [U_2098,U_2096] :
        ( U_2096 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP195(U_2098,U_2096) )
    & ! [U_2098,U_2096] :
        ( U_2098 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP194(U_2098,U_2096) )
    & ! [U_2098,U_2096] :
        ( U_2096 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP194(U_2098,U_2096) )
    & ! [U_2097,U_2099] :
        ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2097,U_2099) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | sP196(U_2097,U_2099) )
    & ! [U_2098,U_2096] :
        ( sP195(U_2098,U_2096)
        | sP194(U_2098,U_2096)
        | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2096,U_2098) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP194,sP195,sP196])],[f_635_3]) ).

cnf(f_635_5,plain,
    ( sP195(U_2098,U_2096)
    | sP194(U_2098,U_2096)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2096,U_2098) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_635_4]) ).

cnf(f_635_6,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2097,U_2099) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | sP196(U_2097,U_2099) ),
    inference(clausify,[status(thm)],[f_635_4]) ).

cnf(f_635_7,plain,
    ( U_2096 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP194(U_2098,U_2096) ),
    inference(clausify,[status(thm)],[f_635_4]) ).

cnf(f_635_8,plain,
    ( U_2098 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP194(U_2098,U_2096) ),
    inference(clausify,[status(thm)],[f_635_4]) ).

cnf(f_635_9,plain,
    ( U_2096 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP195(U_2098,U_2096) ),
    inference(clausify,[status(thm)],[f_635_4]) ).

cnf(f_635_10,plain,
    ( U_2098 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP195(U_2098,U_2096) ),
    inference(clausify,[status(thm)],[f_635_4]) ).

cnf(f_635_11,plain,
    ( U_2099 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2097 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP196(U_2097,U_2099) ),
    inference(clausify,[status(thm)],[f_635_4]) ).

cnf(f_635_12,plain,
    ( U_2099 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_2097 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP196(U_2097,U_2099) ),
    inference(clausify,[status(thm)],[f_635_4]) ).

fof(f_636_1,plain,
    ! [V_ab_2,V_x_2] :
      ( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_ab_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | V_x_2 != V_ab_2 )
      & ( V_x_2 = V_ab_2
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_ab_2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(fof_nnf,[status(thm)],[fact_real__add__minus__iff]) ).

fof(f_636_2,plain,
    ! [U_2101,U_2100] :
      ( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2100,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2101)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_2100 != U_2101 )
      & ( U_2100 = U_2101
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2100,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2101)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(variable_rename,[status(thm)],[f_636_1]) ).

fof(f_636_3,plain,
    ( ! [U_2105,U_2103] :
        ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2103,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2105)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_2103 != U_2105 )
    & ! [U_2104,U_2102] :
        ( U_2102 = U_2104
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2102,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2104)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(miniscope,[status(thm)],[f_636_2]) ).

fof(f_636_4,plain,
    ( ! [U_2105,U_2103] :
        ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2103,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2105)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_2103 != U_2105 )
    & ! [U_2104,U_2102] :
        ( U_2102 = U_2104
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2102,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2104)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(definitional_conversion,[status(esa)],[f_636_3]) ).

cnf(f_636_5,plain,
    ( U_2102 = U_2104
    | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2102,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2104)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(clausify,[status(thm)],[f_636_4]) ).

cnf(f_636_6,plain,
    ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2103,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2105)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | U_2103 != U_2105 ),
    inference(clausify,[status(thm)],[f_636_4]) ).

fof(f_637_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | V_y_2 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2) )
      & ( V_y_2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(fof_nnf,[status(thm)],[fact_real__add__eq__0__iff]) ).

fof(f_637_2,plain,
    ! [U_2107,U_2106] :
      ( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2106,U_2107) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_2107 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2106) )
      & ( U_2107 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2106)
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2106,U_2107) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(variable_rename,[status(thm)],[f_637_1]) ).

fof(f_637_3,plain,
    ( ! [U_2111,U_2109] :
        ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2109,U_2111) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_2111 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2109) )
    & ! [U_2110,U_2108] :
        ( U_2110 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2108)
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2108,U_2110) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(miniscope,[status(thm)],[f_637_2]) ).

fof(f_637_4,plain,
    ( ! [U_2109,U_2111] :
        ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2109,U_2111) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_2111 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2109) )
    & ! [U_2108,U_2110] :
        ( U_2110 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2108)
        | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2108,U_2110) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(definitional_conversion,[status(esa)],[f_637_3]) ).

cnf(f_637_5,plain,
    ( U_2110 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2108)
    | c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2108,U_2110) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(clausify,[status(thm)],[f_637_4]) ).

cnf(f_637_6,plain,
    ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2109,U_2111) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | U_2111 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2109) ),
    inference(clausify,[status(thm)],[f_637_4]) ).

fof(f_638_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | V_n_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | V_m_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( ( V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(fof_nnf,[status(thm)],[fact_mult__eq__1__iff]) ).

fof(f_638_2,plain,
    ! [U_2113,U_2112] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2112),U_2113) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2113 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2112 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( ( U_2113 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_2112 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2112),U_2113) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_638_1]) ).

fof(f_638_3,plain,
    ( ! [U_2117,U_2115] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2115),U_2117) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2117 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2115 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    & ! [U_2116,U_2114] :
        ( ( U_2116 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_2114 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2114),U_2116) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_638_2]) ).

fof(f_638_4,plain,
    ( ! [U_2116,U_2114] :
        ( U_2116 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP197(U_2116,U_2114) )
    & ! [U_2116,U_2114] :
        ( U_2114 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP197(U_2116,U_2114) )
    & ! [U_2117,U_2115] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2115),U_2117) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2117 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2115 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    & ! [U_2116,U_2114] :
        ( sP197(U_2116,U_2114)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2114),U_2116) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP197])],[f_638_3]) ).

cnf(f_638_5,plain,
    ( sP197(U_2116,U_2114)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2114),U_2116) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_638_4]) ).

cnf(f_638_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2115),U_2117) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_2117 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_2115 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_638_4]) ).

cnf(f_638_7,plain,
    ( U_2114 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP197(U_2116,U_2114) ),
    inference(clausify,[status(thm)],[f_638_4]) ).

cnf(f_638_8,plain,
    ( U_2116 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP197(U_2116,U_2114) ),
    inference(clausify,[status(thm)],[f_638_4]) ).

fof(f_639_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
        | ! [B_k] : V_n_2 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)) )
      & ( ? [B_k] : V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__iff__Suc__add]) ).

fof(f_639_2,plain,
    ! [U_2121,U_2120] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2120,U_2121)
        | ! [U_2119] : U_2121 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2120,U_2119)) )
      & ( ? [U_2118] : U_2121 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2120,U_2118))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2120,U_2121) ) ),
    inference(variable_rename,[status(thm)],[f_639_1]) ).

fof(f_639_3,plain,
    ( ! [U_2125,U_2123] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2123,U_2125)
        | ! [U_2119] : U_2125 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2123,U_2119)) )
    & ! [U_2124,U_2122] :
        ( ? [U_2118] : U_2124 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2122,U_2118))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2122,U_2124) ) ),
    inference(miniscope,[status(thm)],[f_639_2]) ).

fof(f_639_4,plain,
    ( ! [U_2125,U_2123] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2123,U_2125)
        | ! [U_2119] : U_2125 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2123,U_2119)) )
    & ! [U_2124,U_2122] :
        ( U_2124 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2122,sK18(U_2124,U_2122)))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2122,U_2124) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_2118,sK18(U_2124,U_2122))],[f_639_3]) ).

fof(f_639_5,plain,
    ( ! [U_2125,U_2119,U_2123] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2123,U_2125)
        | U_2125 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2123,U_2119)) )
    & ! [U_2124,U_2122] :
        ( U_2124 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2122,sK18(U_2124,U_2122)))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2122,U_2124) ) ),
    inference(definitional_conversion,[status(esa)],[f_639_4]) ).

cnf(f_639_6,plain,
    ( U_2124 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2122,sK18(U_2124,U_2122)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2122,U_2124) ),
    inference(clausify,[status(thm)],[f_639_5]) ).

cnf(f_639_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2123,U_2125)
    | U_2125 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2123,U_2119)) ),
    inference(clausify,[status(thm)],[f_639_5]) ).

fof(f_640_1,plain,
    ! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i))),
    inference(fof_nnf,[status(thm)],[fact_less__add__Suc2]) ).

fof(f_640_2,plain,
    ! [U_2127,U_2126] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2126,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2127,U_2126))),
    inference(variable_rename,[status(thm)],[f_640_1]) ).

fof(f_640_3,plain,
    ! [U_2126,U_2127] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2126,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2127,U_2126))),
    inference(definitional_conversion,[status(esa)],[f_640_2]) ).

cnf(f_640_4,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2126,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2127,U_2126))),
    inference(clausify,[status(thm)],[f_640_3]) ).

fof(f_641_1,plain,
    ! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m))),
    inference(fof_nnf,[status(thm)],[fact_less__add__Suc1]) ).

fof(f_641_2,plain,
    ! [U_2129,U_2128] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2128,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2128,U_2129))),
    inference(variable_rename,[status(thm)],[f_641_1]) ).

fof(f_641_3,plain,
    ! [U_2128,U_2129] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2128,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2128,U_2129))),
    inference(definitional_conversion,[status(esa)],[f_641_2]) ).

cnf(f_641_4,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2128,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2128,U_2129))),
    inference(clausify,[status(thm)],[f_641_3]) ).

fof(f_642_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le]) ).

fof(f_642_2,plain,
    ! [U_2131,U_2130] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2130,U_2131)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2130),U_2131) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2130),U_2131)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2130,U_2131) ) ),
    inference(variable_rename,[status(thm)],[f_642_1]) ).

fof(f_642_3,plain,
    ( ! [U_2135,U_2133] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2133,U_2135)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2133),U_2135) )
    & ! [U_2134,U_2132] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2132),U_2134)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2132,U_2134) ) ),
    inference(miniscope,[status(thm)],[f_642_2]) ).

fof(f_642_4,plain,
    ( ! [U_2133,U_2135] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2133,U_2135)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2133),U_2135) )
    & ! [U_2134,U_2132] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2132),U_2134)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2132,U_2134) ) ),
    inference(definitional_conversion,[status(esa)],[f_642_3]) ).

cnf(f_642_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2132),U_2134)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2132,U_2134) ),
    inference(clausify,[status(thm)],[f_642_4]) ).

cnf(f_642_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2133,U_2135)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2133),U_2135) ),
    inference(clausify,[status(thm)],[f_642_4]) ).

fof(f_643_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le]) ).

fof(f_643_2,plain,
    ! [U_2137,U_2136] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2136,c_Nat_OSuc(U_2137))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2136,U_2137) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2136,U_2137)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2136,c_Nat_OSuc(U_2137)) ) ),
    inference(variable_rename,[status(thm)],[f_643_1]) ).

fof(f_643_3,plain,
    ( ! [U_2141,U_2139] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2139,c_Nat_OSuc(U_2141))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2139,U_2141) )
    & ! [U_2140,U_2138] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2138,U_2140)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2138,c_Nat_OSuc(U_2140)) ) ),
    inference(miniscope,[status(thm)],[f_643_2]) ).

fof(f_643_4,plain,
    ( ! [U_2139,U_2141] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2139,c_Nat_OSuc(U_2141))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2139,U_2141) )
    & ! [U_2138,U_2140] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2138,U_2140)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2138,c_Nat_OSuc(U_2140)) ) ),
    inference(definitional_conversion,[status(esa)],[f_643_3]) ).

cnf(f_643_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2138,U_2140)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2138,c_Nat_OSuc(U_2140)) ),
    inference(clausify,[status(thm)],[f_643_4]) ).

cnf(f_643_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2139,c_Nat_OSuc(U_2141))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2139,U_2141) ),
    inference(clausify,[status(thm)],[f_643_4]) ).

fof(f_644_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_n_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_n_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__le__eq]) ).

fof(f_644_2,plain,
    ! [U_2143,U_2142] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2142),U_2143)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2142,U_2143) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2142,U_2143)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2142),U_2143) ) ),
    inference(variable_rename,[status(thm)],[f_644_1]) ).

fof(f_644_3,plain,
    ( ! [U_2147,U_2145] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2145),U_2147)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2145,U_2147) )
    & ! [U_2146,U_2144] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2144,U_2146)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2144),U_2146) ) ),
    inference(miniscope,[status(thm)],[f_644_2]) ).

fof(f_644_4,plain,
    ( ! [U_2145,U_2147] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2145),U_2147)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2145,U_2147) )
    & ! [U_2144,U_2146] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2144,U_2146)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2144),U_2146) ) ),
    inference(definitional_conversion,[status(esa)],[f_644_3]) ).

cnf(f_644_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2144,U_2146)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2144),U_2146) ),
    inference(clausify,[status(thm)],[f_644_4]) ).

cnf(f_644_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2145),U_2147)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2145,U_2147) ),
    inference(clausify,[status(thm)],[f_644_4]) ).

fof(f_645_1,plain,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ),
    inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc]) ).

fof(f_645_2,plain,
    ! [U_2149,U_2148] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2148,c_Nat_OSuc(U_2149))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2148,U_2149) ),
    inference(variable_rename,[status(thm)],[f_645_1]) ).

fof(f_645_3,plain,
    ! [U_2149,U_2148] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2148,c_Nat_OSuc(U_2149))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2148,U_2149) ),
    inference(definitional_conversion,[status(esa)],[f_645_2]) ).

cnf(f_645_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2148,c_Nat_OSuc(U_2149))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2148,U_2149) ),
    inference(clausify,[status(thm)],[f_645_3]) ).

fof(f_646_1,plain,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__leI]) ).

fof(f_646_2,plain,
    ! [U_2151,U_2150] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2150),U_2151)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2150,U_2151) ),
    inference(variable_rename,[status(thm)],[f_646_1]) ).

fof(f_646_3,plain,
    ! [U_2150,U_2151] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2150),U_2151)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2150,U_2151) ),
    inference(definitional_conversion,[status(esa)],[f_646_2]) ).

cnf(f_646_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2150),U_2151)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2150,U_2151) ),
    inference(clausify,[status(thm)],[f_646_3]) ).

fof(f_647_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))
          | V_n_2 != V_m_2 )
        & ( V_n_2 = V_m_2
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) ),
    inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq]) ).

fof(f_647_2,plain,
    ! [U_2153,U_2152] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2153,c_Nat_OSuc(U_2152))
          | U_2153 != U_2152 )
        & ( U_2153 = U_2152
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2153,c_Nat_OSuc(U_2152)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2152,U_2153) ),
    inference(variable_rename,[status(thm)],[f_647_1]) ).

fof(f_647_3,plain,
    ( ! [U_2152,U_2153] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2153,c_Nat_OSuc(U_2152))
        | U_2153 != U_2152
        | ~ sP198(U_2152,U_2153) )
    & ! [U_2152,U_2153] :
        ( U_2153 = U_2152
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2153,c_Nat_OSuc(U_2152))
        | ~ sP198(U_2152,U_2153) )
    & ! [U_2152,U_2153] :
        ( sP198(U_2152,U_2153)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2152,U_2153) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP198])],[f_647_2]) ).

cnf(f_647_4,plain,
    ( sP198(U_2152,U_2153)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2152,U_2153) ),
    inference(clausify,[status(thm)],[f_647_3]) ).

cnf(f_647_5,plain,
    ( U_2153 = U_2152
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2153,c_Nat_OSuc(U_2152))
    | ~ sP198(U_2152,U_2153) ),
    inference(clausify,[status(thm)],[f_647_3]) ).

cnf(f_647_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2153,c_Nat_OSuc(U_2152))
    | U_2153 != U_2152
    | ~ sP198(U_2152,U_2153) ),
    inference(clausify,[status(thm)],[f_647_3]) ).

fof(f_648_1,plain,
    ! [V_n,V_m] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD]) ).

fof(f_648_2,plain,
    ! [U_2155,U_2154] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2154,U_2155)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2154),U_2155) ),
    inference(variable_rename,[status(thm)],[f_648_1]) ).

fof(f_648_3,plain,
    ! [U_2154,U_2155] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2154,U_2155)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2154),U_2155) ),
    inference(definitional_conversion,[status(esa)],[f_648_2]) ).

cnf(f_648_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2154,U_2155)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2154),U_2155) ),
    inference(clausify,[status(thm)],[f_648_3]) ).

fof(f_649_1,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_One__nat__def]) ).

fof(f_649_2,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_649_1]) ).

cnf(f_649_3,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_649_2]) ).

fof(f_650_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__mult__less__cancel1]) ).

fof(f_650_2,plain,
    ! [U_2158,U_2157,U_2156] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2156)),U_2157),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2156)),U_2158))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2157,U_2158) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2157,U_2158)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2156)),U_2157),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2156)),U_2158)) ) ),
    inference(variable_rename,[status(thm)],[f_650_1]) ).

fof(f_650_3,plain,
    ( ! [U_2164,U_2162] :
        ( ! [U_2160] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2160)),U_2162),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2160)),U_2164))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2162,U_2164) )
    & ! [U_2163,U_2161] :
        ( ! [U_2159] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2159)),U_2161),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2159)),U_2163))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2161,U_2163) ) ),
    inference(miniscope,[status(thm)],[f_650_2]) ).

fof(f_650_4,plain,
    ( ! [U_2162,U_2164,U_2160] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2160)),U_2162),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2160)),U_2164))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2162,U_2164) )
    & ! [U_2163,U_2161,U_2159] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2159)),U_2161),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2159)),U_2163))
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2161,U_2163) ) ),
    inference(definitional_conversion,[status(esa)],[f_650_3]) ).

cnf(f_650_5,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2159)),U_2161),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2159)),U_2163))
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2161,U_2163) ),
    inference(clausify,[status(thm)],[f_650_4]) ).

cnf(f_650_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2160)),U_2162),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2160)),U_2164))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2162,U_2164) ),
    inference(clausify,[status(thm)],[f_650_4]) ).

fof(f_651_1,plain,
    ! [V_n,V_m] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m)),
    inference(fof_nnf,[status(thm)],[fact_diff__less__Suc]) ).

fof(f_651_2,plain,
    ! [U_2166,U_2165] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2165,U_2166),c_Nat_OSuc(U_2165)),
    inference(variable_rename,[status(thm)],[f_651_1]) ).

fof(f_651_3,plain,
    ! [U_2166,U_2165] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2165,U_2166),c_Nat_OSuc(U_2165)),
    inference(definitional_conversion,[status(esa)],[f_651_2]) ).

cnf(f_651_4,plain,
    c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2165,U_2166),c_Nat_OSuc(U_2165)),
    inference(clausify,[status(thm)],[f_651_3]) ).

fof(f_652_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
    inference(fof_nnf,[status(thm)],[fact_mult__Suc__right]) ).

fof(f_652_2,plain,
    ! [U_2168,U_2167] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2167),c_Nat_OSuc(U_2168)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2167,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2167),U_2168)),
    inference(variable_rename,[status(thm)],[f_652_1]) ).

fof(f_652_3,plain,
    ! [U_2167,U_2168] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2167),c_Nat_OSuc(U_2168)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2167,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2167),U_2168)),
    inference(definitional_conversion,[status(esa)],[f_652_2]) ).

cnf(f_652_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2167),c_Nat_OSuc(U_2168)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2167,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2167),U_2168)),
    inference(clausify,[status(thm)],[f_652_3]) ).

fof(f_653_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
    inference(fof_nnf,[status(thm)],[fact_mult__Suc]) ).

fof(f_653_2,plain,
    ! [U_2170,U_2169] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2169)),U_2170) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2170,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2169),U_2170)),
    inference(variable_rename,[status(thm)],[f_653_1]) ).

fof(f_653_3,plain,
    ! [U_2169,U_2170] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2169)),U_2170) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2170,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2169),U_2170)),
    inference(definitional_conversion,[status(esa)],[f_653_2]) ).

cnf(f_653_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2169)),U_2170) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2170,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2169),U_2170)),
    inference(clausify,[status(thm)],[f_653_3]) ).

fof(f_654_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,V_n_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__mult__le__cancel1]) ).

fof(f_654_2,plain,
    ! [U_2173,U_2172,U_2171] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2171)),U_2172),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2171)),U_2173))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2172,U_2173) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2172,U_2173)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2171)),U_2172),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2171)),U_2173)) ) ),
    inference(variable_rename,[status(thm)],[f_654_1]) ).

fof(f_654_3,plain,
    ( ! [U_2179,U_2177] :
        ( ! [U_2175] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2175)),U_2177),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2175)),U_2179))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2177,U_2179) )
    & ! [U_2178,U_2176] :
        ( ! [U_2174] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2174)),U_2176),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2174)),U_2178))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2176,U_2178) ) ),
    inference(miniscope,[status(thm)],[f_654_2]) ).

fof(f_654_4,plain,
    ( ! [U_2179,U_2175,U_2177] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2175)),U_2177),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2175)),U_2179))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2177,U_2179) )
    & ! [U_2178,U_2176,U_2174] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2174)),U_2176),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2174)),U_2178))
        | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2176,U_2178) ) ),
    inference(definitional_conversion,[status(esa)],[f_654_3]) ).

cnf(f_654_5,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2174)),U_2176),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2174)),U_2178))
    | c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2176,U_2178) ),
    inference(clausify,[status(thm)],[f_654_4]) ).

cnf(f_654_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2175)),U_2177),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2175)),U_2179))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2177,U_2179) ),
    inference(clausify,[status(thm)],[f_654_4]) ).

fof(f_655_1,plain,
    ! [V_m,V_n] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__diff__le]) ).

fof(f_655_2,plain,
    ! [U_2181,U_2180] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2181),U_2180) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2181,U_2180))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2180,U_2181) ),
    inference(variable_rename,[status(thm)],[f_655_1]) ).

fof(f_655_3,plain,
    ! [U_2180,U_2181] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2181),U_2180) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2181,U_2180))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2180,U_2181) ),
    inference(definitional_conversion,[status(esa)],[f_655_2]) ).

cnf(f_655_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2181),U_2180) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2181,U_2180))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2180,U_2181) ),
    inference(clausify,[status(thm)],[f_655_3]) ).

fof(f_656_1,plain,
    ! [V_n] : c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n),
    inference(fof_nnf,[status(thm)],[fact_Suc__eq__plus1__left]) ).

fof(f_656_2,plain,
    ! [U_2182] : c_Nat_OSuc(U_2182) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_2182),
    inference(variable_rename,[status(thm)],[f_656_1]) ).

fof(f_656_3,plain,
    ! [U_2182] : c_Nat_OSuc(U_2182) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_2182),
    inference(definitional_conversion,[status(esa)],[f_656_2]) ).

cnf(f_656_4,plain,
    c_Nat_OSuc(U_2182) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_2182),
    inference(clausify,[status(thm)],[f_656_3]) ).

fof(f_657_1,plain,
    ! [V_n] : c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_Suc__eq__plus1]) ).

fof(f_657_2,plain,
    ! [U_2183] : c_Nat_OSuc(U_2183) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2183,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_657_1]) ).

fof(f_657_3,plain,
    ! [U_2183] : c_Nat_OSuc(U_2183) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2183,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_657_2]) ).

cnf(f_657_4,plain,
    c_Nat_OSuc(U_2183) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2183,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_657_3]) ).

fof(f_658_1,plain,
    ! [V_x] :
      ( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
    inference(fof_nnf,[status(thm)],[fact_natfloor__add__one]) ).

fof(f_658_2,plain,
    ! [U_2184] :
      ( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2184,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_2184),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2184) ),
    inference(variable_rename,[status(thm)],[f_658_1]) ).

fof(f_658_3,plain,
    ! [U_2184] :
      ( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2184,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_2184),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2184) ),
    inference(definitional_conversion,[status(esa)],[f_658_2]) ).

cnf(f_658_4,plain,
    ( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2184,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_2184),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2184) ),
    inference(clausify,[status(thm)],[f_658_3]) ).

fof(f_659_1,plain,
    ! [V_n] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n,
    inference(fof_nnf,[status(thm)],[fact_diff__Suc__1]) ).

fof(f_659_2,plain,
    ! [U_2185] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2185),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2185,
    inference(variable_rename,[status(thm)],[f_659_1]) ).

fof(f_659_3,plain,
    ! [U_2185] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2185),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2185,
    inference(definitional_conversion,[status(esa)],[f_659_2]) ).

cnf(f_659_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2185),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2185,
    inference(clausify,[status(thm)],[f_659_3]) ).

fof(f_660_1,plain,
    ! [V_n,V_m] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n),
    inference(fof_nnf,[status(thm)],[fact_diff__Suc__eq__diff__pred]) ).

fof(f_660_2,plain,
    ! [U_2187,U_2186] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2186,c_Nat_OSuc(U_2187)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2186,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2187),
    inference(variable_rename,[status(thm)],[f_660_1]) ).

fof(f_660_3,plain,
    ! [U_2186,U_2187] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2186,c_Nat_OSuc(U_2187)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2186,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2187),
    inference(definitional_conversion,[status(esa)],[f_660_2]) ).

cnf(f_660_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2186,c_Nat_OSuc(U_2187)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2186,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2187),
    inference(clausify,[status(thm)],[f_660_3]) ).

fof(f_661_1,plain,
    ! [V_s,V_r] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_r,V_s) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_s)),
    inference(fof_nnf,[status(thm)],[fact_real__diff__def]) ).

fof(f_661_2,plain,
    ! [U_2189,U_2188] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2188,U_2189) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2188,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2189)),
    inference(variable_rename,[status(thm)],[f_661_1]) ).

fof(f_661_3,plain,
    ! [U_2188,U_2189] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2188,U_2189) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2188,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2189)),
    inference(definitional_conversion,[status(esa)],[f_661_2]) ).

cnf(f_661_4,plain,
    c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2188,U_2189) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2188,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2189)),
    inference(clausify,[status(thm)],[f_661_3]) ).

fof(f_662_1,plain,
    ! [V_y,V_x] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y)),
    inference(fof_nnf,[status(thm)],[fact_minus__real__def]) ).

fof(f_662_2,plain,
    ! [U_2191,U_2190] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2190,U_2191) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2190,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2191)),
    inference(variable_rename,[status(thm)],[f_662_1]) ).

fof(f_662_3,plain,
    ! [U_2191,U_2190] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2190,U_2191) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2190,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2191)),
    inference(definitional_conversion,[status(esa)],[f_662_2]) ).

cnf(f_662_4,plain,
    c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2190,U_2191) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2190,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2191)),
    inference(clausify,[status(thm)],[f_662_3]) ).

fof(f_663_1,plain,
    ! [V_y,V_x,V_z] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_y))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z) ),
    inference(fof_nnf,[status(thm)],[fact_real__mult__less__mono2]) ).

fof(f_663_2,plain,
    ! [U_2194,U_2193,U_2192] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2192),U_2193),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2192),U_2194))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2193,U_2194)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2192) ),
    inference(variable_rename,[status(thm)],[f_663_1]) ).

fof(f_663_3,plain,
    ! [U_2192,U_2193,U_2194] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2192),U_2193),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2192),U_2194))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2193,U_2194)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2192) ),
    inference(definitional_conversion,[status(esa)],[f_663_2]) ).

cnf(f_663_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2192),U_2193),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2192),U_2194))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2193,U_2194)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2192) ),
    inference(clausify,[status(thm)],[f_663_3]) ).

fof(f_664_1,plain,
    ! [V_y,V_x] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
    inference(fof_nnf,[status(thm)],[fact_real__mult__order]) ).

fof(f_664_2,plain,
    ! [U_2196,U_2195] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2195),U_2196))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2196)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2195) ),
    inference(variable_rename,[status(thm)],[f_664_1]) ).

fof(f_664_3,plain,
    ! [U_2195,U_2196] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2195),U_2196))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2196)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2195) ),
    inference(definitional_conversion,[status(esa)],[f_664_2]) ).

cnf(f_664_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2195),U_2196))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2196)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2195) ),
    inference(clausify,[status(thm)],[f_664_3]) ).

fof(f_665_1,plain,
    ! [V_y_2,V_x_2,V_z_2] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))
          | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) )
        & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
          | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2) ),
    inference(fof_nnf,[status(thm)],[fact_real__mult__less__iff1]) ).

fof(f_665_2,plain,
    ! [U_2199,U_2198,U_2197] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2198),U_2197),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2199),U_2197))
          | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2198,U_2199) )
        & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2198,U_2199)
          | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2198),U_2197),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2199),U_2197)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2197) ),
    inference(variable_rename,[status(thm)],[f_665_1]) ).

fof(f_665_3,plain,
    ( ! [U_2197,U_2198,U_2199] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2198),U_2197),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2199),U_2197))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2198,U_2199)
        | ~ sP199(U_2197,U_2198,U_2199) )
    & ! [U_2197,U_2198,U_2199] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2198,U_2199)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2198),U_2197),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2199),U_2197))
        | ~ sP199(U_2197,U_2198,U_2199) )
    & ! [U_2197,U_2198,U_2199] :
        ( sP199(U_2197,U_2198,U_2199)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2197) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP199])],[f_665_2]) ).

cnf(f_665_4,plain,
    ( sP199(U_2197,U_2198,U_2199)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2197) ),
    inference(clausify,[status(thm)],[f_665_3]) ).

cnf(f_665_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2198,U_2199)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2198),U_2197),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2199),U_2197))
    | ~ sP199(U_2197,U_2198,U_2199) ),
    inference(clausify,[status(thm)],[f_665_3]) ).

cnf(f_665_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2198),U_2197),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2199),U_2197))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2198,U_2199)
    | ~ sP199(U_2197,U_2198,U_2199) ),
    inference(clausify,[status(thm)],[f_665_3]) ).

fof(f_666_1,plain,
    ! [V_x,T_a] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_norm__not__less__zero]) ).

fof(f_666_2,plain,
    ! [U_2201,U_2200] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2200,U_2201),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      | ~ class_RealVector_Oreal__normed__vector(U_2200) ),
    inference(variable_rename,[status(thm)],[f_666_1]) ).

fof(f_666_3,plain,
    ! [U_2200,U_2201] :
      ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2200,U_2201),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
      | ~ class_RealVector_Oreal__normed__vector(U_2200) ),
    inference(definitional_conversion,[status(esa)],[f_666_2]) ).

cnf(f_666_4,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2200,U_2201),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ class_RealVector_Oreal__normed__vector(U_2200) ),
    inference(clausify,[status(thm)],[f_666_3]) ).

fof(f_667_1,plain,
    ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)),
    inference(fof_nnf,[status(thm)],[fact_complex__mod__minus__le__complex__mod]) ).

fof(f_667_2,plain,
    ! [U_2202] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2202)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2202)),
    inference(variable_rename,[status(thm)],[f_667_1]) ).

fof(f_667_3,plain,
    ! [U_2202] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2202)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2202)),
    inference(definitional_conversion,[status(esa)],[f_667_2]) ).

cnf(f_667_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2202)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2202)),
    inference(clausify,[status(thm)],[f_667_3]) ).

fof(f_668_1,plain,
    ! [V_q,V_p,T_a] :
      ( c_Polynomial_Opos__poly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q))
      | ~ c_Polynomial_Opos__poly(T_a,V_q)
      | ~ c_Polynomial_Opos__poly(T_a,V_p)
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_pos__poly__add]) ).

fof(f_668_2,plain,
    ! [U_2205,U_2204,U_2203] :
      ( c_Polynomial_Opos__poly(U_2203,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_2203),U_2204,U_2205))
      | ~ c_Polynomial_Opos__poly(U_2203,U_2205)
      | ~ c_Polynomial_Opos__poly(U_2203,U_2204)
      | ~ class_Rings_Olinordered__idom(U_2203) ),
    inference(variable_rename,[status(thm)],[f_668_1]) ).

fof(f_668_3,plain,
    ! [U_2205,U_2203,U_2204] :
      ( c_Polynomial_Opos__poly(U_2203,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_2203),U_2204,U_2205))
      | ~ c_Polynomial_Opos__poly(U_2203,U_2205)
      | ~ c_Polynomial_Opos__poly(U_2203,U_2204)
      | ~ class_Rings_Olinordered__idom(U_2203) ),
    inference(definitional_conversion,[status(esa)],[f_668_2]) ).

cnf(f_668_4,plain,
    ( c_Polynomial_Opos__poly(U_2203,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_2203),U_2204,U_2205))
    | ~ c_Polynomial_Opos__poly(U_2203,U_2205)
    | ~ c_Polynomial_Opos__poly(U_2203,U_2204)
    | ~ class_Rings_Olinordered__idom(U_2203) ),
    inference(clausify,[status(thm)],[f_668_3]) ).

fof(f_669_1,plain,
    ! [V_q,V_p,T_a] :
      ( c_Polynomial_Opos__poly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))
      | ~ c_Polynomial_Opos__poly(T_a,V_q)
      | ~ c_Polynomial_Opos__poly(T_a,V_p)
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_pos__poly__mult]) ).

fof(f_669_2,plain,
    ! [U_2208,U_2207,U_2206] :
      ( c_Polynomial_Opos__poly(U_2206,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_2206)),U_2207),U_2208))
      | ~ c_Polynomial_Opos__poly(U_2206,U_2208)
      | ~ c_Polynomial_Opos__poly(U_2206,U_2207)
      | ~ class_Rings_Olinordered__idom(U_2206) ),
    inference(variable_rename,[status(thm)],[f_669_1]) ).

fof(f_669_3,plain,
    ! [U_2206,U_2207,U_2208] :
      ( c_Polynomial_Opos__poly(U_2206,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_2206)),U_2207),U_2208))
      | ~ c_Polynomial_Opos__poly(U_2206,U_2208)
      | ~ c_Polynomial_Opos__poly(U_2206,U_2207)
      | ~ class_Rings_Olinordered__idom(U_2206) ),
    inference(definitional_conversion,[status(esa)],[f_669_2]) ).

cnf(f_669_4,plain,
    ( c_Polynomial_Opos__poly(U_2206,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_2206)),U_2207),U_2208))
    | ~ c_Polynomial_Opos__poly(U_2206,U_2208)
    | ~ c_Polynomial_Opos__poly(U_2206,U_2207)
    | ~ class_Rings_Olinordered__idom(U_2206) ),
    inference(clausify,[status(thm)],[f_669_3]) ).

fof(f_670_1,plain,
    ! [V_q,T_a] :
      ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_q)
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_diff__poly__code_I1_J]) ).

fof(f_670_2,plain,
    ! [U_2210,U_2209] :
      ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2209),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2209)),U_2210) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_2209),U_2210)
      | ~ class_Groups_Oab__group__add(U_2209) ),
    inference(variable_rename,[status(thm)],[f_670_1]) ).

fof(f_670_3,plain,
    ! [U_2209,U_2210] :
      ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2209),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2209)),U_2210) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_2209),U_2210)
      | ~ class_Groups_Oab__group__add(U_2209) ),
    inference(definitional_conversion,[status(esa)],[f_670_2]) ).

cnf(f_670_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2209),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2209)),U_2210) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_2209),U_2210)
    | ~ class_Groups_Oab__group__add(U_2209) ),
    inference(clausify,[status(thm)],[f_670_3]) ).

fof(f_671_1,plain,
    ! [V_x] :
      ( c_RComplete_Onatfloor(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(fof_nnf,[status(thm)],[fact_natfloor__neg]) ).

fof(f_671_2,plain,
    ! [U_2211] :
      ( c_RComplete_Onatfloor(U_2211) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2211,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(variable_rename,[status(thm)],[f_671_1]) ).

fof(f_671_3,plain,
    ! [U_2211] :
      ( c_RComplete_Onatfloor(U_2211) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2211,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(definitional_conversion,[status(esa)],[f_671_2]) ).

cnf(f_671_4,plain,
    ( c_RComplete_Onatfloor(U_2211) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2211,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(clausify,[status(thm)],[f_671_3]) ).

fof(f_672_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)
          | ( ~ c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2))
            & V_x_2 != V_y_2 ) )
        & ( c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2))
          | V_x_2 = V_y_2
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2) ) )
      | ~ class_Rings_Olinordered__idom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_less__eq__poly__def]) ).

fof(f_672_2,plain,
    ! [U_2214,U_2213,U_2212] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(U_2212),U_2213,U_2214)
          | ( ~ c_Polynomial_Opos__poly(U_2212,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2212),U_2214,U_2213))
            & U_2213 != U_2214 ) )
        & ( c_Polynomial_Opos__poly(U_2212,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2212),U_2214,U_2213))
          | U_2213 = U_2214
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(U_2212),U_2213,U_2214) ) )
      | ~ class_Rings_Olinordered__idom(U_2212) ),
    inference(variable_rename,[status(thm)],[f_672_1]) ).

fof(f_672_3,plain,
    ( ! [U_2213,U_2212,U_2214] :
        ( ~ c_Polynomial_Opos__poly(U_2212,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2212),U_2214,U_2213))
        | ~ sP200(U_2213,U_2212,U_2214) )
    & ! [U_2213,U_2212,U_2214] :
        ( U_2213 != U_2214
        | ~ sP200(U_2213,U_2212,U_2214) )
    & ! [U_2213,U_2212,U_2214] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(U_2212),U_2213,U_2214)
        | sP200(U_2213,U_2212,U_2214)
        | ~ sP201(U_2213,U_2212,U_2214) )
    & ! [U_2213,U_2212,U_2214] :
        ( c_Polynomial_Opos__poly(U_2212,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2212),U_2214,U_2213))
        | U_2213 = U_2214
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(U_2212),U_2213,U_2214)
        | ~ sP201(U_2213,U_2212,U_2214) )
    & ! [U_2213,U_2212,U_2214] :
        ( sP201(U_2213,U_2212,U_2214)
        | ~ class_Rings_Olinordered__idom(U_2212) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP200,sP201])],[f_672_2]) ).

cnf(f_672_4,plain,
    ( sP201(U_2213,U_2212,U_2214)
    | ~ class_Rings_Olinordered__idom(U_2212) ),
    inference(clausify,[status(thm)],[f_672_3]) ).

cnf(f_672_5,plain,
    ( c_Polynomial_Opos__poly(U_2212,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2212),U_2214,U_2213))
    | U_2213 = U_2214
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(U_2212),U_2213,U_2214)
    | ~ sP201(U_2213,U_2212,U_2214) ),
    inference(clausify,[status(thm)],[f_672_3]) ).

cnf(f_672_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(U_2212),U_2213,U_2214)
    | sP200(U_2213,U_2212,U_2214)
    | ~ sP201(U_2213,U_2212,U_2214) ),
    inference(clausify,[status(thm)],[f_672_3]) ).

cnf(f_672_7,plain,
    ( U_2213 != U_2214
    | ~ sP200(U_2213,U_2212,U_2214) ),
    inference(clausify,[status(thm)],[f_672_3]) ).

cnf(f_672_8,plain,
    ( ~ c_Polynomial_Opos__poly(U_2212,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2212),U_2214,U_2213))
    | ~ sP200(U_2213,U_2212,U_2214) ),
    inference(clausify,[status(thm)],[f_672_3]) ).

fof(f_673_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_real__0__le__add__iff]) ).

fof(f_673_2,plain,
    ! [U_2216,U_2215] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2215,U_2216))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2215),U_2216) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2215),U_2216)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2215,U_2216)) ) ),
    inference(variable_rename,[status(thm)],[f_673_1]) ).

fof(f_673_3,plain,
    ( ! [U_2220,U_2218] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2218,U_2220))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2218),U_2220) )
    & ! [U_2219,U_2217] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2217),U_2219)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2217,U_2219)) ) ),
    inference(miniscope,[status(thm)],[f_673_2]) ).

fof(f_673_4,plain,
    ( ! [U_2220,U_2218] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2218,U_2220))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2218),U_2220) )
    & ! [U_2219,U_2217] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2217),U_2219)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2217,U_2219)) ) ),
    inference(definitional_conversion,[status(esa)],[f_673_3]) ).

cnf(f_673_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2217),U_2219)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2217,U_2219)) ),
    inference(clausify,[status(thm)],[f_673_4]) ).

cnf(f_673_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2218,U_2220))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2218),U_2220) ),
    inference(clausify,[status(thm)],[f_673_4]) ).

fof(f_674_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
    inference(fof_nnf,[status(thm)],[fact_real__add__le__0__iff]) ).

fof(f_674_2,plain,
    ! [U_2222,U_2221] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2221,U_2222),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2222,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2221)) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2222,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2221))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2221,U_2222),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
    inference(variable_rename,[status(thm)],[f_674_1]) ).

fof(f_674_3,plain,
    ( ! [U_2226,U_2224] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2224,U_2226),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2226,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2224)) )
    & ! [U_2225,U_2223] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2225,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2223))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2223,U_2225),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
    inference(miniscope,[status(thm)],[f_674_2]) ).

fof(f_674_4,plain,
    ( ! [U_2226,U_2224] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2224,U_2226),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2226,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2224)) )
    & ! [U_2223,U_2225] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2225,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2223))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2223,U_2225),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
    inference(definitional_conversion,[status(esa)],[f_674_3]) ).

cnf(f_674_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2225,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2223))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2223,U_2225),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(clausify,[status(thm)],[f_674_4]) ).

cnf(f_674_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2224,U_2226),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2226,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_2224)) ),
    inference(clausify,[status(thm)],[f_674_4]) ).

fof(f_675_1,plain,
    ! [V_m,V_n] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) ),
    inference(fof_nnf,[status(thm)],[fact_n__less__m__mult__n]) ).

fof(f_675_2,plain,
    ! [U_2228,U_2227] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2227,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2228),U_2227))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2228)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2227) ),
    inference(variable_rename,[status(thm)],[f_675_1]) ).

fof(f_675_3,plain,
    ! [U_2227,U_2228] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2227,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2228),U_2227))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2228)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2227) ),
    inference(definitional_conversion,[status(esa)],[f_675_2]) ).

cnf(f_675_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2227,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2228),U_2227))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2228)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2227) ),
    inference(clausify,[status(thm)],[f_675_3]) ).

fof(f_676_1,plain,
    ! [V_m,V_n] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) ),
    inference(fof_nnf,[status(thm)],[fact_n__less__n__mult__m]) ).

fof(f_676_2,plain,
    ! [U_2230,U_2229] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2229,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2229),U_2230))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2230)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2229) ),
    inference(variable_rename,[status(thm)],[f_676_1]) ).

fof(f_676_3,plain,
    ! [U_2229,U_2230] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2229,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2229),U_2230))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2230)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2229) ),
    inference(definitional_conversion,[status(esa)],[f_676_2]) ).

cnf(f_676_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2229,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2229),U_2230))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2230)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2229) ),
    inference(clausify,[status(thm)],[f_676_3]) ).

fof(f_677_1,plain,
    ! [V_m,V_n] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) ),
    inference(fof_nnf,[status(thm)],[fact_one__less__mult]) ).

fof(f_677_2,plain,
    ! [U_2232,U_2231] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2232),U_2231))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2232)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2231) ),
    inference(variable_rename,[status(thm)],[f_677_1]) ).

fof(f_677_3,plain,
    ! [U_2232,U_2231] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2232),U_2231))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2232)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2231) ),
    inference(definitional_conversion,[status(esa)],[f_677_2]) ).

cnf(f_677_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2232),U_2231))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2232)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2231) ),
    inference(clausify,[status(thm)],[f_677_3]) ).

fof(f_678_1,plain,
    ! [V_n] :
      ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__pred]) ).

fof(f_678_2,plain,
    ! [U_2233] :
      ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2233,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_2233
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2233) ),
    inference(variable_rename,[status(thm)],[f_678_1]) ).

fof(f_678_3,plain,
    ! [U_2233] :
      ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2233,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_2233
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2233) ),
    inference(definitional_conversion,[status(esa)],[f_678_2]) ).

cnf(f_678_4,plain,
    ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2233,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_2233
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2233) ),
    inference(clausify,[status(thm)],[f_678_3]) ).

fof(f_679_1,plain,
    ! [V_i,V_n] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i)),V_n)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
    inference(fof_nnf,[status(thm)],[fact_diff__Suc__less]) ).

fof(f_679_2,plain,
    ! [U_2235,U_2234] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2234,c_Nat_OSuc(U_2235)),U_2234)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2234) ),
    inference(variable_rename,[status(thm)],[f_679_1]) ).

fof(f_679_3,plain,
    ! [U_2235,U_2234] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2234,c_Nat_OSuc(U_2235)),U_2234)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2234) ),
    inference(definitional_conversion,[status(esa)],[f_679_2]) ).

cnf(f_679_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2234,c_Nat_OSuc(U_2235)),U_2234)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2234) ),
    inference(clausify,[status(thm)],[f_679_3]) ).

fof(f_680_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2) )
      & ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)
          & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2) )
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_one__le__mult__iff]) ).

fof(f_680_2,plain,
    ! [U_2237,U_2236] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2236),U_2237))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2237)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2236) )
      & ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2237)
          & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2236) )
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2236),U_2237)) ) ),
    inference(variable_rename,[status(thm)],[f_680_1]) ).

fof(f_680_3,plain,
    ( ! [U_2241,U_2239] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2239),U_2241))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2241)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2239) )
    & ! [U_2240,U_2238] :
        ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2240)
          & c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2238) )
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2238),U_2240)) ) ),
    inference(miniscope,[status(thm)],[f_680_2]) ).

fof(f_680_4,plain,
    ( ! [U_2240,U_2238] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2240)
        | ~ sP202(U_2240,U_2238) )
    & ! [U_2240,U_2238] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2238)
        | ~ sP202(U_2240,U_2238) )
    & ! [U_2241,U_2239] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2239),U_2241))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2241)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2239) )
    & ! [U_2240,U_2238] :
        ( sP202(U_2240,U_2238)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2238),U_2240)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP202])],[f_680_3]) ).

cnf(f_680_5,plain,
    ( sP202(U_2240,U_2238)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2238),U_2240)) ),
    inference(clausify,[status(thm)],[f_680_4]) ).

cnf(f_680_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2239),U_2241))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2241)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2239) ),
    inference(clausify,[status(thm)],[f_680_4]) ).

cnf(f_680_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2238)
    | ~ sP202(U_2240,U_2238) ),
    inference(clausify,[status(thm)],[f_680_4]) ).

cnf(f_680_8,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2240)
    | ~ sP202(U_2240,U_2238) ),
    inference(clausify,[status(thm)],[f_680_4]) ).

fof(f_681_1,plain,
    ! [V_x_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))
          | V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
          | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) )
      | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__norm__iff]) ).

fof(f_681_2,plain,
    ! [U_2243,U_2242] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2242,U_2243))
          | U_2243 = c_Groups_Ozero__class_Ozero(U_2242) )
        & ( U_2243 != c_Groups_Ozero__class_Ozero(U_2242)
          | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2242,U_2243)) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_2242) ),
    inference(variable_rename,[status(thm)],[f_681_1]) ).

fof(f_681_3,plain,
    ( ! [U_2243,U_2242] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2242,U_2243))
        | U_2243 = c_Groups_Ozero__class_Ozero(U_2242)
        | ~ sP203(U_2243,U_2242) )
    & ! [U_2243,U_2242] :
        ( U_2243 != c_Groups_Ozero__class_Ozero(U_2242)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2242,U_2243))
        | ~ sP203(U_2243,U_2242) )
    & ! [U_2243,U_2242] :
        ( sP203(U_2243,U_2242)
        | ~ class_RealVector_Oreal__normed__vector(U_2242) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP203])],[f_681_2]) ).

cnf(f_681_4,plain,
    ( sP203(U_2243,U_2242)
    | ~ class_RealVector_Oreal__normed__vector(U_2242) ),
    inference(clausify,[status(thm)],[f_681_3]) ).

cnf(f_681_5,plain,
    ( U_2243 != c_Groups_Ozero__class_Ozero(U_2242)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2242,U_2243))
    | ~ sP203(U_2243,U_2242) ),
    inference(clausify,[status(thm)],[f_681_3]) ).

cnf(f_681_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2242,U_2243))
    | U_2243 = c_Groups_Ozero__class_Ozero(U_2242)
    | ~ sP203(U_2243,U_2242) ),
    inference(clausify,[status(thm)],[f_681_3]) ).

fof(f_682_1,plain,
    ! [V_m,V_j,V_k] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq2]) ).

fof(f_682_2,plain,
    ! [U_2246,U_2245,U_2244] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2245,U_2244)),U_2246) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2245),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2244,U_2246))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2244,U_2245) ),
    inference(variable_rename,[status(thm)],[f_682_1]) ).

fof(f_682_3,plain,
    ! [U_2245,U_2244,U_2246] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2245,U_2244)),U_2246) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2245),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2244,U_2246))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2244,U_2245) ),
    inference(definitional_conversion,[status(esa)],[f_682_2]) ).

cnf(f_682_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2245,U_2244)),U_2246) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2245),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2244,U_2246))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2244,U_2245) ),
    inference(clausify,[status(thm)],[f_682_3]) ).

fof(f_683_1,plain,
    ! [V_m,V_j,V_k] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Nat_OSuc(V_j))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq1]) ).

fof(f_683_2,plain,
    ! [U_2249,U_2248,U_2247] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2249,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2248,U_2247))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2249,U_2247),c_Nat_OSuc(U_2248))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2247,U_2248) ),
    inference(variable_rename,[status(thm)],[f_683_1]) ).

fof(f_683_3,plain,
    ! [U_2247,U_2248,U_2249] :
      ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2249,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2248,U_2247))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2249,U_2247),c_Nat_OSuc(U_2248))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2247,U_2248) ),
    inference(definitional_conversion,[status(esa)],[f_683_2]) ).

cnf(f_683_4,plain,
    ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2249,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2248,U_2247))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2249,U_2247),c_Nat_OSuc(U_2248))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2247,U_2248) ),
    inference(clausify,[status(thm)],[f_683_3]) ).

fof(f_684_1,plain,
    ! [V_s,V_y,V_r,V_x,T_a] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_s))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_norm__mult__less]) ).

fof(f_684_2,plain,
    ! [U_2254,U_2253,U_2252,U_2251,U_2250] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2250,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2250),U_2251),U_2253)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2252),U_2254))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2250,U_2253),U_2254)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2250,U_2251),U_2252)
      | ~ class_RealVector_Oreal__normed__algebra(U_2250) ),
    inference(variable_rename,[status(thm)],[f_684_1]) ).

fof(f_684_3,plain,
    ! [U_2250,U_2251,U_2252,U_2253,U_2254] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2250,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2250),U_2251),U_2253)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2252),U_2254))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2250,U_2253),U_2254)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2250,U_2251),U_2252)
      | ~ class_RealVector_Oreal__normed__algebra(U_2250) ),
    inference(definitional_conversion,[status(esa)],[f_684_2]) ).

cnf(f_684_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2250,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2250),U_2251),U_2253)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2252),U_2254))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2250,U_2253),U_2254)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2250,U_2251),U_2252)
    | ~ class_RealVector_Oreal__normed__algebra(U_2250) ),
    inference(clausify,[status(thm)],[f_684_3]) ).

fof(f_685_1,plain,
    ! [V_y_2,V_x_2,V_z_2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2) ),
    inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff1]) ).

fof(f_685_2,plain,
    ! [U_2257,U_2256,U_2255] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2256),U_2255),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2257),U_2255))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2256,U_2257) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2256,U_2257)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2256),U_2255),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2257),U_2255)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2255) ),
    inference(variable_rename,[status(thm)],[f_685_1]) ).

fof(f_685_3,plain,
    ( ! [U_2255,U_2256,U_2257] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2256),U_2255),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2257),U_2255))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2256,U_2257)
        | ~ sP204(U_2255,U_2256,U_2257) )
    & ! [U_2255,U_2256,U_2257] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2256,U_2257)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2256),U_2255),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2257),U_2255))
        | ~ sP204(U_2255,U_2256,U_2257) )
    & ! [U_2255,U_2256,U_2257] :
        ( sP204(U_2255,U_2256,U_2257)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2255) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP204])],[f_685_2]) ).

cnf(f_685_4,plain,
    ( sP204(U_2255,U_2256,U_2257)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2255) ),
    inference(clausify,[status(thm)],[f_685_3]) ).

cnf(f_685_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2256,U_2257)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2256),U_2255),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2257),U_2255))
    | ~ sP204(U_2255,U_2256,U_2257) ),
    inference(clausify,[status(thm)],[f_685_3]) ).

cnf(f_685_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2256),U_2255),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2257),U_2255))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2256,U_2257)
    | ~ sP204(U_2255,U_2256,U_2257) ),
    inference(clausify,[status(thm)],[f_685_3]) ).

fof(f_686_1,plain,
    ! [V_y_2,V_x_2,V_z_2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2) ),
    inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff2]) ).

fof(f_686_2,plain,
    ! [U_2260,U_2259,U_2258] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2258),U_2259),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2258),U_2260))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2259,U_2260) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2259,U_2260)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2258),U_2259),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2258),U_2260)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2258) ),
    inference(variable_rename,[status(thm)],[f_686_1]) ).

fof(f_686_3,plain,
    ( ! [U_2260,U_2258,U_2259] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2258),U_2259),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2258),U_2260))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2259,U_2260)
        | ~ sP205(U_2260,U_2258,U_2259) )
    & ! [U_2260,U_2258,U_2259] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2259,U_2260)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2258),U_2259),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2258),U_2260))
        | ~ sP205(U_2260,U_2258,U_2259) )
    & ! [U_2260,U_2258,U_2259] :
        ( sP205(U_2260,U_2258,U_2259)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2258) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP205])],[f_686_2]) ).

cnf(f_686_4,plain,
    ( sP205(U_2260,U_2258,U_2259)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2258) ),
    inference(clausify,[status(thm)],[f_686_3]) ).

cnf(f_686_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2259,U_2260)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2258),U_2259),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2258),U_2260))
    | ~ sP205(U_2260,U_2258,U_2259) ),
    inference(clausify,[status(thm)],[f_686_3]) ).

cnf(f_686_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2258),U_2259),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2258),U_2260))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2259,U_2260)
    | ~ sP205(U_2260,U_2258,U_2259) ),
    inference(clausify,[status(thm)],[f_686_3]) ).

fof(f_687_1,plain,
    ! [V_s,V_y,V_r,V_x,T_a] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,V_s))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_y),V_s)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),V_r)
      | ~ class_RealVector_Oreal__normed__vector(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_norm__add__less]) ).

fof(f_687_2,plain,
    ! [U_2265,U_2264,U_2263,U_2262,U_2261] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2261,c_Groups_Oplus__class_Oplus(U_2261,U_2262,U_2264)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2263,U_2265))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2261,U_2264),U_2265)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2261,U_2262),U_2263)
      | ~ class_RealVector_Oreal__normed__vector(U_2261) ),
    inference(variable_rename,[status(thm)],[f_687_1]) ).

fof(f_687_3,plain,
    ! [U_2262,U_2264,U_2263,U_2261,U_2265] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2261,c_Groups_Oplus__class_Oplus(U_2261,U_2262,U_2264)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2263,U_2265))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2261,U_2264),U_2265)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2261,U_2262),U_2263)
      | ~ class_RealVector_Oreal__normed__vector(U_2261) ),
    inference(definitional_conversion,[status(esa)],[f_687_2]) ).

cnf(f_687_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2261,c_Groups_Oplus__class_Oplus(U_2261,U_2262,U_2264)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2263,U_2265))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2261,U_2264),U_2265)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2261,U_2262),U_2263)
    | ~ class_RealVector_Oreal__normed__vector(U_2261) ),
    inference(clausify,[status(thm)],[f_687_3]) ).

fof(f_688_1,plain,
    ! [V_x,V_n,V_a,T_a] :
      ( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_poly__monom]) ).

fof(f_688_2,plain,
    ! [U_2269,U_2268,U_2267,U_2266] :
      ( hAPP(c_Polynomial_Opoly(U_2266,c_Polynomial_Omonom(U_2266,U_2267,U_2268)),U_2269) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2266),U_2267),hAPP(hAPP(c_Power_Opower__class_Opower(U_2266),U_2269),U_2268))
      | ~ class_Rings_Ocomm__semiring__1(U_2266) ),
    inference(variable_rename,[status(thm)],[f_688_1]) ).

fof(f_688_3,plain,
    ! [U_2269,U_2268,U_2266,U_2267] :
      ( hAPP(c_Polynomial_Opoly(U_2266,c_Polynomial_Omonom(U_2266,U_2267,U_2268)),U_2269) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2266),U_2267),hAPP(hAPP(c_Power_Opower__class_Opower(U_2266),U_2269),U_2268))
      | ~ class_Rings_Ocomm__semiring__1(U_2266) ),
    inference(definitional_conversion,[status(esa)],[f_688_2]) ).

cnf(f_688_4,plain,
    ( hAPP(c_Polynomial_Opoly(U_2266,c_Polynomial_Omonom(U_2266,U_2267,U_2268)),U_2269) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2266),U_2267),hAPP(hAPP(c_Power_Opower__class_Opower(U_2266),U_2269),U_2268))
    | ~ class_Rings_Ocomm__semiring__1(U_2266) ),
    inference(clausify,[status(thm)],[f_688_3]) ).

fof(f_689_1,plain,
    ! [V_n,V_a,T_a] :
      ( c_Polynomial_Omonom(T_a,V_a,c_Nat_OSuc(V_n)) = c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Polynomial_Omonom(T_a,V_a,V_n))
      | ~ class_Groups_Ozero(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_monom__Suc]) ).

fof(f_689_2,plain,
    ! [U_2272,U_2271,U_2270] :
      ( c_Polynomial_Omonom(U_2270,U_2271,c_Nat_OSuc(U_2272)) = c_Polynomial_OpCons(U_2270,c_Groups_Ozero__class_Ozero(U_2270),c_Polynomial_Omonom(U_2270,U_2271,U_2272))
      | ~ class_Groups_Ozero(U_2270) ),
    inference(variable_rename,[status(thm)],[f_689_1]) ).

fof(f_689_3,plain,
    ! [U_2271,U_2270,U_2272] :
      ( c_Polynomial_Omonom(U_2270,U_2271,c_Nat_OSuc(U_2272)) = c_Polynomial_OpCons(U_2270,c_Groups_Ozero__class_Ozero(U_2270),c_Polynomial_Omonom(U_2270,U_2271,U_2272))
      | ~ class_Groups_Ozero(U_2270) ),
    inference(definitional_conversion,[status(esa)],[f_689_2]) ).

cnf(f_689_4,plain,
    ( c_Polynomial_Omonom(U_2270,U_2271,c_Nat_OSuc(U_2272)) = c_Polynomial_OpCons(U_2270,c_Groups_Ozero__class_Ozero(U_2270),c_Polynomial_Omonom(U_2270,U_2271,U_2272))
    | ~ class_Groups_Ozero(U_2270) ),
    inference(clausify,[status(thm)],[f_689_3]) ).

fof(f_690_1,plain,
    ! [V_p,V_m] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_nnf,[status(thm)],[fact_power__eq__if]) ).

fof(f_690_2,plain,
    ! [U_2274,U_2273] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2274),U_2273) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2274),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2274),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2273,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | U_2273 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2274),U_2273) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2273 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_690_1]) ).

fof(f_690_3,plain,
    ( ! [U_2278,U_2276] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2278),U_2276) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2278),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2278),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2276,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | U_2276 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2277,U_2275] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2277),U_2275) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2275 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_690_2]) ).

fof(f_690_4,plain,
    ( ! [U_2276,U_2278] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2278),U_2276) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2278),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2278),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2276,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | U_2276 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2277,U_2275] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2277),U_2275) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2275 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_690_3]) ).

cnf(f_690_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2277),U_2275) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_2275 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_690_4]) ).

cnf(f_690_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2278),U_2276) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2278),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2278),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2276,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | U_2276 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_690_4]) ).

fof(f_691_1,plain,
    ! [V_n] :
      ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = V_n
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__diff__1]) ).

fof(f_691_2,plain,
    ! [U_2279] :
      ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2279,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_2279
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2279) ),
    inference(variable_rename,[status(thm)],[f_691_1]) ).

fof(f_691_3,plain,
    ! [U_2279] :
      ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2279,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_2279
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2279) ),
    inference(definitional_conversion,[status(esa)],[f_691_2]) ).

cnf(f_691_4,plain,
    ( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2279,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_2279
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2279) ),
    inference(clausify,[status(thm)],[f_691_3]) ).

fof(f_692_1,plain,
    ! [V_n] :
      ( V_n = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
    inference(fof_nnf,[status(thm)],[fact_Suc__pred_H]) ).

fof(f_692_2,plain,
    ! [U_2280] :
      ( U_2280 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2280,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2280) ),
    inference(variable_rename,[status(thm)],[f_692_1]) ).

fof(f_692_3,plain,
    ! [U_2280] :
      ( U_2280 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2280,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2280) ),
    inference(definitional_conversion,[status(esa)],[f_692_2]) ).

cnf(f_692_4,plain,
    ( U_2280 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2280,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2280) ),
    inference(clausify,[status(thm)],[f_692_3]) ).

fof(f_693_1,plain,
    ! [V_m,V_n,T_a] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = c_Groups_Oone__class_Oone(T_a)
          | V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ class_Power_Opower(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_realpow__num__eq__if]) ).

fof(f_693_2,plain,
    ! [U_2283,U_2282,U_2281] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2281),U_2283),U_2282) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2281),U_2283),hAPP(hAPP(c_Power_Opower__class_Opower(U_2281),U_2283),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2282,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          | U_2282 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2281),U_2283),U_2282) = c_Groups_Oone__class_Oone(U_2281)
          | U_2282 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ class_Power_Opower(U_2281) ),
    inference(variable_rename,[status(thm)],[f_693_1]) ).

fof(f_693_3,plain,
    ( ! [U_2281,U_2282,U_2283] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2281),U_2283),U_2282) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2281),U_2283),hAPP(hAPP(c_Power_Opower__class_Opower(U_2281),U_2283),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2282,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | U_2282 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP206(U_2281,U_2282,U_2283) )
    & ! [U_2281,U_2282,U_2283] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2281),U_2283),U_2282) = c_Groups_Oone__class_Oone(U_2281)
        | U_2282 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP206(U_2281,U_2282,U_2283) )
    & ! [U_2281,U_2282,U_2283] :
        ( sP206(U_2281,U_2282,U_2283)
        | ~ class_Power_Opower(U_2281) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP206])],[f_693_2]) ).

cnf(f_693_4,plain,
    ( sP206(U_2281,U_2282,U_2283)
    | ~ class_Power_Opower(U_2281) ),
    inference(clausify,[status(thm)],[f_693_3]) ).

cnf(f_693_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2281),U_2283),U_2282) = c_Groups_Oone__class_Oone(U_2281)
    | U_2282 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP206(U_2281,U_2282,U_2283) ),
    inference(clausify,[status(thm)],[f_693_3]) ).

cnf(f_693_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2281),U_2283),U_2282) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2281),U_2283),hAPP(hAPP(c_Power_Opower__class_Opower(U_2281),U_2283),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2282,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | U_2282 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP206(U_2281,U_2282,U_2283) ),
    inference(clausify,[status(thm)],[f_693_3]) ).

fof(f_694_1,plain,
    ! [V_n,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__strict__mono]) ).

fof(f_694_2,plain,
    ! [U_2287,U_2286,U_2285,U_2284] :
      ( c_Orderings_Oord__class_Oless(U_2284,hAPP(hAPP(c_Power_Opower__class_Opower(U_2284),U_2285),U_2287),hAPP(hAPP(c_Power_Opower__class_Opower(U_2284),U_2286),U_2287))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2287)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2284,c_Groups_Ozero__class_Ozero(U_2284),U_2285)
      | ~ c_Orderings_Oord__class_Oless(U_2284,U_2285,U_2286)
      | ~ class_Rings_Olinordered__semidom(U_2284) ),
    inference(variable_rename,[status(thm)],[f_694_1]) ).

fof(f_694_3,plain,
    ! [U_2284,U_2287,U_2286,U_2285] :
      ( c_Orderings_Oord__class_Oless(U_2284,hAPP(hAPP(c_Power_Opower__class_Opower(U_2284),U_2285),U_2287),hAPP(hAPP(c_Power_Opower__class_Opower(U_2284),U_2286),U_2287))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2287)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2284,c_Groups_Ozero__class_Ozero(U_2284),U_2285)
      | ~ c_Orderings_Oord__class_Oless(U_2284,U_2285,U_2286)
      | ~ class_Rings_Olinordered__semidom(U_2284) ),
    inference(definitional_conversion,[status(esa)],[f_694_2]) ).

cnf(f_694_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2284,hAPP(hAPP(c_Power_Opower__class_Opower(U_2284),U_2285),U_2287),hAPP(hAPP(c_Power_Opower__class_Opower(U_2284),U_2286),U_2287))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2287)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2284,c_Groups_Ozero__class_Ozero(U_2284),U_2285)
    | ~ c_Orderings_Oord__class_Oless(U_2284,U_2285,U_2286)
    | ~ class_Rings_Olinordered__semidom(U_2284) ),
    inference(clausify,[status(thm)],[f_694_3]) ).

fof(f_695_1,plain,
    ! [V_y,V_n,V_p,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),V_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_p))),V_y)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_p,V_n)
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_lemma__realpow__diff]) ).

fof(f_695_2,plain,
    ! [U_2291,U_2290,U_2289,U_2288] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2288),U_2291),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2290),U_2289)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2288),hAPP(hAPP(c_Power_Opower__class_Opower(U_2288),U_2291),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2290,U_2289))),U_2291)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2289,U_2290)
      | ~ class_Groups_Omonoid__mult(U_2288) ),
    inference(variable_rename,[status(thm)],[f_695_1]) ).

fof(f_695_3,plain,
    ! [U_2289,U_2290,U_2288,U_2291] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2288),U_2291),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2290),U_2289)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2288),hAPP(hAPP(c_Power_Opower__class_Opower(U_2288),U_2291),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2290,U_2289))),U_2291)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2289,U_2290)
      | ~ class_Groups_Omonoid__mult(U_2288) ),
    inference(definitional_conversion,[status(esa)],[f_695_2]) ).

cnf(f_695_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2288),U_2291),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_2290),U_2289)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2288),hAPP(hAPP(c_Power_Opower__class_Opower(U_2288),U_2291),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2290,U_2289))),U_2291)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2289,U_2290)
    | ~ class_Groups_Omonoid__mult(U_2288) ),
    inference(clausify,[status(thm)],[f_695_3]) ).

fof(f_696_1,plain,
    ! [V_n,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_one__less__power]) ).

fof(f_696_2,plain,
    ! [U_2294,U_2293,U_2292] :
      ( c_Orderings_Oord__class_Oless(U_2292,c_Groups_Oone__class_Oone(U_2292),hAPP(hAPP(c_Power_Opower__class_Opower(U_2292),U_2293),U_2294))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2294)
      | ~ c_Orderings_Oord__class_Oless(U_2292,c_Groups_Oone__class_Oone(U_2292),U_2293)
      | ~ class_Rings_Olinordered__semidom(U_2292) ),
    inference(variable_rename,[status(thm)],[f_696_1]) ).

fof(f_696_3,plain,
    ! [U_2293,U_2292,U_2294] :
      ( c_Orderings_Oord__class_Oless(U_2292,c_Groups_Oone__class_Oone(U_2292),hAPP(hAPP(c_Power_Opower__class_Opower(U_2292),U_2293),U_2294))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2294)
      | ~ c_Orderings_Oord__class_Oless(U_2292,c_Groups_Oone__class_Oone(U_2292),U_2293)
      | ~ class_Rings_Olinordered__semidom(U_2292) ),
    inference(definitional_conversion,[status(esa)],[f_696_2]) ).

cnf(f_696_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2292,c_Groups_Oone__class_Oone(U_2292),hAPP(hAPP(c_Power_Opower__class_Opower(U_2292),U_2293),U_2294))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2294)
    | ~ c_Orderings_Oord__class_Oless(U_2292,c_Groups_Oone__class_Oone(U_2292),U_2293)
    | ~ class_Rings_Olinordered__semidom(U_2292) ),
    inference(clausify,[status(thm)],[f_696_3]) ).

fof(f_697_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
          | V_n_2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
          | V_m_2 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
        & ( ( V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
            & V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m_2) ),
    inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff]) ).

fof(f_697_2,plain,
    ! [U_2296,U_2295] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2295),U_2296) = c_Groups_Oone__class_Oone(tc_Int_Oint)
          | U_2296 != c_Groups_Oone__class_Oone(tc_Int_Oint)
          | U_2295 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
        & ( ( U_2296 = c_Groups_Oone__class_Oone(tc_Int_Oint)
            & U_2295 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2295),U_2296) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2295) ),
    inference(variable_rename,[status(thm)],[f_697_1]) ).

fof(f_697_3,plain,
    ( ! [U_2295,U_2296] :
        ( U_2296 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP207(U_2295,U_2296) )
    & ! [U_2295,U_2296] :
        ( U_2295 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP207(U_2295,U_2296) )
    & ! [U_2295,U_2296] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2295),U_2296) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | U_2296 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | U_2295 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP208(U_2295,U_2296) )
    & ! [U_2295,U_2296] :
        ( sP207(U_2295,U_2296)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2295),U_2296) != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP208(U_2295,U_2296) )
    & ! [U_2295,U_2296] :
        ( sP208(U_2295,U_2296)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2295) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP207,sP208])],[f_697_2]) ).

cnf(f_697_4,plain,
    ( sP208(U_2295,U_2296)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2295) ),
    inference(clausify,[status(thm)],[f_697_3]) ).

cnf(f_697_5,plain,
    ( sP207(U_2295,U_2296)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2295),U_2296) != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP208(U_2295,U_2296) ),
    inference(clausify,[status(thm)],[f_697_3]) ).

cnf(f_697_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2295),U_2296) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_2296 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_2295 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP208(U_2295,U_2296) ),
    inference(clausify,[status(thm)],[f_697_3]) ).

cnf(f_697_7,plain,
    ( U_2295 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP207(U_2295,U_2296) ),
    inference(clausify,[status(thm)],[f_697_3]) ).

cnf(f_697_8,plain,
    ( U_2296 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP207(U_2295,U_2296) ),
    inference(clausify,[status(thm)],[f_697_3]) ).

fof(f_698_1,plain,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2]) ).

fof(f_698_2,plain,
    ! [U_2299,U_2298,U_2297] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2299),U_2297),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2299),U_2298))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2299)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2297,U_2298) ),
    inference(variable_rename,[status(thm)],[f_698_1]) ).

fof(f_698_3,plain,
    ! [U_2298,U_2297,U_2299] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2299),U_2297),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2299),U_2298))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2299)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2297,U_2298) ),
    inference(definitional_conversion,[status(esa)],[f_698_2]) ).

cnf(f_698_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2299),U_2297),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2299),U_2298))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2299)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2297,U_2298) ),
    inference(clausify,[status(thm)],[f_698_3]) ).

fof(f_699_1,plain,
    ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z,
    inference(fof_nnf,[status(thm)],[fact_zmult__1__right]) ).

fof(f_699_2,plain,
    ! [U_2300] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2300),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_2300,
    inference(variable_rename,[status(thm)],[f_699_1]) ).

fof(f_699_3,plain,
    ! [U_2300] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2300),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_2300,
    inference(definitional_conversion,[status(esa)],[f_699_2]) ).

cnf(f_699_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2300),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_2300,
    inference(clausify,[status(thm)],[f_699_3]) ).

fof(f_700_1,plain,
    ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z,
    inference(fof_nnf,[status(thm)],[fact_zmult__1]) ).

fof(f_700_2,plain,
    ! [U_2301] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2301) = U_2301,
    inference(variable_rename,[status(thm)],[f_700_1]) ).

fof(f_700_3,plain,
    ! [U_2301] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2301) = U_2301,
    inference(definitional_conversion,[status(esa)],[f_700_2]) ).

cnf(f_700_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2301) = U_2301,
    inference(clausify,[status(thm)],[f_700_3]) ).

fof(f_701_1,plain,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)),V_w) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)),
    inference(fof_nnf,[status(thm)],[fact_zmult__zminus]) ).

fof(f_701_2,plain,
    ! [U_2303,U_2302] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2302)),U_2303) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2302),U_2303)),
    inference(variable_rename,[status(thm)],[f_701_1]) ).

fof(f_701_3,plain,
    ! [U_2303,U_2302] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2302)),U_2303) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2302),U_2303)),
    inference(definitional_conversion,[status(esa)],[f_701_2]) ).

cnf(f_701_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2302)),U_2303) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2302),U_2303)),
    inference(clausify,[status(thm)],[f_701_3]) ).

fof(f_702_1,plain,
    ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)),
    inference(fof_nnf,[status(thm)],[fact_zadd__zmult__distrib2]) ).

fof(f_702_2,plain,
    ! [U_2306,U_2305,U_2304] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2304),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2305,U_2306)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2304),U_2305),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2304),U_2306)),
    inference(variable_rename,[status(thm)],[f_702_1]) ).

fof(f_702_3,plain,
    ! [U_2304,U_2305,U_2306] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2304),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2305,U_2306)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2304),U_2305),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2304),U_2306)),
    inference(definitional_conversion,[status(esa)],[f_702_2]) ).

cnf(f_702_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2304),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2305,U_2306)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2304),U_2305),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2304),U_2306)),
    inference(clausify,[status(thm)],[f_702_3]) ).

fof(f_703_1,plain,
    ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)),V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)),
    inference(fof_nnf,[status(thm)],[fact_zadd__zmult__distrib]) ).

fof(f_703_2,plain,
    ! [U_2309,U_2308,U_2307] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2307,U_2308)),U_2309) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2307),U_2309),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2308),U_2309)),
    inference(variable_rename,[status(thm)],[f_703_1]) ).

fof(f_703_3,plain,
    ! [U_2307,U_2308,U_2309] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2307,U_2308)),U_2309) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2307),U_2309),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2308),U_2309)),
    inference(definitional_conversion,[status(esa)],[f_703_2]) ).

cnf(f_703_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2307,U_2308)),U_2309) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2307),U_2309),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2308),U_2309)),
    inference(clausify,[status(thm)],[f_703_3]) ).

fof(f_704_1,plain,
    ! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)),V_w) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)),
    inference(fof_nnf,[status(thm)],[fact_zdiff__zmult__distrib]) ).

fof(f_704_2,plain,
    ! [U_2312,U_2311,U_2310] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2310,U_2311)),U_2312) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2310),U_2312),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2311),U_2312)),
    inference(variable_rename,[status(thm)],[f_704_1]) ).

fof(f_704_3,plain,
    ! [U_2310,U_2311,U_2312] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2310,U_2311)),U_2312) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2310),U_2312),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2311),U_2312)),
    inference(definitional_conversion,[status(esa)],[f_704_2]) ).

cnf(f_704_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2310,U_2311)),U_2312) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2310),U_2312),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2311),U_2312)),
    inference(clausify,[status(thm)],[f_704_3]) ).

fof(f_705_1,plain,
    ! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)),
    inference(fof_nnf,[status(thm)],[fact_zmult__assoc]) ).

fof(f_705_2,plain,
    ! [U_2315,U_2314,U_2313] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2313),U_2314)),U_2315) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2313),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2314),U_2315)),
    inference(variable_rename,[status(thm)],[f_705_1]) ).

fof(f_705_3,plain,
    ! [U_2313,U_2314,U_2315] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2313),U_2314)),U_2315) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2313),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2314),U_2315)),
    inference(definitional_conversion,[status(esa)],[f_705_2]) ).

cnf(f_705_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2313),U_2314)),U_2315) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2313),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2314),U_2315)),
    inference(clausify,[status(thm)],[f_705_3]) ).

fof(f_706_1,plain,
    ! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)),
    inference(fof_nnf,[status(thm)],[fact_zdiff__zmult__distrib2]) ).

fof(f_706_2,plain,
    ! [U_2318,U_2317,U_2316] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2316),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2317,U_2318)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2316),U_2317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2316),U_2318)),
    inference(variable_rename,[status(thm)],[f_706_1]) ).

fof(f_706_3,plain,
    ! [U_2316,U_2317,U_2318] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2316),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2317,U_2318)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2316),U_2317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2316),U_2318)),
    inference(definitional_conversion,[status(esa)],[f_706_2]) ).

cnf(f_706_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2316),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2317,U_2318)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2316),U_2317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2316),U_2318)),
    inference(clausify,[status(thm)],[f_706_3]) ).

fof(f_707_1,plain,
    ! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z),
    inference(fof_nnf,[status(thm)],[fact_zmult__commute]) ).

fof(f_707_2,plain,
    ! [U_2320,U_2319] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2319),U_2320) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2320),U_2319),
    inference(variable_rename,[status(thm)],[f_707_1]) ).

fof(f_707_3,plain,
    ! [U_2319,U_2320] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2319),U_2320) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2320),U_2319),
    inference(definitional_conversion,[status(esa)],[f_707_2]) ).

cnf(f_707_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2319),U_2320) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2320),U_2319),
    inference(clausify,[status(thm)],[f_707_3]) ).

fof(f_708_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a)
      | V_a = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Oring__1__no__zero__divisors(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_field__power__not__zero]) ).

fof(f_708_2,plain,
    ! [U_2323,U_2322,U_2321] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2321),U_2322),U_2323) != c_Groups_Ozero__class_Ozero(U_2321)
      | U_2322 = c_Groups_Ozero__class_Ozero(U_2321)
      | ~ class_Rings_Oring__1__no__zero__divisors(U_2321) ),
    inference(variable_rename,[status(thm)],[f_708_1]) ).

fof(f_708_3,plain,
    ! [U_2321,U_2322,U_2323] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2321),U_2322),U_2323) != c_Groups_Ozero__class_Ozero(U_2321)
      | U_2322 = c_Groups_Ozero__class_Ozero(U_2321)
      | ~ class_Rings_Oring__1__no__zero__divisors(U_2321) ),
    inference(definitional_conversion,[status(esa)],[f_708_2]) ).

cnf(f_708_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2321),U_2322),U_2323) != c_Groups_Ozero__class_Ozero(U_2321)
    | U_2322 = c_Groups_Ozero__class_Ozero(U_2321)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_2321) ),
    inference(clausify,[status(thm)],[f_708_3]) ).

fof(f_709_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__commutes]) ).

fof(f_709_2,plain,
    ! [U_2326,U_2325,U_2324] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2324),hAPP(hAPP(c_Power_Opower__class_Opower(U_2324),U_2325),U_2326)),U_2325) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2324),U_2325),hAPP(hAPP(c_Power_Opower__class_Opower(U_2324),U_2325),U_2326))
      | ~ class_Groups_Omonoid__mult(U_2324) ),
    inference(variable_rename,[status(thm)],[f_709_1]) ).

fof(f_709_3,plain,
    ! [U_2324,U_2325,U_2326] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2324),hAPP(hAPP(c_Power_Opower__class_Opower(U_2324),U_2325),U_2326)),U_2325) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2324),U_2325),hAPP(hAPP(c_Power_Opower__class_Opower(U_2324),U_2325),U_2326))
      | ~ class_Groups_Omonoid__mult(U_2324) ),
    inference(definitional_conversion,[status(esa)],[f_709_2]) ).

cnf(f_709_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2324),hAPP(hAPP(c_Power_Opower__class_Opower(U_2324),U_2325),U_2326)),U_2325) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2324),U_2325),hAPP(hAPP(c_Power_Opower__class_Opower(U_2324),U_2325),U_2326))
    | ~ class_Groups_Omonoid__mult(U_2324) ),
    inference(clausify,[status(thm)],[f_709_3]) ).

fof(f_710_1,plain,
    ! [V_n,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))
      | ~ class_Groups_Ocomm__monoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__mult__distrib]) ).

fof(f_710_2,plain,
    ! [U_2330,U_2329,U_2328,U_2327] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2327),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2327),U_2328),U_2329)),U_2330) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2327),hAPP(hAPP(c_Power_Opower__class_Opower(U_2327),U_2328),U_2330)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2327),U_2329),U_2330))
      | ~ class_Groups_Ocomm__monoid__mult(U_2327) ),
    inference(variable_rename,[status(thm)],[f_710_1]) ).

fof(f_710_3,plain,
    ! [U_2327,U_2328,U_2329,U_2330] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2327),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2327),U_2328),U_2329)),U_2330) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2327),hAPP(hAPP(c_Power_Opower__class_Opower(U_2327),U_2328),U_2330)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2327),U_2329),U_2330))
      | ~ class_Groups_Ocomm__monoid__mult(U_2327) ),
    inference(definitional_conversion,[status(esa)],[f_710_2]) ).

cnf(f_710_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2327),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2327),U_2328),U_2329)),U_2330) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2327),hAPP(hAPP(c_Power_Opower__class_Opower(U_2327),U_2328),U_2330)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2327),U_2329),U_2330))
    | ~ class_Groups_Ocomm__monoid__mult(U_2327) ),
    inference(clausify,[status(thm)],[f_710_3]) ).

fof(f_711_1,plain,
    ! [V_n,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__one]) ).

fof(f_711_2,plain,
    ! [U_2332,U_2331] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2331),c_Groups_Oone__class_Oone(U_2331)),U_2332) = c_Groups_Oone__class_Oone(U_2331)
      | ~ class_Groups_Omonoid__mult(U_2331) ),
    inference(variable_rename,[status(thm)],[f_711_1]) ).

fof(f_711_3,plain,
    ! [U_2332,U_2331] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2331),c_Groups_Oone__class_Oone(U_2331)),U_2332) = c_Groups_Oone__class_Oone(U_2331)
      | ~ class_Groups_Omonoid__mult(U_2331) ),
    inference(definitional_conversion,[status(esa)],[f_711_2]) ).

cnf(f_711_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2331),c_Groups_Oone__class_Oone(U_2331)),U_2332) = c_Groups_Oone__class_Oone(U_2331)
    | ~ class_Groups_Omonoid__mult(U_2331) ),
    inference(clausify,[status(thm)],[f_711_3]) ).

fof(f_712_1,plain,
    ! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_power__Suc__0]) ).

fof(f_712_2,plain,
    ! [U_2333] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2333) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_712_1]) ).

fof(f_712_3,plain,
    ! [U_2333] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2333) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_712_2]) ).

cnf(f_712_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2333) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_712_3]) ).

fof(f_713_1,plain,
    ! [V_m_2,V_x_2] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( V_x_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( V_x_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__power__eq__Suc__0__iff]) ).

fof(f_713_2,plain,
    ! [U_2335,U_2334] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2334),U_2335) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( U_2334 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_2335 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_2334 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2335 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2334),U_2335) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_713_1]) ).

fof(f_713_3,plain,
    ( ! [U_2339,U_2337] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2337),U_2339) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( U_2337 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_2339 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_2338,U_2336] :
        ( U_2336 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2338 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2336),U_2338) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_713_2]) ).

fof(f_713_4,plain,
    ( ! [U_2339,U_2337] :
        ( U_2337 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP209(U_2339,U_2337) )
    & ! [U_2339,U_2337] :
        ( U_2339 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP209(U_2339,U_2337) )
    & ! [U_2339,U_2337] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2337),U_2339) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | sP209(U_2339,U_2337) )
    & ! [U_2338,U_2336] :
        ( U_2336 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2338 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2336),U_2338) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP209])],[f_713_3]) ).

cnf(f_713_5,plain,
    ( U_2336 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_2338 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2336),U_2338) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_713_4]) ).

cnf(f_713_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2337),U_2339) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | sP209(U_2339,U_2337) ),
    inference(clausify,[status(thm)],[f_713_4]) ).

cnf(f_713_7,plain,
    ( U_2339 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP209(U_2339,U_2337) ),
    inference(clausify,[status(thm)],[f_713_4]) ).

cnf(f_713_8,plain,
    ( U_2337 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP209(U_2339,U_2337) ),
    inference(clausify,[status(thm)],[f_713_4]) ).

fof(f_714_1,plain,
    ! [V_n_2,V_x_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))
        | ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff]) ).

fof(f_714_2,plain,
    ! [U_2341,U_2340] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2340),U_2341))
        | ( U_2341 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2340) ) )
      & ( U_2341 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2340)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2340),U_2341)) ) ),
    inference(variable_rename,[status(thm)],[f_714_1]) ).

fof(f_714_3,plain,
    ( ! [U_2345,U_2343] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2343),U_2345))
        | ( U_2345 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2343) ) )
    & ! [U_2344,U_2342] :
        ( U_2344 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2342)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2342),U_2344)) ) ),
    inference(miniscope,[status(thm)],[f_714_2]) ).

fof(f_714_4,plain,
    ( ! [U_2345,U_2343] :
        ( U_2345 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP210(U_2345,U_2343) )
    & ! [U_2345,U_2343] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2343)
        | ~ sP210(U_2345,U_2343) )
    & ! [U_2345,U_2343] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2343),U_2345))
        | sP210(U_2345,U_2343) )
    & ! [U_2342,U_2344] :
        ( U_2344 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2342)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2342),U_2344)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP210])],[f_714_3]) ).

cnf(f_714_5,plain,
    ( U_2344 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2342)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2342),U_2344)) ),
    inference(clausify,[status(thm)],[f_714_4]) ).

cnf(f_714_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2343),U_2345))
    | sP210(U_2345,U_2343) ),
    inference(clausify,[status(thm)],[f_714_4]) ).

cnf(f_714_7,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2343)
    | ~ sP210(U_2345,U_2343) ),
    inference(clausify,[status(thm)],[f_714_4]) ).

cnf(f_714_8,plain,
    ( U_2345 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP210(U_2345,U_2343) ),
    inference(clausify,[status(thm)],[f_714_4]) ).

fof(f_715_1,plain,
    ! [V_n,V_m,V_i] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i) ),
    inference(fof_nnf,[status(thm)],[fact_nat__power__less__imp__less]) ).

fof(f_715_2,plain,
    ! [U_2348,U_2347,U_2346] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2347,U_2348)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2346),U_2347),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2346),U_2348))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2346) ),
    inference(variable_rename,[status(thm)],[f_715_1]) ).

fof(f_715_3,plain,
    ! [U_2347,U_2348,U_2346] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2347,U_2348)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2346),U_2347),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2346),U_2348))
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2346) ),
    inference(definitional_conversion,[status(esa)],[f_715_2]) ).

cnf(f_715_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2347,U_2348)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2346),U_2347),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2346),U_2348))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2346) ),
    inference(clausify,[status(thm)],[f_715_3]) ).

fof(f_716_1,plain,
    ! [V_n,V_m,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n)
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__mult]) ).

fof(f_716_2,plain,
    ! [U_2352,U_2351,U_2350,U_2349] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2349),U_2350),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2351),U_2352)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2349),hAPP(hAPP(c_Power_Opower__class_Opower(U_2349),U_2350),U_2351)),U_2352)
      | ~ class_Groups_Omonoid__mult(U_2349) ),
    inference(variable_rename,[status(thm)],[f_716_1]) ).

fof(f_716_3,plain,
    ! [U_2350,U_2349,U_2351,U_2352] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2349),U_2350),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2351),U_2352)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2349),hAPP(hAPP(c_Power_Opower__class_Opower(U_2349),U_2350),U_2351)),U_2352)
      | ~ class_Groups_Omonoid__mult(U_2349) ),
    inference(definitional_conversion,[status(esa)],[f_716_2]) ).

cnf(f_716_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2349),U_2350),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2351),U_2352)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2349),hAPP(hAPP(c_Power_Opower__class_Opower(U_2349),U_2350),U_2351)),U_2352)
    | ~ class_Groups_Omonoid__mult(U_2349) ),
    inference(clausify,[status(thm)],[f_716_3]) ).

fof(f_717_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__one__right]) ).

fof(f_717_2,plain,
    ! [U_2354,U_2353] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2353),U_2354),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2354
      | ~ class_Groups_Omonoid__mult(U_2353) ),
    inference(variable_rename,[status(thm)],[f_717_1]) ).

fof(f_717_3,plain,
    ! [U_2354,U_2353] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2353),U_2354),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2354
      | ~ class_Groups_Omonoid__mult(U_2353) ),
    inference(definitional_conversion,[status(esa)],[f_717_2]) ).

cnf(f_717_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2353),U_2354),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2354
    | ~ class_Groups_Omonoid__mult(U_2353) ),
    inference(clausify,[status(thm)],[f_717_3]) ).

fof(f_718_1,plain,
    ! [V_n,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__le__power]) ).

fof(f_718_2,plain,
    ! [U_2357,U_2356,U_2355] :
      ( c_Orderings_Oord__class_Oless__eq(U_2355,c_Groups_Ozero__class_Ozero(U_2355),hAPP(hAPP(c_Power_Opower__class_Opower(U_2355),U_2356),U_2357))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2355,c_Groups_Ozero__class_Ozero(U_2355),U_2356)
      | ~ class_Rings_Olinordered__semidom(U_2355) ),
    inference(variable_rename,[status(thm)],[f_718_1]) ).

fof(f_718_3,plain,
    ! [U_2355,U_2356,U_2357] :
      ( c_Orderings_Oord__class_Oless__eq(U_2355,c_Groups_Ozero__class_Ozero(U_2355),hAPP(hAPP(c_Power_Opower__class_Opower(U_2355),U_2356),U_2357))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2355,c_Groups_Ozero__class_Ozero(U_2355),U_2356)
      | ~ class_Rings_Olinordered__semidom(U_2355) ),
    inference(definitional_conversion,[status(esa)],[f_718_2]) ).

cnf(f_718_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2355,c_Groups_Ozero__class_Ozero(U_2355),hAPP(hAPP(c_Power_Opower__class_Opower(U_2355),U_2356),U_2357))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2355,c_Groups_Ozero__class_Ozero(U_2355),U_2356)
    | ~ class_Rings_Olinordered__semidom(U_2355) ),
    inference(clausify,[status(thm)],[f_718_3]) ).

fof(f_719_1,plain,
    ! [V_n,V_b,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__mono]) ).

fof(f_719_2,plain,
    ! [U_2361,U_2360,U_2359,U_2358] :
      ( c_Orderings_Oord__class_Oless__eq(U_2358,hAPP(hAPP(c_Power_Opower__class_Opower(U_2358),U_2359),U_2361),hAPP(hAPP(c_Power_Opower__class_Opower(U_2358),U_2360),U_2361))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2358,c_Groups_Ozero__class_Ozero(U_2358),U_2359)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2358,U_2359,U_2360)
      | ~ class_Rings_Olinordered__semidom(U_2358) ),
    inference(variable_rename,[status(thm)],[f_719_1]) ).

fof(f_719_3,plain,
    ! [U_2358,U_2359,U_2360,U_2361] :
      ( c_Orderings_Oord__class_Oless__eq(U_2358,hAPP(hAPP(c_Power_Opower__class_Opower(U_2358),U_2359),U_2361),hAPP(hAPP(c_Power_Opower__class_Opower(U_2358),U_2360),U_2361))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2358,c_Groups_Ozero__class_Ozero(U_2358),U_2359)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2358,U_2359,U_2360)
      | ~ class_Rings_Olinordered__semidom(U_2358) ),
    inference(definitional_conversion,[status(esa)],[f_719_2]) ).

cnf(f_719_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2358,hAPP(hAPP(c_Power_Opower__class_Opower(U_2358),U_2359),U_2361),hAPP(hAPP(c_Power_Opower__class_Opower(U_2358),U_2360),U_2361))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2358,c_Groups_Ozero__class_Ozero(U_2358),U_2359)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2358,U_2359,U_2360)
    | ~ class_Rings_Olinordered__semidom(U_2358) ),
    inference(clausify,[status(thm)],[f_719_3]) ).

fof(f_720_1,plain,
    ! [V_n,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__power]) ).

fof(f_720_2,plain,
    ! [U_2364,U_2363,U_2362] :
      ( c_Orderings_Oord__class_Oless(U_2362,c_Groups_Ozero__class_Ozero(U_2362),hAPP(hAPP(c_Power_Opower__class_Opower(U_2362),U_2363),U_2364))
      | ~ c_Orderings_Oord__class_Oless(U_2362,c_Groups_Ozero__class_Ozero(U_2362),U_2363)
      | ~ class_Rings_Olinordered__semidom(U_2362) ),
    inference(variable_rename,[status(thm)],[f_720_1]) ).

fof(f_720_3,plain,
    ! [U_2364,U_2362,U_2363] :
      ( c_Orderings_Oord__class_Oless(U_2362,c_Groups_Ozero__class_Ozero(U_2362),hAPP(hAPP(c_Power_Opower__class_Opower(U_2362),U_2363),U_2364))
      | ~ c_Orderings_Oord__class_Oless(U_2362,c_Groups_Ozero__class_Ozero(U_2362),U_2363)
      | ~ class_Rings_Olinordered__semidom(U_2362) ),
    inference(definitional_conversion,[status(esa)],[f_720_2]) ).

cnf(f_720_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2362,c_Groups_Ozero__class_Ozero(U_2362),hAPP(hAPP(c_Power_Opower__class_Opower(U_2362),U_2363),U_2364))
    | ~ c_Orderings_Oord__class_Oless(U_2362,c_Groups_Ozero__class_Ozero(U_2362),U_2363)
    | ~ class_Rings_Olinordered__semidom(U_2362) ),
    inference(clausify,[status(thm)],[f_720_3]) ).

fof(f_721_1,plain,
    ! [V_n,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_one__le__power]) ).

fof(f_721_2,plain,
    ! [U_2367,U_2366,U_2365] :
      ( c_Orderings_Oord__class_Oless__eq(U_2365,c_Groups_Oone__class_Oone(U_2365),hAPP(hAPP(c_Power_Opower__class_Opower(U_2365),U_2366),U_2367))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2365,c_Groups_Oone__class_Oone(U_2365),U_2366)
      | ~ class_Rings_Olinordered__semidom(U_2365) ),
    inference(variable_rename,[status(thm)],[f_721_1]) ).

fof(f_721_3,plain,
    ! [U_2365,U_2366,U_2367] :
      ( c_Orderings_Oord__class_Oless__eq(U_2365,c_Groups_Oone__class_Oone(U_2365),hAPP(hAPP(c_Power_Opower__class_Opower(U_2365),U_2366),U_2367))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2365,c_Groups_Oone__class_Oone(U_2365),U_2366)
      | ~ class_Rings_Olinordered__semidom(U_2365) ),
    inference(definitional_conversion,[status(esa)],[f_721_2]) ).

cnf(f_721_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2365,c_Groups_Oone__class_Oone(U_2365),hAPP(hAPP(c_Power_Opower__class_Opower(U_2365),U_2366),U_2367))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2365,c_Groups_Oone__class_Oone(U_2365),U_2366)
    | ~ class_Rings_Olinordered__semidom(U_2365) ),
    inference(clausify,[status(thm)],[f_721_3]) ).

fof(f_722_1,plain,
    ! [V_n_2,V_ab_2,T_a] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ab_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a)
          | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) )
        & ( ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) )
          | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ab_2),V_n_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Rings_Ozero__neq__one(T_a)
      | ~ class_Rings_Ono__zero__divisors(T_a)
      | ~ class_Rings_Omult__zero(T_a)
      | ~ class_Power_Opower(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff]) ).

fof(f_722_2,plain,
    ! [U_2370,U_2369,U_2368] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2368),U_2369),U_2370) = c_Groups_Ozero__class_Ozero(U_2368)
          | U_2370 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | U_2369 != c_Groups_Ozero__class_Ozero(U_2368) )
        & ( ( U_2370 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & U_2369 = c_Groups_Ozero__class_Ozero(U_2368) )
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_2368),U_2369),U_2370) != c_Groups_Ozero__class_Ozero(U_2368) ) )
      | ~ class_Rings_Ozero__neq__one(U_2368)
      | ~ class_Rings_Ono__zero__divisors(U_2368)
      | ~ class_Rings_Omult__zero(U_2368)
      | ~ class_Power_Opower(U_2368) ),
    inference(variable_rename,[status(thm)],[f_722_1]) ).

fof(f_722_3,plain,
    ( ! [U_2368,U_2369,U_2370] :
        ( U_2370 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP211(U_2368,U_2369,U_2370) )
    & ! [U_2368,U_2369,U_2370] :
        ( U_2369 = c_Groups_Ozero__class_Ozero(U_2368)
        | ~ sP211(U_2368,U_2369,U_2370) )
    & ! [U_2368,U_2369,U_2370] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2368),U_2369),U_2370) = c_Groups_Ozero__class_Ozero(U_2368)
        | U_2370 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2369 != c_Groups_Ozero__class_Ozero(U_2368)
        | ~ sP212(U_2368,U_2369,U_2370) )
    & ! [U_2368,U_2369,U_2370] :
        ( sP211(U_2368,U_2369,U_2370)
        | hAPP(hAPP(c_Power_Opower__class_Opower(U_2368),U_2369),U_2370) != c_Groups_Ozero__class_Ozero(U_2368)
        | ~ sP212(U_2368,U_2369,U_2370) )
    & ! [U_2368,U_2369,U_2370] :
        ( sP212(U_2368,U_2369,U_2370)
        | ~ class_Rings_Ozero__neq__one(U_2368)
        | ~ class_Rings_Ono__zero__divisors(U_2368)
        | ~ class_Rings_Omult__zero(U_2368)
        | ~ class_Power_Opower(U_2368) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP211,sP212])],[f_722_2]) ).

cnf(f_722_4,plain,
    ( sP212(U_2368,U_2369,U_2370)
    | ~ class_Rings_Ozero__neq__one(U_2368)
    | ~ class_Rings_Ono__zero__divisors(U_2368)
    | ~ class_Rings_Omult__zero(U_2368)
    | ~ class_Power_Opower(U_2368) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

cnf(f_722_5,plain,
    ( sP211(U_2368,U_2369,U_2370)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_2368),U_2369),U_2370) != c_Groups_Ozero__class_Ozero(U_2368)
    | ~ sP212(U_2368,U_2369,U_2370) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

cnf(f_722_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2368),U_2369),U_2370) = c_Groups_Ozero__class_Ozero(U_2368)
    | U_2370 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2369 != c_Groups_Ozero__class_Ozero(U_2368)
    | ~ sP212(U_2368,U_2369,U_2370) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

cnf(f_722_7,plain,
    ( U_2369 = c_Groups_Ozero__class_Ozero(U_2368)
    | ~ sP211(U_2368,U_2369,U_2370) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

cnf(f_722_8,plain,
    ( U_2370 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP211(U_2368,U_2369,U_2370) ),
    inference(clausify,[status(thm)],[f_722_3]) ).

fof(f_723_1,plain,
    ! [V_n_2,V_m_2,V_ab_2,T_a] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ab_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ab_2),V_n_2)
          | V_m_2 != V_n_2 )
        & ( V_m_2 = V_n_2
          | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ab_2),V_m_2) != hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ab_2),V_n_2) ) )
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_ab_2)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__inject__exp]) ).

fof(f_723_2,plain,
    ! [U_2374,U_2373,U_2372,U_2371] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2371),U_2372),U_2373) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2371),U_2372),U_2374)
          | U_2373 != U_2374 )
        & ( U_2373 = U_2374
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_2371),U_2372),U_2373) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2371),U_2372),U_2374) ) )
      | ~ c_Orderings_Oord__class_Oless(U_2371,c_Groups_Oone__class_Oone(U_2371),U_2372)
      | ~ class_Rings_Olinordered__semidom(U_2371) ),
    inference(variable_rename,[status(thm)],[f_723_1]) ).

fof(f_723_3,plain,
    ( ! [U_2372,U_2374,U_2373,U_2371] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2371),U_2372),U_2373) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2371),U_2372),U_2374)
        | U_2373 != U_2374
        | ~ sP213(U_2372,U_2374,U_2373,U_2371) )
    & ! [U_2372,U_2374,U_2373,U_2371] :
        ( U_2373 = U_2374
        | hAPP(hAPP(c_Power_Opower__class_Opower(U_2371),U_2372),U_2373) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2371),U_2372),U_2374)
        | ~ sP213(U_2372,U_2374,U_2373,U_2371) )
    & ! [U_2372,U_2374,U_2373,U_2371] :
        ( sP213(U_2372,U_2374,U_2373,U_2371)
        | ~ c_Orderings_Oord__class_Oless(U_2371,c_Groups_Oone__class_Oone(U_2371),U_2372)
        | ~ class_Rings_Olinordered__semidom(U_2371) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP213])],[f_723_2]) ).

cnf(f_723_4,plain,
    ( sP213(U_2372,U_2374,U_2373,U_2371)
    | ~ c_Orderings_Oord__class_Oless(U_2371,c_Groups_Oone__class_Oone(U_2371),U_2372)
    | ~ class_Rings_Olinordered__semidom(U_2371) ),
    inference(clausify,[status(thm)],[f_723_3]) ).

cnf(f_723_5,plain,
    ( U_2373 = U_2374
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_2371),U_2372),U_2373) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2371),U_2372),U_2374)
    | ~ sP213(U_2372,U_2374,U_2373,U_2371) ),
    inference(clausify,[status(thm)],[f_723_3]) ).

cnf(f_723_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2371),U_2372),U_2373) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2371),U_2372),U_2374)
    | U_2373 != U_2374
    | ~ sP213(U_2372,U_2374,U_2373,U_2371) ),
    inference(clausify,[status(thm)],[f_723_3]) ).

fof(f_724_1,plain,
    ! [V_n,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_OSuc(V_n)) = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Rings_Osemiring__0(T_a)
      | ~ class_Power_Opower(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__0__Suc]) ).

fof(f_724_2,plain,
    ! [U_2376,U_2375] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2375),c_Groups_Ozero__class_Ozero(U_2375)),c_Nat_OSuc(U_2376)) = c_Groups_Ozero__class_Ozero(U_2375)
      | ~ class_Rings_Osemiring__0(U_2375)
      | ~ class_Power_Opower(U_2375) ),
    inference(variable_rename,[status(thm)],[f_724_1]) ).

fof(f_724_3,plain,
    ! [U_2376,U_2375] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2375),c_Groups_Ozero__class_Ozero(U_2375)),c_Nat_OSuc(U_2376)) = c_Groups_Ozero__class_Ozero(U_2375)
      | ~ class_Rings_Osemiring__0(U_2375)
      | ~ class_Power_Opower(U_2375) ),
    inference(definitional_conversion,[status(esa)],[f_724_2]) ).

cnf(f_724_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2375),c_Groups_Ozero__class_Ozero(U_2375)),c_Nat_OSuc(U_2376)) = c_Groups_Ozero__class_Ozero(U_2375)
    | ~ class_Rings_Osemiring__0(U_2375)
    | ~ class_Power_Opower(U_2375) ),
    inference(clausify,[status(thm)],[f_724_3]) ).

fof(f_725_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ class_Power_Opower(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__Suc]) ).

fof(f_725_2,plain,
    ! [U_2379,U_2378,U_2377] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2377),U_2378),c_Nat_OSuc(U_2379)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2377),U_2378),hAPP(hAPP(c_Power_Opower__class_Opower(U_2377),U_2378),U_2379))
      | ~ class_Power_Opower(U_2377) ),
    inference(variable_rename,[status(thm)],[f_725_1]) ).

fof(f_725_3,plain,
    ! [U_2377,U_2378,U_2379] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2377),U_2378),c_Nat_OSuc(U_2379)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2377),U_2378),hAPP(hAPP(c_Power_Opower__class_Opower(U_2377),U_2378),U_2379))
      | ~ class_Power_Opower(U_2377) ),
    inference(definitional_conversion,[status(esa)],[f_725_2]) ).

cnf(f_725_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2377),U_2378),c_Nat_OSuc(U_2379)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2377),U_2378),hAPP(hAPP(c_Power_Opower__class_Opower(U_2377),U_2378),U_2379))
    | ~ class_Power_Opower(U_2377) ),
    inference(clausify,[status(thm)],[f_725_3]) ).

fof(f_726_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a)
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__Suc2]) ).

fof(f_726_2,plain,
    ! [U_2382,U_2381,U_2380] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2380),U_2381),c_Nat_OSuc(U_2382)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2380),hAPP(hAPP(c_Power_Opower__class_Opower(U_2380),U_2381),U_2382)),U_2381)
      | ~ class_Groups_Omonoid__mult(U_2380) ),
    inference(variable_rename,[status(thm)],[f_726_1]) ).

fof(f_726_3,plain,
    ! [U_2380,U_2381,U_2382] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2380),U_2381),c_Nat_OSuc(U_2382)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2380),hAPP(hAPP(c_Power_Opower__class_Opower(U_2380),U_2381),U_2382)),U_2381)
      | ~ class_Groups_Omonoid__mult(U_2380) ),
    inference(definitional_conversion,[status(esa)],[f_726_2]) ).

cnf(f_726_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2380),U_2381),c_Nat_OSuc(U_2382)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2380),hAPP(hAPP(c_Power_Opower__class_Opower(U_2380),U_2381),U_2382)),U_2381)
    | ~ class_Groups_Omonoid__mult(U_2380) ),
    inference(clausify,[status(thm)],[f_726_3]) ).

fof(f_727_1,plain,
    ! [V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a)
      | ~ class_Power_Opower(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__0]) ).

fof(f_727_2,plain,
    ! [U_2384,U_2383] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2383),U_2384),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2383)
      | ~ class_Power_Opower(U_2383) ),
    inference(variable_rename,[status(thm)],[f_727_1]) ).

fof(f_727_3,plain,
    ! [U_2383,U_2384] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2383),U_2384),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2383)
      | ~ class_Power_Opower(U_2383) ),
    inference(definitional_conversion,[status(esa)],[f_727_2]) ).

cnf(f_727_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2383),U_2384),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_2383)
    | ~ class_Power_Opower(U_2383) ),
    inference(clausify,[status(thm)],[f_727_3]) ).

fof(f_728_1,plain,
    ! [V_n,V_m,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ class_Groups_Omonoid__mult(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__add]) ).

fof(f_728_2,plain,
    ! [U_2388,U_2387,U_2386,U_2385] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2385),U_2386),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2387,U_2388)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2385),hAPP(hAPP(c_Power_Opower__class_Opower(U_2385),U_2386),U_2387)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2385),U_2386),U_2388))
      | ~ class_Groups_Omonoid__mult(U_2385) ),
    inference(variable_rename,[status(thm)],[f_728_1]) ).

fof(f_728_3,plain,
    ! [U_2385,U_2386,U_2387,U_2388] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2385),U_2386),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2387,U_2388)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2385),hAPP(hAPP(c_Power_Opower__class_Opower(U_2385),U_2386),U_2387)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2385),U_2386),U_2388))
      | ~ class_Groups_Omonoid__mult(U_2385) ),
    inference(definitional_conversion,[status(esa)],[f_728_2]) ).

cnf(f_728_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2385),U_2386),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2387,U_2388)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2385),hAPP(hAPP(c_Power_Opower__class_Opower(U_2385),U_2386),U_2387)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2385),U_2386),U_2388))
    | ~ class_Groups_Omonoid__mult(U_2385) ),
    inference(clausify,[status(thm)],[f_728_3]) ).

fof(f_729_1,plain,
    ! [V_n,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i) ),
    inference(fof_nnf,[status(thm)],[fact_nat__one__le__power]) ).

fof(f_729_2,plain,
    ! [U_2390,U_2389] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2389),U_2390))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2389) ),
    inference(variable_rename,[status(thm)],[f_729_1]) ).

fof(f_729_3,plain,
    ! [U_2390,U_2389] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2389),U_2390))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2389) ),
    inference(definitional_conversion,[status(esa)],[f_729_2]) ).

cnf(f_729_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2389),U_2390))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2389) ),
    inference(clausify,[status(thm)],[f_729_3]) ).

fof(f_730_1,plain,
    ! [V_b,V_n,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,V_a,V_b)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
      | ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__base]) ).

fof(f_730_2,plain,
    ! [U_2394,U_2393,U_2392,U_2391] :
      ( c_Orderings_Oord__class_Oless(U_2391,U_2392,U_2394)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2391,c_Groups_Ozero__class_Ozero(U_2391),U_2394)
      | ~ c_Orderings_Oord__class_Oless(U_2391,hAPP(hAPP(c_Power_Opower__class_Opower(U_2391),U_2392),U_2393),hAPP(hAPP(c_Power_Opower__class_Opower(U_2391),U_2394),U_2393))
      | ~ class_Rings_Olinordered__semidom(U_2391) ),
    inference(variable_rename,[status(thm)],[f_730_1]) ).

fof(f_730_3,plain,
    ! [U_2391,U_2392,U_2393,U_2394] :
      ( c_Orderings_Oord__class_Oless(U_2391,U_2392,U_2394)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2391,c_Groups_Ozero__class_Ozero(U_2391),U_2394)
      | ~ c_Orderings_Oord__class_Oless(U_2391,hAPP(hAPP(c_Power_Opower__class_Opower(U_2391),U_2392),U_2393),hAPP(hAPP(c_Power_Opower__class_Opower(U_2391),U_2394),U_2393))
      | ~ class_Rings_Olinordered__semidom(U_2391) ),
    inference(definitional_conversion,[status(esa)],[f_730_2]) ).

cnf(f_730_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2391,U_2392,U_2394)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2391,c_Groups_Ozero__class_Ozero(U_2391),U_2394)
    | ~ c_Orderings_Oord__class_Oless(U_2391,hAPP(hAPP(c_Power_Opower__class_Opower(U_2391),U_2392),U_2393),hAPP(hAPP(c_Power_Opower__class_Opower(U_2391),U_2394),U_2393))
    | ~ class_Rings_Olinordered__semidom(U_2391) ),
    inference(clausify,[status(thm)],[f_730_3]) ).

fof(f_731_1,plain,
    ! [V_b,V_n,V_a,T_a] :
      ( V_a = V_b
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) != hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__inject__base]) ).

fof(f_731_2,plain,
    ! [U_2398,U_2397,U_2396,U_2395] :
      ( U_2396 = U_2398
      | ~ c_Orderings_Oord__class_Oless__eq(U_2395,c_Groups_Ozero__class_Ozero(U_2395),U_2398)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2395,c_Groups_Ozero__class_Ozero(U_2395),U_2396)
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_2395),U_2396),c_Nat_OSuc(U_2397)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2395),U_2398),c_Nat_OSuc(U_2397))
      | ~ class_Rings_Olinordered__semidom(U_2395) ),
    inference(variable_rename,[status(thm)],[f_731_1]) ).

fof(f_731_3,plain,
    ! [U_2395,U_2396,U_2397,U_2398] :
      ( U_2396 = U_2398
      | ~ c_Orderings_Oord__class_Oless__eq(U_2395,c_Groups_Ozero__class_Ozero(U_2395),U_2398)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2395,c_Groups_Ozero__class_Ozero(U_2395),U_2396)
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_2395),U_2396),c_Nat_OSuc(U_2397)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2395),U_2398),c_Nat_OSuc(U_2397))
      | ~ class_Rings_Olinordered__semidom(U_2395) ),
    inference(definitional_conversion,[status(esa)],[f_731_2]) ).

cnf(f_731_4,plain,
    ( U_2396 = U_2398
    | ~ c_Orderings_Oord__class_Oless__eq(U_2395,c_Groups_Ozero__class_Ozero(U_2395),U_2398)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2395,c_Groups_Ozero__class_Ozero(U_2395),U_2396)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_2395),U_2396),c_Nat_OSuc(U_2397)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2395),U_2398),c_Nat_OSuc(U_2397))
    | ~ class_Rings_Olinordered__semidom(U_2395) ),
    inference(clausify,[status(thm)],[f_731_3]) ).

fof(f_732_1,plain,
    ! [V_b,V_n,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Nat_OSuc(V_n)))
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__base]) ).

fof(f_732_2,plain,
    ! [U_2402,U_2401,U_2400,U_2399] :
      ( c_Orderings_Oord__class_Oless__eq(U_2399,U_2400,U_2402)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2399,c_Groups_Ozero__class_Ozero(U_2399),U_2402)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2399,hAPP(hAPP(c_Power_Opower__class_Opower(U_2399),U_2400),c_Nat_OSuc(U_2401)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2399),U_2402),c_Nat_OSuc(U_2401)))
      | ~ class_Rings_Olinordered__semidom(U_2399) ),
    inference(variable_rename,[status(thm)],[f_732_1]) ).

fof(f_732_3,plain,
    ! [U_2399,U_2400,U_2401,U_2402] :
      ( c_Orderings_Oord__class_Oless__eq(U_2399,U_2400,U_2402)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2399,c_Groups_Ozero__class_Ozero(U_2399),U_2402)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2399,hAPP(hAPP(c_Power_Opower__class_Opower(U_2399),U_2400),c_Nat_OSuc(U_2401)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2399),U_2402),c_Nat_OSuc(U_2401)))
      | ~ class_Rings_Olinordered__semidom(U_2399) ),
    inference(definitional_conversion,[status(esa)],[f_732_2]) ).

cnf(f_732_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2399,U_2400,U_2402)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2399,c_Groups_Ozero__class_Ozero(U_2399),U_2402)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2399,hAPP(hAPP(c_Power_Opower__class_Opower(U_2399),U_2400),c_Nat_OSuc(U_2401)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2399),U_2402),c_Nat_OSuc(U_2401)))
    | ~ class_Rings_Olinordered__semidom(U_2399) ),
    inference(clausify,[status(thm)],[f_732_3]) ).

fof(f_733_1,plain,
    ! [V_n,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__gt1__lemma]) ).

fof(f_733_2,plain,
    ! [U_2405,U_2404,U_2403] :
      ( c_Orderings_Oord__class_Oless(U_2403,c_Groups_Oone__class_Oone(U_2403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2403),U_2404),hAPP(hAPP(c_Power_Opower__class_Opower(U_2403),U_2404),U_2405)))
      | ~ c_Orderings_Oord__class_Oless(U_2403,c_Groups_Oone__class_Oone(U_2403),U_2404)
      | ~ class_Rings_Olinordered__semidom(U_2403) ),
    inference(variable_rename,[status(thm)],[f_733_1]) ).

fof(f_733_3,plain,
    ! [U_2403,U_2404,U_2405] :
      ( c_Orderings_Oord__class_Oless(U_2403,c_Groups_Oone__class_Oone(U_2403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2403),U_2404),hAPP(hAPP(c_Power_Opower__class_Opower(U_2403),U_2404),U_2405)))
      | ~ c_Orderings_Oord__class_Oless(U_2403,c_Groups_Oone__class_Oone(U_2403),U_2404)
      | ~ class_Rings_Olinordered__semidom(U_2403) ),
    inference(definitional_conversion,[status(esa)],[f_733_2]) ).

cnf(f_733_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2403,c_Groups_Oone__class_Oone(U_2403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2403),U_2404),hAPP(hAPP(c_Power_Opower__class_Opower(U_2403),U_2404),U_2405)))
    | ~ c_Orderings_Oord__class_Oless(U_2403,c_Groups_Oone__class_Oone(U_2403),U_2404)
    | ~ class_Rings_Olinordered__semidom(U_2403) ),
    inference(clausify,[status(thm)],[f_733_3]) ).

fof(f_734_1,plain,
    ! [V_n,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__less__power__Suc]) ).

fof(f_734_2,plain,
    ! [U_2408,U_2407,U_2406] :
      ( c_Orderings_Oord__class_Oless(U_2406,hAPP(hAPP(c_Power_Opower__class_Opower(U_2406),U_2407),U_2408),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2406),U_2407),hAPP(hAPP(c_Power_Opower__class_Opower(U_2406),U_2407),U_2408)))
      | ~ c_Orderings_Oord__class_Oless(U_2406,c_Groups_Oone__class_Oone(U_2406),U_2407)
      | ~ class_Rings_Olinordered__semidom(U_2406) ),
    inference(variable_rename,[status(thm)],[f_734_1]) ).

fof(f_734_3,plain,
    ! [U_2406,U_2407,U_2408] :
      ( c_Orderings_Oord__class_Oless(U_2406,hAPP(hAPP(c_Power_Opower__class_Opower(U_2406),U_2407),U_2408),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2406),U_2407),hAPP(hAPP(c_Power_Opower__class_Opower(U_2406),U_2407),U_2408)))
      | ~ c_Orderings_Oord__class_Oless(U_2406,c_Groups_Oone__class_Oone(U_2406),U_2407)
      | ~ class_Rings_Olinordered__semidom(U_2406) ),
    inference(definitional_conversion,[status(esa)],[f_734_2]) ).

cnf(f_734_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2406,hAPP(hAPP(c_Power_Opower__class_Opower(U_2406),U_2407),U_2408),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2406),U_2407),hAPP(hAPP(c_Power_Opower__class_Opower(U_2406),U_2407),U_2408)))
    | ~ c_Orderings_Oord__class_Oless(U_2406,c_Groups_Oone__class_Oone(U_2406),U_2407)
    | ~ class_Rings_Olinordered__semidom(U_2406) ),
    inference(clausify,[status(thm)],[f_734_3]) ).

fof(f_735_1,plain,
    ! [V_n,T_a] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a)
          | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a)
          | V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ class_Rings_Osemiring__0(T_a)
      | ~ class_Power_Opower(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__0__left]) ).

fof(f_735_2,plain,
    ! [U_2410,U_2409] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2409),c_Groups_Ozero__class_Ozero(U_2409)),U_2410) = c_Groups_Ozero__class_Ozero(U_2409)
          | U_2410 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2409),c_Groups_Ozero__class_Ozero(U_2409)),U_2410) = c_Groups_Oone__class_Oone(U_2409)
          | U_2410 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ class_Rings_Osemiring__0(U_2409)
      | ~ class_Power_Opower(U_2409) ),
    inference(variable_rename,[status(thm)],[f_735_1]) ).

fof(f_735_3,plain,
    ( ! [U_2409,U_2410] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2409),c_Groups_Ozero__class_Ozero(U_2409)),U_2410) = c_Groups_Ozero__class_Ozero(U_2409)
        | U_2410 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP214(U_2409,U_2410) )
    & ! [U_2409,U_2410] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2409),c_Groups_Ozero__class_Ozero(U_2409)),U_2410) = c_Groups_Oone__class_Oone(U_2409)
        | U_2410 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP214(U_2409,U_2410) )
    & ! [U_2409,U_2410] :
        ( sP214(U_2409,U_2410)
        | ~ class_Rings_Osemiring__0(U_2409)
        | ~ class_Power_Opower(U_2409) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP214])],[f_735_2]) ).

cnf(f_735_4,plain,
    ( sP214(U_2409,U_2410)
    | ~ class_Rings_Osemiring__0(U_2409)
    | ~ class_Power_Opower(U_2409) ),
    inference(clausify,[status(thm)],[f_735_3]) ).

cnf(f_735_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2409),c_Groups_Ozero__class_Ozero(U_2409)),U_2410) = c_Groups_Oone__class_Oone(U_2409)
    | U_2410 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP214(U_2409,U_2410) ),
    inference(clausify,[status(thm)],[f_735_3]) ).

cnf(f_735_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2409),c_Groups_Ozero__class_Ozero(U_2409)),U_2410) = c_Groups_Ozero__class_Ozero(U_2409)
    | U_2410 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP214(U_2409,U_2410) ),
    inference(clausify,[status(thm)],[f_735_3]) ).

fof(f_736_1,plain,
    ! [V_n,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)))
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__gt1]) ).

fof(f_736_2,plain,
    ! [U_2413,U_2412,U_2411] :
      ( c_Orderings_Oord__class_Oless(U_2411,c_Groups_Oone__class_Oone(U_2411),hAPP(hAPP(c_Power_Opower__class_Opower(U_2411),U_2412),c_Nat_OSuc(U_2413)))
      | ~ c_Orderings_Oord__class_Oless(U_2411,c_Groups_Oone__class_Oone(U_2411),U_2412)
      | ~ class_Rings_Olinordered__semidom(U_2411) ),
    inference(variable_rename,[status(thm)],[f_736_1]) ).

fof(f_736_3,plain,
    ! [U_2412,U_2411,U_2413] :
      ( c_Orderings_Oord__class_Oless(U_2411,c_Groups_Oone__class_Oone(U_2411),hAPP(hAPP(c_Power_Opower__class_Opower(U_2411),U_2412),c_Nat_OSuc(U_2413)))
      | ~ c_Orderings_Oord__class_Oless(U_2411,c_Groups_Oone__class_Oone(U_2411),U_2412)
      | ~ class_Rings_Olinordered__semidom(U_2411) ),
    inference(definitional_conversion,[status(esa)],[f_736_2]) ).

cnf(f_736_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2411,c_Groups_Oone__class_Oone(U_2411),hAPP(hAPP(c_Power_Opower__class_Opower(U_2411),U_2412),c_Nat_OSuc(U_2413)))
    | ~ c_Orderings_Oord__class_Oless(U_2411,c_Groups_Oone__class_Oone(U_2411),U_2412)
    | ~ class_Rings_Olinordered__semidom(U_2411) ),
    inference(clausify,[status(thm)],[f_736_3]) ).

fof(f_737_1,plain,
    ! [V_n,V_a,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ class_Rings_Oring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__minus]) ).

fof(f_737_2,plain,
    ! [U_2416,U_2415,U_2414] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2414),c_Groups_Ouminus__class_Ouminus(U_2414,U_2415)),U_2416) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2414),hAPP(hAPP(c_Power_Opower__class_Opower(U_2414),c_Groups_Ouminus__class_Ouminus(U_2414,c_Groups_Oone__class_Oone(U_2414))),U_2416)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2414),U_2415),U_2416))
      | ~ class_Rings_Oring__1(U_2414) ),
    inference(variable_rename,[status(thm)],[f_737_1]) ).

fof(f_737_3,plain,
    ! [U_2414,U_2415,U_2416] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2414),c_Groups_Ouminus__class_Ouminus(U_2414,U_2415)),U_2416) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2414),hAPP(hAPP(c_Power_Opower__class_Opower(U_2414),c_Groups_Ouminus__class_Ouminus(U_2414,c_Groups_Oone__class_Oone(U_2414))),U_2416)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2414),U_2415),U_2416))
      | ~ class_Rings_Oring__1(U_2414) ),
    inference(definitional_conversion,[status(esa)],[f_737_2]) ).

cnf(f_737_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2414),c_Groups_Ouminus__class_Ouminus(U_2414,U_2415)),U_2416) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2414),hAPP(hAPP(c_Power_Opower__class_Opower(U_2414),c_Groups_Ouminus__class_Ouminus(U_2414,c_Groups_Oone__class_Oone(U_2414))),U_2416)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2414),U_2415),U_2416))
    | ~ class_Rings_Oring__1(U_2414) ),
    inference(clausify,[status(thm)],[f_737_3]) ).

fof(f_738_1,plain,
    ! [V_y_2,V_x_2,V_b_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) )
        & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2)
          | ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2)) ) )
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff]) ).

fof(f_738_2,plain,
    ! [U_2420,U_2419,U_2418,U_2417] :
      ( ( ( c_Orderings_Oord__class_Oless(U_2417,hAPP(hAPP(c_Power_Opower__class_Opower(U_2417),U_2418),U_2419),hAPP(hAPP(c_Power_Opower__class_Opower(U_2417),U_2418),U_2420))
          | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2419,U_2420) )
        & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2419,U_2420)
          | ~ c_Orderings_Oord__class_Oless(U_2417,hAPP(hAPP(c_Power_Opower__class_Opower(U_2417),U_2418),U_2419),hAPP(hAPP(c_Power_Opower__class_Opower(U_2417),U_2418),U_2420)) ) )
      | ~ c_Orderings_Oord__class_Oless(U_2417,c_Groups_Oone__class_Oone(U_2417),U_2418)
      | ~ class_Rings_Olinordered__semidom(U_2417) ),
    inference(variable_rename,[status(thm)],[f_738_1]) ).

fof(f_738_3,plain,
    ( ! [U_2417,U_2418,U_2419,U_2420] :
        ( c_Orderings_Oord__class_Oless(U_2417,hAPP(hAPP(c_Power_Opower__class_Opower(U_2417),U_2418),U_2419),hAPP(hAPP(c_Power_Opower__class_Opower(U_2417),U_2418),U_2420))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2419,U_2420)
        | ~ sP215(U_2417,U_2418,U_2419,U_2420) )
    & ! [U_2417,U_2418,U_2419,U_2420] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2419,U_2420)
        | ~ c_Orderings_Oord__class_Oless(U_2417,hAPP(hAPP(c_Power_Opower__class_Opower(U_2417),U_2418),U_2419),hAPP(hAPP(c_Power_Opower__class_Opower(U_2417),U_2418),U_2420))
        | ~ sP215(U_2417,U_2418,U_2419,U_2420) )
    & ! [U_2417,U_2418,U_2419,U_2420] :
        ( sP215(U_2417,U_2418,U_2419,U_2420)
        | ~ c_Orderings_Oord__class_Oless(U_2417,c_Groups_Oone__class_Oone(U_2417),U_2418)
        | ~ class_Rings_Olinordered__semidom(U_2417) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP215])],[f_738_2]) ).

cnf(f_738_4,plain,
    ( sP215(U_2417,U_2418,U_2419,U_2420)
    | ~ c_Orderings_Oord__class_Oless(U_2417,c_Groups_Oone__class_Oone(U_2417),U_2418)
    | ~ class_Rings_Olinordered__semidom(U_2417) ),
    inference(clausify,[status(thm)],[f_738_3]) ).

cnf(f_738_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2419,U_2420)
    | ~ c_Orderings_Oord__class_Oless(U_2417,hAPP(hAPP(c_Power_Opower__class_Opower(U_2417),U_2418),U_2419),hAPP(hAPP(c_Power_Opower__class_Opower(U_2417),U_2418),U_2420))
    | ~ sP215(U_2417,U_2418,U_2419,U_2420) ),
    inference(clausify,[status(thm)],[f_738_3]) ).

cnf(f_738_6,plain,
    ( c_Orderings_Oord__class_Oless(U_2417,hAPP(hAPP(c_Power_Opower__class_Opower(U_2417),U_2418),U_2419),hAPP(hAPP(c_Power_Opower__class_Opower(U_2417),U_2418),U_2420))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2419,U_2420)
    | ~ sP215(U_2417,U_2418,U_2419,U_2420) ),
    inference(clausify,[status(thm)],[f_738_3]) ).

fof(f_739_1,plain,
    ! [V_n,V_m,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
      | ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__exp]) ).

fof(f_739_2,plain,
    ! [U_2424,U_2423,U_2422,U_2421] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2423,U_2424)
      | ~ c_Orderings_Oord__class_Oless(U_2421,hAPP(hAPP(c_Power_Opower__class_Opower(U_2421),U_2422),U_2423),hAPP(hAPP(c_Power_Opower__class_Opower(U_2421),U_2422),U_2424))
      | ~ c_Orderings_Oord__class_Oless(U_2421,c_Groups_Oone__class_Oone(U_2421),U_2422)
      | ~ class_Rings_Olinordered__semidom(U_2421) ),
    inference(variable_rename,[status(thm)],[f_739_1]) ).

fof(f_739_3,plain,
    ! [U_2421,U_2424,U_2423,U_2422] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2423,U_2424)
      | ~ c_Orderings_Oord__class_Oless(U_2421,hAPP(hAPP(c_Power_Opower__class_Opower(U_2421),U_2422),U_2423),hAPP(hAPP(c_Power_Opower__class_Opower(U_2421),U_2422),U_2424))
      | ~ c_Orderings_Oord__class_Oless(U_2421,c_Groups_Oone__class_Oone(U_2421),U_2422)
      | ~ class_Rings_Olinordered__semidom(U_2421) ),
    inference(definitional_conversion,[status(esa)],[f_739_2]) ).

cnf(f_739_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2423,U_2424)
    | ~ c_Orderings_Oord__class_Oless(U_2421,hAPP(hAPP(c_Power_Opower__class_Opower(U_2421),U_2422),U_2423),hAPP(hAPP(c_Power_Opower__class_Opower(U_2421),U_2422),U_2424))
    | ~ c_Orderings_Oord__class_Oless(U_2421,c_Groups_Oone__class_Oone(U_2421),U_2422)
    | ~ class_Rings_Olinordered__semidom(U_2421) ),
    inference(clausify,[status(thm)],[f_739_3]) ).

fof(f_740_1,plain,
    ! [V_a,V_N,V_n,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__strict__increasing]) ).

fof(f_740_2,plain,
    ! [U_2428,U_2427,U_2426,U_2425] :
      ( c_Orderings_Oord__class_Oless(U_2425,hAPP(hAPP(c_Power_Opower__class_Opower(U_2425),U_2428),U_2426),hAPP(hAPP(c_Power_Opower__class_Opower(U_2425),U_2428),U_2427))
      | ~ c_Orderings_Oord__class_Oless(U_2425,c_Groups_Oone__class_Oone(U_2425),U_2428)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2426,U_2427)
      | ~ class_Rings_Olinordered__semidom(U_2425) ),
    inference(variable_rename,[status(thm)],[f_740_1]) ).

fof(f_740_3,plain,
    ! [U_2425,U_2426,U_2427,U_2428] :
      ( c_Orderings_Oord__class_Oless(U_2425,hAPP(hAPP(c_Power_Opower__class_Opower(U_2425),U_2428),U_2426),hAPP(hAPP(c_Power_Opower__class_Opower(U_2425),U_2428),U_2427))
      | ~ c_Orderings_Oord__class_Oless(U_2425,c_Groups_Oone__class_Oone(U_2425),U_2428)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2426,U_2427)
      | ~ class_Rings_Olinordered__semidom(U_2425) ),
    inference(definitional_conversion,[status(esa)],[f_740_2]) ).

cnf(f_740_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2425,hAPP(hAPP(c_Power_Opower__class_Opower(U_2425),U_2428),U_2426),hAPP(hAPP(c_Power_Opower__class_Opower(U_2425),U_2428),U_2427))
    | ~ c_Orderings_Oord__class_Oless(U_2425,c_Groups_Oone__class_Oone(U_2425),U_2428)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2426,U_2427)
    | ~ class_Rings_Olinordered__semidom(U_2425) ),
    inference(clausify,[status(thm)],[f_740_3]) ).

fof(f_741_1,plain,
    ! [V_a,V_N,V_n,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__increasing]) ).

fof(f_741_2,plain,
    ! [U_2432,U_2431,U_2430,U_2429] :
      ( c_Orderings_Oord__class_Oless__eq(U_2429,hAPP(hAPP(c_Power_Opower__class_Opower(U_2429),U_2432),U_2430),hAPP(hAPP(c_Power_Opower__class_Opower(U_2429),U_2432),U_2431))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2429,c_Groups_Oone__class_Oone(U_2429),U_2432)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2430,U_2431)
      | ~ class_Rings_Olinordered__semidom(U_2429) ),
    inference(variable_rename,[status(thm)],[f_741_1]) ).

fof(f_741_3,plain,
    ! [U_2429,U_2430,U_2431,U_2432] :
      ( c_Orderings_Oord__class_Oless__eq(U_2429,hAPP(hAPP(c_Power_Opower__class_Opower(U_2429),U_2432),U_2430),hAPP(hAPP(c_Power_Opower__class_Opower(U_2429),U_2432),U_2431))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2429,c_Groups_Oone__class_Oone(U_2429),U_2432)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2430,U_2431)
      | ~ class_Rings_Olinordered__semidom(U_2429) ),
    inference(definitional_conversion,[status(esa)],[f_741_2]) ).

cnf(f_741_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2429,hAPP(hAPP(c_Power_Opower__class_Opower(U_2429),U_2432),U_2430),hAPP(hAPP(c_Power_Opower__class_Opower(U_2429),U_2432),U_2431))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2429,c_Groups_Oone__class_Oone(U_2429),U_2432)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2430,U_2431)
    | ~ class_Rings_Olinordered__semidom(U_2429) ),
    inference(clausify,[status(thm)],[f_741_3]) ).

fof(f_742_1,plain,
    ! [V_n,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__Suc__less]) ).

fof(f_742_2,plain,
    ! [U_2435,U_2434,U_2433] :
      ( c_Orderings_Oord__class_Oless(U_2433,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2433),U_2434),hAPP(hAPP(c_Power_Opower__class_Opower(U_2433),U_2434),U_2435)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2433),U_2434),U_2435))
      | ~ c_Orderings_Oord__class_Oless(U_2433,U_2434,c_Groups_Oone__class_Oone(U_2433))
      | ~ c_Orderings_Oord__class_Oless(U_2433,c_Groups_Ozero__class_Ozero(U_2433),U_2434)
      | ~ class_Rings_Olinordered__semidom(U_2433) ),
    inference(variable_rename,[status(thm)],[f_742_1]) ).

fof(f_742_3,plain,
    ! [U_2433,U_2434,U_2435] :
      ( c_Orderings_Oord__class_Oless(U_2433,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2433),U_2434),hAPP(hAPP(c_Power_Opower__class_Opower(U_2433),U_2434),U_2435)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2433),U_2434),U_2435))
      | ~ c_Orderings_Oord__class_Oless(U_2433,U_2434,c_Groups_Oone__class_Oone(U_2433))
      | ~ c_Orderings_Oord__class_Oless(U_2433,c_Groups_Ozero__class_Ozero(U_2433),U_2434)
      | ~ class_Rings_Olinordered__semidom(U_2433) ),
    inference(definitional_conversion,[status(esa)],[f_742_2]) ).

cnf(f_742_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2433,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2433),U_2434),hAPP(hAPP(c_Power_Opower__class_Opower(U_2433),U_2434),U_2435)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2433),U_2434),U_2435))
    | ~ c_Orderings_Oord__class_Oless(U_2433,U_2434,c_Groups_Oone__class_Oone(U_2433))
    | ~ c_Orderings_Oord__class_Oless(U_2433,c_Groups_Ozero__class_Ozero(U_2433),U_2434)
    | ~ class_Rings_Olinordered__semidom(U_2433) ),
    inference(clausify,[status(thm)],[f_742_3]) ).

fof(f_743_1,plain,
    ! [V_n,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),c_Groups_Oone__class_Oone(T_a))
      | ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__Suc__less__one]) ).

fof(f_743_2,plain,
    ! [U_2438,U_2437,U_2436] :
      ( c_Orderings_Oord__class_Oless(U_2436,hAPP(hAPP(c_Power_Opower__class_Opower(U_2436),U_2437),c_Nat_OSuc(U_2438)),c_Groups_Oone__class_Oone(U_2436))
      | ~ c_Orderings_Oord__class_Oless(U_2436,U_2437,c_Groups_Oone__class_Oone(U_2436))
      | ~ c_Orderings_Oord__class_Oless(U_2436,c_Groups_Ozero__class_Ozero(U_2436),U_2437)
      | ~ class_Rings_Olinordered__semidom(U_2436) ),
    inference(variable_rename,[status(thm)],[f_743_1]) ).

fof(f_743_3,plain,
    ! [U_2436,U_2437,U_2438] :
      ( c_Orderings_Oord__class_Oless(U_2436,hAPP(hAPP(c_Power_Opower__class_Opower(U_2436),U_2437),c_Nat_OSuc(U_2438)),c_Groups_Oone__class_Oone(U_2436))
      | ~ c_Orderings_Oord__class_Oless(U_2436,U_2437,c_Groups_Oone__class_Oone(U_2436))
      | ~ c_Orderings_Oord__class_Oless(U_2436,c_Groups_Ozero__class_Ozero(U_2436),U_2437)
      | ~ class_Rings_Olinordered__semidom(U_2436) ),
    inference(definitional_conversion,[status(esa)],[f_743_2]) ).

cnf(f_743_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2436,hAPP(hAPP(c_Power_Opower__class_Opower(U_2436),U_2437),c_Nat_OSuc(U_2438)),c_Groups_Oone__class_Oone(U_2436))
    | ~ c_Orderings_Oord__class_Oless(U_2436,U_2437,c_Groups_Oone__class_Oone(U_2436))
    | ~ c_Orderings_Oord__class_Oless(U_2436,c_Groups_Ozero__class_Ozero(U_2436),U_2437)
    | ~ class_Rings_Olinordered__semidom(U_2436) ),
    inference(clausify,[status(thm)],[f_743_3]) ).

fof(f_744_1,plain,
    ! [V_a,V_N,V_n,T_a] :
      ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_N)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__strict__decreasing]) ).

fof(f_744_2,plain,
    ! [U_2442,U_2441,U_2440,U_2439] :
      ( c_Orderings_Oord__class_Oless(U_2439,hAPP(hAPP(c_Power_Opower__class_Opower(U_2439),U_2442),U_2441),hAPP(hAPP(c_Power_Opower__class_Opower(U_2439),U_2442),U_2440))
      | ~ c_Orderings_Oord__class_Oless(U_2439,U_2442,c_Groups_Oone__class_Oone(U_2439))
      | ~ c_Orderings_Oord__class_Oless(U_2439,c_Groups_Ozero__class_Ozero(U_2439),U_2442)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2440,U_2441)
      | ~ class_Rings_Olinordered__semidom(U_2439) ),
    inference(variable_rename,[status(thm)],[f_744_1]) ).

fof(f_744_3,plain,
    ! [U_2439,U_2440,U_2441,U_2442] :
      ( c_Orderings_Oord__class_Oless(U_2439,hAPP(hAPP(c_Power_Opower__class_Opower(U_2439),U_2442),U_2441),hAPP(hAPP(c_Power_Opower__class_Opower(U_2439),U_2442),U_2440))
      | ~ c_Orderings_Oord__class_Oless(U_2439,U_2442,c_Groups_Oone__class_Oone(U_2439))
      | ~ c_Orderings_Oord__class_Oless(U_2439,c_Groups_Ozero__class_Ozero(U_2439),U_2442)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2440,U_2441)
      | ~ class_Rings_Olinordered__semidom(U_2439) ),
    inference(definitional_conversion,[status(esa)],[f_744_2]) ).

cnf(f_744_4,plain,
    ( c_Orderings_Oord__class_Oless(U_2439,hAPP(hAPP(c_Power_Opower__class_Opower(U_2439),U_2442),U_2441),hAPP(hAPP(c_Power_Opower__class_Opower(U_2439),U_2442),U_2440))
    | ~ c_Orderings_Oord__class_Oless(U_2439,U_2442,c_Groups_Oone__class_Oone(U_2439))
    | ~ c_Orderings_Oord__class_Oless(U_2439,c_Groups_Ozero__class_Ozero(U_2439),U_2442)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2440,U_2441)
    | ~ class_Rings_Olinordered__semidom(U_2439) ),
    inference(clausify,[status(thm)],[f_744_3]) ).

fof(f_745_1,plain,
    ! [V_b,V_n,V_a,T_a] :
      ( V_a = V_b
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__eq__imp__eq__base]) ).

fof(f_745_2,plain,
    ! [U_2446,U_2445,U_2444,U_2443] :
      ( U_2444 = U_2446
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2445)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2443,c_Groups_Ozero__class_Ozero(U_2443),U_2446)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2443,c_Groups_Ozero__class_Ozero(U_2443),U_2444)
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_2443),U_2444),U_2445) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2443),U_2446),U_2445)
      | ~ class_Rings_Olinordered__semidom(U_2443) ),
    inference(variable_rename,[status(thm)],[f_745_1]) ).

fof(f_745_3,plain,
    ! [U_2443,U_2444,U_2445,U_2446] :
      ( U_2444 = U_2446
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2445)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2443,c_Groups_Ozero__class_Ozero(U_2443),U_2446)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2443,c_Groups_Ozero__class_Ozero(U_2443),U_2444)
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_2443),U_2444),U_2445) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2443),U_2446),U_2445)
      | ~ class_Rings_Olinordered__semidom(U_2443) ),
    inference(definitional_conversion,[status(esa)],[f_745_2]) ).

cnf(f_745_4,plain,
    ( U_2444 = U_2446
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2445)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2443,c_Groups_Ozero__class_Ozero(U_2443),U_2446)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2443,c_Groups_Ozero__class_Ozero(U_2443),U_2444)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_2443),U_2444),U_2445) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2443),U_2446),U_2445)
    | ~ class_Rings_Olinordered__semidom(U_2443) ),
    inference(clausify,[status(thm)],[f_745_3]) ).

fof(f_746_1,plain,
    ! [V_a,V_N,V_n,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__decreasing]) ).

fof(f_746_2,plain,
    ! [U_2450,U_2449,U_2448,U_2447] :
      ( c_Orderings_Oord__class_Oless__eq(U_2447,hAPP(hAPP(c_Power_Opower__class_Opower(U_2447),U_2450),U_2449),hAPP(hAPP(c_Power_Opower__class_Opower(U_2447),U_2450),U_2448))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2447,U_2450,c_Groups_Oone__class_Oone(U_2447))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2447,c_Groups_Ozero__class_Ozero(U_2447),U_2450)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2448,U_2449)
      | ~ class_Rings_Olinordered__semidom(U_2447) ),
    inference(variable_rename,[status(thm)],[f_746_1]) ).

fof(f_746_3,plain,
    ! [U_2447,U_2448,U_2450,U_2449] :
      ( c_Orderings_Oord__class_Oless__eq(U_2447,hAPP(hAPP(c_Power_Opower__class_Opower(U_2447),U_2450),U_2449),hAPP(hAPP(c_Power_Opower__class_Opower(U_2447),U_2450),U_2448))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2447,U_2450,c_Groups_Oone__class_Oone(U_2447))
      | ~ c_Orderings_Oord__class_Oless__eq(U_2447,c_Groups_Ozero__class_Ozero(U_2447),U_2450)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2448,U_2449)
      | ~ class_Rings_Olinordered__semidom(U_2447) ),
    inference(definitional_conversion,[status(esa)],[f_746_2]) ).

cnf(f_746_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2447,hAPP(hAPP(c_Power_Opower__class_Opower(U_2447),U_2450),U_2449),hAPP(hAPP(c_Power_Opower__class_Opower(U_2447),U_2450),U_2448))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2447,U_2450,c_Groups_Oone__class_Oone(U_2447))
    | ~ c_Orderings_Oord__class_Oless__eq(U_2447,c_Groups_Ozero__class_Ozero(U_2447),U_2450)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2448,U_2449)
    | ~ class_Rings_Olinordered__semidom(U_2447) ),
    inference(clausify,[status(thm)],[f_746_3]) ).

fof(f_747_1,plain,
    ! [V_n,V_m,V_a,T_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
      | ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__exp]) ).

fof(f_747_2,plain,
    ! [U_2454,U_2453,U_2452,U_2451] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2453,U_2454)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2451,hAPP(hAPP(c_Power_Opower__class_Opower(U_2451),U_2452),U_2453),hAPP(hAPP(c_Power_Opower__class_Opower(U_2451),U_2452),U_2454))
      | ~ c_Orderings_Oord__class_Oless(U_2451,c_Groups_Oone__class_Oone(U_2451),U_2452)
      | ~ class_Rings_Olinordered__semidom(U_2451) ),
    inference(variable_rename,[status(thm)],[f_747_1]) ).

fof(f_747_3,plain,
    ! [U_2454,U_2451,U_2453,U_2452] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2453,U_2454)
      | ~ c_Orderings_Oord__class_Oless__eq(U_2451,hAPP(hAPP(c_Power_Opower__class_Opower(U_2451),U_2452),U_2453),hAPP(hAPP(c_Power_Opower__class_Opower(U_2451),U_2452),U_2454))
      | ~ c_Orderings_Oord__class_Oless(U_2451,c_Groups_Oone__class_Oone(U_2451),U_2452)
      | ~ class_Rings_Olinordered__semidom(U_2451) ),
    inference(definitional_conversion,[status(esa)],[f_747_2]) ).

cnf(f_747_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2453,U_2454)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2451,hAPP(hAPP(c_Power_Opower__class_Opower(U_2451),U_2452),U_2453),hAPP(hAPP(c_Power_Opower__class_Opower(U_2451),U_2452),U_2454))
    | ~ c_Orderings_Oord__class_Oless(U_2451,c_Groups_Oone__class_Oone(U_2451),U_2452)
    | ~ class_Rings_Olinordered__semidom(U_2451) ),
    inference(clausify,[status(thm)],[f_747_3]) ).

fof(f_748_1,plain,
    ! [V_y_2,V_x_2,V_b_2,T_a] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2)
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2)) ) )
      | ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
      | ~ class_Rings_Olinordered__semidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__increasing__iff]) ).

fof(f_748_2,plain,
    ! [U_2458,U_2457,U_2456,U_2455] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(U_2455,hAPP(hAPP(c_Power_Opower__class_Opower(U_2455),U_2456),U_2457),hAPP(hAPP(c_Power_Opower__class_Opower(U_2455),U_2456),U_2458))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2457,U_2458) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2457,U_2458)
          | ~ c_Orderings_Oord__class_Oless__eq(U_2455,hAPP(hAPP(c_Power_Opower__class_Opower(U_2455),U_2456),U_2457),hAPP(hAPP(c_Power_Opower__class_Opower(U_2455),U_2456),U_2458)) ) )
      | ~ c_Orderings_Oord__class_Oless(U_2455,c_Groups_Oone__class_Oone(U_2455),U_2456)
      | ~ class_Rings_Olinordered__semidom(U_2455) ),
    inference(variable_rename,[status(thm)],[f_748_1]) ).

fof(f_748_3,plain,
    ( ! [U_2457,U_2458,U_2455,U_2456] :
        ( c_Orderings_Oord__class_Oless__eq(U_2455,hAPP(hAPP(c_Power_Opower__class_Opower(U_2455),U_2456),U_2457),hAPP(hAPP(c_Power_Opower__class_Opower(U_2455),U_2456),U_2458))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2457,U_2458)
        | ~ sP216(U_2457,U_2458,U_2455,U_2456) )
    & ! [U_2457,U_2458,U_2455,U_2456] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2457,U_2458)
        | ~ c_Orderings_Oord__class_Oless__eq(U_2455,hAPP(hAPP(c_Power_Opower__class_Opower(U_2455),U_2456),U_2457),hAPP(hAPP(c_Power_Opower__class_Opower(U_2455),U_2456),U_2458))
        | ~ sP216(U_2457,U_2458,U_2455,U_2456) )
    & ! [U_2457,U_2458,U_2455,U_2456] :
        ( sP216(U_2457,U_2458,U_2455,U_2456)
        | ~ c_Orderings_Oord__class_Oless(U_2455,c_Groups_Oone__class_Oone(U_2455),U_2456)
        | ~ class_Rings_Olinordered__semidom(U_2455) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP216])],[f_748_2]) ).

cnf(f_748_4,plain,
    ( sP216(U_2457,U_2458,U_2455,U_2456)
    | ~ c_Orderings_Oord__class_Oless(U_2455,c_Groups_Oone__class_Oone(U_2455),U_2456)
    | ~ class_Rings_Olinordered__semidom(U_2455) ),
    inference(clausify,[status(thm)],[f_748_3]) ).

cnf(f_748_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2457,U_2458)
    | ~ c_Orderings_Oord__class_Oless__eq(U_2455,hAPP(hAPP(c_Power_Opower__class_Opower(U_2455),U_2456),U_2457),hAPP(hAPP(c_Power_Opower__class_Opower(U_2455),U_2456),U_2458))
    | ~ sP216(U_2457,U_2458,U_2455,U_2456) ),
    inference(clausify,[status(thm)],[f_748_3]) ).

cnf(f_748_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_2455,hAPP(hAPP(c_Power_Opower__class_Opower(U_2455),U_2456),U_2457),hAPP(hAPP(c_Power_Opower__class_Opower(U_2455),U_2456),U_2458))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2457,U_2458)
    | ~ sP216(U_2457,U_2458,U_2455,U_2456) ),
    inference(clausify,[status(thm)],[f_748_3]) ).

fof(f_749_1,plain,
    ! [V_n_2,V_x_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
          & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
        | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_zero__less__power__nat__eq]) ).

fof(f_749_2,plain,
    ! [U_2460,U_2459] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2459),U_2460))
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2459)
          & U_2460 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2459)
        | U_2460 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2459),U_2460)) ) ),
    inference(variable_rename,[status(thm)],[f_749_1]) ).

fof(f_749_3,plain,
    ( ! [U_2464,U_2462] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2462),U_2464))
        | ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2462)
          & U_2464 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_2463,U_2461] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2461)
        | U_2463 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2461),U_2463)) ) ),
    inference(miniscope,[status(thm)],[f_749_2]) ).

fof(f_749_4,plain,
    ( ! [U_2462,U_2464] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2462)
        | ~ sP217(U_2462,U_2464) )
    & ! [U_2462,U_2464] :
        ( U_2464 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP217(U_2462,U_2464) )
    & ! [U_2462,U_2464] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2462),U_2464))
        | sP217(U_2462,U_2464) )
    & ! [U_2461,U_2463] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2461)
        | U_2463 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2461),U_2463)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP217])],[f_749_3]) ).

cnf(f_749_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2461)
    | U_2463 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2461),U_2463)) ),
    inference(clausify,[status(thm)],[f_749_4]) ).

cnf(f_749_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2462),U_2464))
    | sP217(U_2462,U_2464) ),
    inference(clausify,[status(thm)],[f_749_4]) ).

cnf(f_749_7,plain,
    ( U_2464 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP217(U_2462,U_2464) ),
    inference(clausify,[status(thm)],[f_749_4]) ).

cnf(f_749_8,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2462)
    | ~ sP217(U_2462,U_2464) ),
    inference(clausify,[status(thm)],[f_749_4]) ).

fof(f_750_1,plain,
    ! [V_x_2] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2))
        | V_x_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_not__real__square__gt__zero]) ).

fof(f_750_2,plain,
    ! [U_2465] :
      ( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2465),U_2465))
        | U_2465 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
      & ( U_2465 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2465),U_2465)) ) ),
    inference(variable_rename,[status(thm)],[f_750_1]) ).

fof(f_750_3,plain,
    ( ! [U_2467] :
        ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2467),U_2467))
        | U_2467 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
    & ! [U_2466] :
        ( U_2466 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2466),U_2466)) ) ),
    inference(miniscope,[status(thm)],[f_750_2]) ).

fof(f_750_4,plain,
    ( ! [U_2467] :
        ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2467),U_2467))
        | U_2467 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
    & ! [U_2466] :
        ( U_2466 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2466),U_2466)) ) ),
    inference(definitional_conversion,[status(esa)],[f_750_3]) ).

cnf(f_750_5,plain,
    ( U_2466 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2466),U_2466)) ),
    inference(clausify,[status(thm)],[f_750_4]) ).

cnf(f_750_6,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2467),U_2467))
    | U_2467 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(clausify,[status(thm)],[f_750_4]) ).

fof(f_751_1,plain,
    ! [V_x] :
      ( V_x = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | V_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(fof_nnf,[status(thm)],[fact_nat__lt__two__imp__zero__or__one]) ).

fof(f_751_2,plain,
    ! [U_2468] :
      ( U_2468 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | U_2468 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2468,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(variable_rename,[status(thm)],[f_751_1]) ).

fof(f_751_3,plain,
    ! [U_2468] :
      ( U_2468 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | U_2468 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2468,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(definitional_conversion,[status(esa)],[f_751_2]) ).

cnf(f_751_4,plain,
    ( U_2468 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_2468 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2468,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(clausify,[status(thm)],[f_751_3]) ).

fof(f_752_1,plain,
    ! [V_l_2,V_k_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_less__bin__lemma]) ).

fof(f_752_2,plain,
    ! [U_2470,U_2469] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2469,U_2470)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2469,U_2470),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2469,U_2470),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2469,U_2470) ) ),
    inference(variable_rename,[status(thm)],[f_752_1]) ).

fof(f_752_3,plain,
    ( ! [U_2474,U_2472] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2472,U_2474)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2472,U_2474),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    & ! [U_2473,U_2471] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2471,U_2473),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2471,U_2473) ) ),
    inference(miniscope,[status(thm)],[f_752_2]) ).

fof(f_752_4,plain,
    ( ! [U_2474,U_2472] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2472,U_2474)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2472,U_2474),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    & ! [U_2471,U_2473] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2471,U_2473),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2471,U_2473) ) ),
    inference(definitional_conversion,[status(esa)],[f_752_3]) ).

cnf(f_752_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2471,U_2473),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2471,U_2473) ),
    inference(clausify,[status(thm)],[f_752_4]) ).

cnf(f_752_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2472,U_2474)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2472,U_2474),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(clausify,[status(thm)],[f_752_4]) ).

fof(f_753_1,plain,
    ! [V_z_2,V_w_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,V_z_2) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,V_z_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zle__add1__eq__le]) ).

fof(f_753_2,plain,
    ! [U_2476,U_2475] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2475,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2476,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2475,U_2476) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2475,U_2476)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2475,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2476,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_753_1]) ).

fof(f_753_3,plain,
    ( ! [U_2480,U_2478] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2478,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2480,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2478,U_2480) )
    & ! [U_2479,U_2477] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2477,U_2479)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2477,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2479,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_753_2]) ).

fof(f_753_4,plain,
    ( ! [U_2478,U_2480] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2478,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2480,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2478,U_2480) )
    & ! [U_2479,U_2477] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2477,U_2479)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2477,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2479,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa)],[f_753_3]) ).

cnf(f_753_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2477,U_2479)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2477,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2479,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_753_4]) ).

cnf(f_753_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2478,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2480,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2478,U_2480) ),
    inference(clausify,[status(thm)],[f_753_4]) ).

fof(f_754_1,plain,
    ! [V_z_2,V_w_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zle__diff1__eq]) ).

fof(f_754_2,plain,
    ! [U_2482,U_2481] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2481,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2482,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2481,U_2482) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2481,U_2482)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2481,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2482,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_754_1]) ).

fof(f_754_3,plain,
    ( ! [U_2486,U_2484] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2484,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2486,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2484,U_2486) )
    & ! [U_2485,U_2483] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2483,U_2485)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2483,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2485,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_754_2]) ).

fof(f_754_4,plain,
    ( ! [U_2484,U_2486] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2484,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2486,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2484,U_2486) )
    & ! [U_2485,U_2483] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2483,U_2485)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2483,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2485,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa)],[f_754_3]) ).

cnf(f_754_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2483,U_2485)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2483,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2485,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_754_4]) ).

cnf(f_754_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2484,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2486,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2484,U_2486) ),
    inference(clausify,[status(thm)],[f_754_4]) ).

fof(f_755_1,plain,
    ! [V_z_2,V_w_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_add1__zle__eq]) ).

fof(f_755_2,plain,
    ! [U_2488,U_2487] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2487,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2488)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2487,U_2488) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2487,U_2488)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2487,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2488) ) ),
    inference(variable_rename,[status(thm)],[f_755_1]) ).

fof(f_755_3,plain,
    ( ! [U_2492,U_2490] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2490,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2492)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2490,U_2492) )
    & ! [U_2491,U_2489] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2489,U_2491)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2489,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2491) ) ),
    inference(miniscope,[status(thm)],[f_755_2]) ).

fof(f_755_4,plain,
    ( ! [U_2490,U_2492] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2490,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2492)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2490,U_2492) )
    & ! [U_2491,U_2489] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2489,U_2491)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2489,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2491) ) ),
    inference(definitional_conversion,[status(esa)],[f_755_3]) ).

cnf(f_755_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2489,U_2491)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2489,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2491) ),
    inference(clausify,[status(thm)],[f_755_4]) ).

cnf(f_755_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2490,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2492)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2490,U_2492) ),
    inference(clausify,[status(thm)],[f_755_4]) ).

fof(f_756_1,plain,
    ! [V_z] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) ),
    inference(fof_nnf,[status(thm)],[fact_le__imp__0__less]) ).

fof(f_756_2,plain,
    ! [U_2493] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2493))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2493) ),
    inference(variable_rename,[status(thm)],[f_756_1]) ).

fof(f_756_3,plain,
    ! [U_2493] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2493))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2493) ),
    inference(definitional_conversion,[status(esa)],[f_756_2]) ).

cnf(f_756_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2493))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2493) ),
    inference(clausify,[status(thm)],[f_756_3]) ).

fof(f_757_1,plain,
    ! [V_z,V_w] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z) ),
    inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle]) ).

fof(f_757_2,plain,
    ! [U_2495,U_2494] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2494,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2495)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2494,U_2495) ),
    inference(variable_rename,[status(thm)],[f_757_1]) ).

fof(f_757_3,plain,
    ! [U_2494,U_2495] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2494,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2495)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2494,U_2495) ),
    inference(definitional_conversion,[status(esa)],[f_757_2]) ).

cnf(f_757_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2494,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2495)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2494,U_2495) ),
    inference(clausify,[status(thm)],[f_757_3]) ).

fof(f_758_1,plain,
    ! [V_z,V_z_H,V_w,V_w_H] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H,V_z)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w) ),
    inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono]) ).

fof(f_758_2,plain,
    ! [U_2499,U_2498,U_2497,U_2496] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2496,U_2498),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2497,U_2499))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2498,U_2499)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2496,U_2497) ),
    inference(variable_rename,[status(thm)],[f_758_1]) ).

fof(f_758_3,plain,
    ! [U_2497,U_2496,U_2498,U_2499] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2496,U_2498),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2497,U_2499))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2498,U_2499)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2496,U_2497) ),
    inference(definitional_conversion,[status(esa)],[f_758_2]) ).

cnf(f_758_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2496,U_2498),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2497,U_2499))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2498,U_2499)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2496,U_2497) ),
    inference(clausify,[status(thm)],[f_758_3]) ).

fof(f_759_1,plain,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_j,V_k))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono]) ).

fof(f_759_2,plain,
    ! [U_2502,U_2501,U_2500] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2500,U_2502),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2501,U_2502))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2500,U_2501) ),
    inference(variable_rename,[status(thm)],[f_759_1]) ).

fof(f_759_3,plain,
    ! [U_2502,U_2500,U_2501] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2500,U_2502),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2501,U_2502))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2500,U_2501) ),
    inference(definitional_conversion,[status(esa)],[f_759_2]) ).

cnf(f_759_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2500,U_2502),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2501,U_2502))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2500,U_2501) ),
    inference(clausify,[status(thm)],[f_759_3]) ).

fof(f_760_1,plain,
    ! [V_z_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(fof_nnf,[status(thm)],[fact_odd__less__0]) ).

fof(f_760_2,plain,
    ! [U_2503] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2503),U_2503),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2503,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2503,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2503),U_2503),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(variable_rename,[status(thm)],[f_760_1]) ).

fof(f_760_3,plain,
    ( ! [U_2505] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2505),U_2505),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2505,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    & ! [U_2504] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2504,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2504),U_2504),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(miniscope,[status(thm)],[f_760_2]) ).

fof(f_760_4,plain,
    ( ! [U_2505] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2505),U_2505),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2505,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
    & ! [U_2504] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2504,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2504),U_2504),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(definitional_conversion,[status(esa)],[f_760_3]) ).

cnf(f_760_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2504,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2504),U_2504),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(clausify,[status(thm)],[f_760_4]) ).

cnf(f_760_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2505),U_2505),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2505,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(clausify,[status(thm)],[f_760_4]) ).

fof(f_761_1,plain,
    ! [V_z_2,V_w_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ( V_w_2 != V_z_2
          & ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ) )
      & ( V_w_2 = V_z_2
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zless__add1__eq]) ).

fof(f_761_2,plain,
    ! [U_2507,U_2506] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2506,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2507,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ( U_2506 != U_2507
          & ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2506,U_2507) ) )
      & ( U_2506 = U_2507
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2506,U_2507)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2506,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2507,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_761_1]) ).

fof(f_761_3,plain,
    ( ! [U_2511,U_2509] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2509,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2511,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ( U_2509 != U_2511
          & ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2509,U_2511) ) )
    & ! [U_2510,U_2508] :
        ( U_2508 = U_2510
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2508,U_2510)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2508,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2510,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_761_2]) ).

fof(f_761_4,plain,
    ( ! [U_2511,U_2509] :
        ( U_2509 != U_2511
        | ~ sP218(U_2511,U_2509) )
    & ! [U_2511,U_2509] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2509,U_2511)
        | ~ sP218(U_2511,U_2509) )
    & ! [U_2511,U_2509] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2509,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2511,c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | sP218(U_2511,U_2509) )
    & ! [U_2508,U_2510] :
        ( U_2508 = U_2510
        | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2508,U_2510)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2508,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2510,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP218])],[f_761_3]) ).

cnf(f_761_5,plain,
    ( U_2508 = U_2510
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2508,U_2510)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2508,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2510,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_761_4]) ).

cnf(f_761_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2509,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2511,c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | sP218(U_2511,U_2509) ),
    inference(clausify,[status(thm)],[f_761_4]) ).

cnf(f_761_7,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2509,U_2511)
    | ~ sP218(U_2511,U_2509) ),
    inference(clausify,[status(thm)],[f_761_4]) ).

cnf(f_761_8,plain,
    ( U_2509 != U_2511
    | ~ sP218(U_2511,U_2509) ),
    inference(clausify,[status(thm)],[f_761_4]) ).

fof(f_762_1,plain,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_int__0__less__1]) ).

fof(f_762_2,plain,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_762_1]) ).

cnf(f_762_3,plain,
    c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_762_2]) ).

fof(f_763_1,plain,
    ! [V_y,V_x] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_y,V_x)
      | V_x = V_y
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,V_x,V_y) ),
    inference(fof_nnf,[status(thm)],[fact_zless__linear]) ).

fof(f_763_2,plain,
    ! [U_2513,U_2512] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2513,U_2512)
      | U_2512 = U_2513
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2512,U_2513) ),
    inference(variable_rename,[status(thm)],[f_763_1]) ).

fof(f_763_3,plain,
    ! [U_2513,U_2512] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2513,U_2512)
      | U_2512 = U_2513
      | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2512,U_2513) ),
    inference(definitional_conversion,[status(esa)],[f_763_2]) ).

cnf(f_763_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2513,U_2512)
    | U_2512 = U_2513
    | c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2512,U_2513) ),
    inference(clausify,[status(thm)],[f_763_3]) ).

fof(f_764_1,plain,
    ! [V_w_2,V_z_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)
        | V_z_2 = V_w_2
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2,V_w_2) )
      & ( ( V_z_2 != V_w_2
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2,V_w_2) )
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_zless__le]) ).

fof(f_764_2,plain,
    ! [U_2515,U_2514] :
      ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2514,U_2515)
        | U_2514 = U_2515
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2514,U_2515) )
      & ( ( U_2514 != U_2515
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2514,U_2515) )
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2514,U_2515) ) ),
    inference(variable_rename,[status(thm)],[f_764_1]) ).

fof(f_764_3,plain,
    ( ! [U_2519,U_2517] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2517,U_2519)
        | U_2517 = U_2519
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2517,U_2519) )
    & ! [U_2518,U_2516] :
        ( ( U_2516 != U_2518
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2516,U_2518) )
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2516,U_2518) ) ),
    inference(miniscope,[status(thm)],[f_764_2]) ).

fof(f_764_4,plain,
    ( ! [U_2516,U_2518] :
        ( U_2516 != U_2518
        | ~ sP219(U_2516,U_2518) )
    & ! [U_2516,U_2518] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2516,U_2518)
        | ~ sP219(U_2516,U_2518) )
    & ! [U_2519,U_2517] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2517,U_2519)
        | U_2517 = U_2519
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2517,U_2519) )
    & ! [U_2516,U_2518] :
        ( sP219(U_2516,U_2518)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2516,U_2518) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP219])],[f_764_3]) ).

cnf(f_764_5,plain,
    ( sP219(U_2516,U_2518)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2516,U_2518) ),
    inference(clausify,[status(thm)],[f_764_4]) ).

cnf(f_764_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2517,U_2519)
    | U_2517 = U_2519
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2517,U_2519) ),
    inference(clausify,[status(thm)],[f_764_4]) ).

cnf(f_764_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2516,U_2518)
    | ~ sP219(U_2516,U_2518) ),
    inference(clausify,[status(thm)],[f_764_4]) ).

cnf(f_764_8,plain,
    ( U_2516 != U_2518
    | ~ sP219(U_2516,U_2518) ),
    inference(clausify,[status(thm)],[f_764_4]) ).

fof(f_765_1,plain,
    ! [V_z_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less]) ).

fof(f_765_2,plain,
    ! [U_2520] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2520)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2520) )
      & ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2520)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2520) ) ),
    inference(variable_rename,[status(thm)],[f_765_1]) ).

fof(f_765_3,plain,
    ( ! [U_2522] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2522)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2522) )
    & ! [U_2521] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2521)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2521) ) ),
    inference(miniscope,[status(thm)],[f_765_2]) ).

fof(f_765_4,plain,
    ( ! [U_2522] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2522)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2522) )
    & ! [U_2521] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2521)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2521) ) ),
    inference(definitional_conversion,[status(esa)],[f_765_3]) ).

cnf(f_765_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2521)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2521) ),
    inference(clausify,[status(thm)],[f_765_4]) ).

cnf(f_765_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2522)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2522) ),
    inference(clausify,[status(thm)],[f_765_4]) ).

fof(f_766_1,plain,
    ! [V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)) = V_z,
    inference(fof_nnf,[status(thm)],[fact_zminus__zminus]) ).

fof(f_766_2,plain,
    ! [U_2523] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2523)) = U_2523,
    inference(variable_rename,[status(thm)],[f_766_1]) ).

fof(f_766_3,plain,
    ! [U_2523] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2523)) = U_2523,
    inference(definitional_conversion,[status(esa)],[f_766_2]) ).

cnf(f_766_4,plain,
    c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2523)) = U_2523,
    inference(clausify,[status(thm)],[f_766_3]) ).

fof(f_767_1,plain,
    c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_zminus__0]) ).

fof(f_767_2,plain,
    c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_767_1]) ).

cnf(f_767_3,plain,
    c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_767_2]) ).

fof(f_768_1,plain,
    ! [V_w,V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)),
    inference(fof_nnf,[status(thm)],[fact_zminus__zadd__distrib]) ).

fof(f_768_2,plain,
    ! [U_2525,U_2524] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2524,U_2525)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2524),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2525)),
    inference(variable_rename,[status(thm)],[f_768_1]) ).

fof(f_768_3,plain,
    ! [U_2524,U_2525] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2524,U_2525)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2524),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2525)),
    inference(definitional_conversion,[status(esa)],[f_768_2]) ).

cnf(f_768_4,plain,
    c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2524,U_2525)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2524),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2525)),
    inference(clausify,[status(thm)],[f_768_3]) ).

fof(f_769_1,plain,
    ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_zadd__zminus__inverse2]) ).

fof(f_769_2,plain,
    ! [U_2526] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2526),U_2526) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_769_1]) ).

fof(f_769_3,plain,
    ! [U_2526] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2526),U_2526) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_769_2]) ).

cnf(f_769_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2526),U_2526) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_769_3]) ).

fof(f_770_1,plain,
    ! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w),
    inference(fof_nnf,[status(thm)],[fact_diff__int__def__symmetric]) ).

fof(f_770_2,plain,
    ! [U_2528,U_2527] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2527,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2528)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2527,U_2528),
    inference(variable_rename,[status(thm)],[f_770_1]) ).

fof(f_770_3,plain,
    ! [U_2527,U_2528] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2527,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2528)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2527,U_2528),
    inference(definitional_conversion,[status(esa)],[f_770_2]) ).

cnf(f_770_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2527,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2528)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2527,U_2528),
    inference(clausify,[status(thm)],[f_770_3]) ).

fof(f_771_1,plain,
    ! [V_w,V_z] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)),
    inference(fof_nnf,[status(thm)],[fact_diff__int__def]) ).

fof(f_771_2,plain,
    ! [U_2530,U_2529] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2529,U_2530) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2529,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2530)),
    inference(variable_rename,[status(thm)],[f_771_1]) ).

fof(f_771_3,plain,
    ! [U_2529,U_2530] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2529,U_2530) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2529,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2530)),
    inference(definitional_conversion,[status(esa)],[f_771_2]) ).

cnf(f_771_4,plain,
    c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2529,U_2530) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2529,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2530)),
    inference(clausify,[status(thm)],[f_771_3]) ).

fof(f_772_1,plain,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_i),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_j))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_zadd__left__mono]) ).

fof(f_772_2,plain,
    ! [U_2533,U_2532,U_2531] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2533,U_2531),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2533,U_2532))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2531,U_2532) ),
    inference(variable_rename,[status(thm)],[f_772_1]) ).

fof(f_772_3,plain,
    ! [U_2531,U_2532,U_2533] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2533,U_2531),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2533,U_2532))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2531,U_2532) ),
    inference(definitional_conversion,[status(esa)],[f_772_2]) ).

cnf(f_772_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2533,U_2531),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2533,U_2532))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2531,U_2532) ),
    inference(clausify,[status(thm)],[f_772_3]) ).

fof(f_773_1,plain,
    ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z,
    inference(fof_nnf,[status(thm)],[fact_zadd__0]) ).

fof(f_773_2,plain,
    ! [U_2534] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2534) = U_2534,
    inference(variable_rename,[status(thm)],[f_773_1]) ).

fof(f_773_3,plain,
    ! [U_2534] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2534) = U_2534,
    inference(definitional_conversion,[status(esa)],[f_773_2]) ).

cnf(f_773_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2534) = U_2534,
    inference(clausify,[status(thm)],[f_773_3]) ).

fof(f_774_1,plain,
    ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z,
    inference(fof_nnf,[status(thm)],[fact_zadd__0__right]) ).

fof(f_774_2,plain,
    ! [U_2535] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2535,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_2535,
    inference(variable_rename,[status(thm)],[f_774_1]) ).

fof(f_774_3,plain,
    ! [U_2535] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2535,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_2535,
    inference(definitional_conversion,[status(esa)],[f_774_2]) ).

cnf(f_774_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2535,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_2535,
    inference(clausify,[status(thm)],[f_774_3]) ).

fof(f_775_1,plain,
    ! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z),
    inference(fof_nnf,[status(thm)],[fact_zadd__commute]) ).

fof(f_775_2,plain,
    ! [U_2537,U_2536] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2536,U_2537) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2537,U_2536),
    inference(variable_rename,[status(thm)],[f_775_1]) ).

fof(f_775_3,plain,
    ! [U_2537,U_2536] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2536,U_2537) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2537,U_2536),
    inference(definitional_conversion,[status(esa)],[f_775_2]) ).

cnf(f_775_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2536,U_2537) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2537,U_2536),
    inference(clausify,[status(thm)],[f_775_3]) ).

fof(f_776_1,plain,
    ! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z)),
    inference(fof_nnf,[status(thm)],[fact_zadd__left__commute]) ).

fof(f_776_2,plain,
    ! [U_2540,U_2539,U_2538] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2538,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2539,U_2540)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2539,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2538,U_2540)),
    inference(variable_rename,[status(thm)],[f_776_1]) ).

fof(f_776_3,plain,
    ! [U_2538,U_2539,U_2540] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2538,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2539,U_2540)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2539,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2538,U_2540)),
    inference(definitional_conversion,[status(esa)],[f_776_2]) ).

cnf(f_776_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2538,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2539,U_2540)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2539,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2538,U_2540)),
    inference(clausify,[status(thm)],[f_776_3]) ).

fof(f_777_1,plain,
    ! [V_z3,V_z2,V_z1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3)),
    inference(fof_nnf,[status(thm)],[fact_zadd__assoc]) ).

fof(f_777_2,plain,
    ! [U_2543,U_2542,U_2541] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2541,U_2542),U_2543) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2541,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2542,U_2543)),
    inference(variable_rename,[status(thm)],[f_777_1]) ).

fof(f_777_3,plain,
    ! [U_2542,U_2541,U_2543] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2541,U_2542),U_2543) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2541,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2542,U_2543)),
    inference(definitional_conversion,[status(esa)],[f_777_2]) ).

cnf(f_777_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2541,U_2542),U_2543) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2541,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2542,U_2543)),
    inference(clausify,[status(thm)],[f_777_3]) ).

fof(f_778_1,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_int__0__neq__1]) ).

fof(f_778_2,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_778_1]) ).

cnf(f_778_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_778_2]) ).

fof(f_779_1,plain,
    ! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z),V_z) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_odd__nonzero]) ).

fof(f_779_2,plain,
    ! [U_2544] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2544),U_2544) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_779_1]) ).

fof(f_779_3,plain,
    ! [U_2544] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2544),U_2544) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_779_2]) ).

cnf(f_779_4,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2544),U_2544) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_779_3]) ).

fof(f_780_1,plain,
    ! [V_q,V_r,V_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)
      | V_a != c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a) ),
    inference(fof_nnf,[status(thm)],[fact_self__quotient__aux1]) ).

fof(f_780_2,plain,
    ! [U_2547,U_2546,U_2545] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2547)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2546,U_2545)
      | U_2545 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2546,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2545),U_2547))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2545) ),
    inference(variable_rename,[status(thm)],[f_780_1]) ).

fof(f_780_3,plain,
    ! [U_2545,U_2546,U_2547] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2547)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2546,U_2545)
      | U_2545 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2546,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2545),U_2547))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2545) ),
    inference(definitional_conversion,[status(esa)],[f_780_2]) ).

cnf(f_780_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2547)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2546,U_2545)
    | U_2545 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2546,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2545),U_2547))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2545) ),
    inference(clausify,[status(thm)],[f_780_3]) ).

fof(f_781_1,plain,
    ! [V_q,V_r,V_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
      | V_a != c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a) ),
    inference(fof_nnf,[status(thm)],[fact_self__quotient__aux2]) ).

fof(f_781_2,plain,
    ! [U_2550,U_2549,U_2548] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2550,c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2549)
      | U_2548 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2549,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2548),U_2550))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2548) ),
    inference(variable_rename,[status(thm)],[f_781_1]) ).

fof(f_781_3,plain,
    ! [U_2550,U_2548,U_2549] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2550,c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2549)
      | U_2548 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2549,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2548),U_2550))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2548) ),
    inference(definitional_conversion,[status(esa)],[f_781_2]) ).

cnf(f_781_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2550,c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2549)
    | U_2548 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2549,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2548),U_2550))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2548) ),
    inference(clausify,[status(thm)],[f_781_3]) ).

fof(f_782_1,plain,
    ! [V_w] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_w),
    inference(fof_nnf,[status(thm)],[fact_zle__refl]) ).

fof(f_782_2,plain,
    ! [U_2551] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2551,U_2551),
    inference(variable_rename,[status(thm)],[f_782_1]) ).

fof(f_782_3,plain,
    ! [U_2551] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2551,U_2551),
    inference(definitional_conversion,[status(esa)],[f_782_2]) ).

cnf(f_782_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2551,U_2551),
    inference(clausify,[status(thm)],[f_782_3]) ).

fof(f_783_1,plain,
    ! [V_w,V_z] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w) ),
    inference(fof_nnf,[status(thm)],[fact_zle__linear]) ).

fof(f_783_2,plain,
    ! [U_2553,U_2552] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2553,U_2552)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2552,U_2553) ),
    inference(variable_rename,[status(thm)],[f_783_1]) ).

fof(f_783_3,plain,
    ! [U_2552,U_2553] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2553,U_2552)
      | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2552,U_2553) ),
    inference(definitional_conversion,[status(esa)],[f_783_2]) ).

cnf(f_783_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2553,U_2552)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2552,U_2553) ),
    inference(clausify,[status(thm)],[f_783_3]) ).

fof(f_784_1,plain,
    ! [V_k,V_j,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_k)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_j,V_k)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i,V_j) ),
    inference(fof_nnf,[status(thm)],[fact_zle__trans]) ).

fof(f_784_2,plain,
    ! [U_2556,U_2555,U_2554] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2554,U_2556)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2555,U_2556)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2554,U_2555) ),
    inference(variable_rename,[status(thm)],[f_784_1]) ).

fof(f_784_3,plain,
    ! [U_2555,U_2554,U_2556] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2554,U_2556)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2555,U_2556)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2554,U_2555) ),
    inference(definitional_conversion,[status(esa)],[f_784_2]) ).

cnf(f_784_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2554,U_2556)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2555,U_2556)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2554,U_2555) ),
    inference(clausify,[status(thm)],[f_784_3]) ).

fof(f_785_1,plain,
    ! [V_w,V_z] :
      ( V_z = V_w
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w,V_z)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_w) ),
    inference(fof_nnf,[status(thm)],[fact_zle__antisym]) ).

fof(f_785_2,plain,
    ! [U_2558,U_2557] :
      ( U_2557 = U_2558
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2558,U_2557)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2557,U_2558) ),
    inference(variable_rename,[status(thm)],[f_785_1]) ).

fof(f_785_3,plain,
    ! [U_2558,U_2557] :
      ( U_2557 = U_2558
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2558,U_2557)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2557,U_2558) ),
    inference(definitional_conversion,[status(esa)],[f_785_2]) ).

cnf(f_785_4,plain,
    ( U_2557 = U_2558
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2558,U_2557)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2557,U_2558) ),
    inference(clausify,[status(thm)],[f_785_3]) ).

fof(f_786_1,plain,
    ! [V_r_H,V_q_H,V_b_H] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)) ),
    inference(fof_nnf,[status(thm)],[fact_q__pos__lemma]) ).

fof(f_786_2,plain,
    ! [U_2561,U_2560,U_2559] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2560)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2559)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2561,U_2559)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2559),U_2560),U_2561)) ),
    inference(variable_rename,[status(thm)],[f_786_1]) ).

fof(f_786_3,plain,
    ! [U_2559,U_2560,U_2561] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2560)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2559)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2561,U_2559)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2559),U_2560),U_2561)) ),
    inference(definitional_conversion,[status(esa)],[f_786_2]) ).

cnf(f_786_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2560)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2559)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2561,U_2559)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2559),U_2560),U_2561)) ),
    inference(clausify,[status(thm)],[f_786_3]) ).

fof(f_787_1,plain,
    ! [V_r_H,V_q_H,V_b_H] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(fof_nnf,[status(thm)],[fact_q__neg__lemma]) ).

fof(f_787_2,plain,
    ! [U_2564,U_2563,U_2562] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2563,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2562)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2564)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2562),U_2563),U_2564),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[f_787_1]) ).

fof(f_787_3,plain,
    ! [U_2562,U_2563,U_2564] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2563,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2562)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2564)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2562),U_2563),U_2564),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(definitional_conversion,[status(esa)],[f_787_2]) ).

cnf(f_787_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2563,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2562)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2564)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2562),U_2563),U_2564),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(clausify,[status(thm)],[f_787_3]) ).

fof(f_788_1,plain,
    ! [V_r,V_q,V_r_H,V_q_H,V_b] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)) ),
    inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma]) ).

fof(f_788_2,plain,
    ! [U_2569,U_2568,U_2567,U_2566,U_2565] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2566,U_2568)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2569,U_2565)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2567,U_2565)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2567)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2565),U_2566),U_2567),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2565),U_2568),U_2569)) ),
    inference(variable_rename,[status(thm)],[f_788_1]) ).

fof(f_788_3,plain,
    ! [U_2565,U_2566,U_2567,U_2568,U_2569] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2566,U_2568)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2569,U_2565)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2567,U_2565)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2567)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2565),U_2566),U_2567),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2565),U_2568),U_2569)) ),
    inference(definitional_conversion,[status(esa)],[f_788_2]) ).

cnf(f_788_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2566,U_2568)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2569,U_2565)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2567,U_2565)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2567)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2565),U_2566),U_2567),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2565),U_2568),U_2569)) ),
    inference(clausify,[status(thm)],[f_788_3]) ).

fof(f_789_1,plain,
    ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H))
      | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__lemma]) ).

fof(f_789_2,plain,
    ! [U_2575,U_2574,U_2573,U_2572,U_2571,U_2570] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2571,U_2574)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2573,U_2570)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2573)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2572)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2575,U_2573)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2573),U_2574),U_2575))
      | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2570),U_2571),U_2572) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2573),U_2574),U_2575) ),
    inference(variable_rename,[status(thm)],[f_789_1]) ).

fof(f_789_3,plain,
    ! [U_2570,U_2571,U_2572,U_2573,U_2574,U_2575] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2571,U_2574)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2573,U_2570)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2573)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2572)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2575,U_2573)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2573),U_2574),U_2575))
      | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2570),U_2571),U_2572) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2573),U_2574),U_2575) ),
    inference(definitional_conversion,[status(esa)],[f_789_2]) ).

cnf(f_789_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2571,U_2574)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2573,U_2570)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2573)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2572)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2575,U_2573)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2573),U_2574),U_2575))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2570),U_2571),U_2572) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2573),U_2574),U_2575) ),
    inference(clausify,[status(thm)],[f_789_3]) ).

fof(f_790_1,plain,
    ! [V_r,V_q,V_r_H,V_q_H,V_b] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)) ),
    inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma__neg]) ).

fof(f_790_2,plain,
    ! [U_2580,U_2579,U_2578,U_2577,U_2576] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2579,U_2577)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2576,U_2578)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2576,U_2580)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2580,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2576),U_2577),U_2578),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2576),U_2579),U_2580)) ),
    inference(variable_rename,[status(thm)],[f_790_1]) ).

fof(f_790_3,plain,
    ! [U_2577,U_2578,U_2576,U_2579,U_2580] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2579,U_2577)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2576,U_2578)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2576,U_2580)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2580,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2576),U_2577),U_2578),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2576),U_2579),U_2580)) ),
    inference(definitional_conversion,[status(esa)],[f_790_2]) ).

cnf(f_790_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2579,U_2577)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2576,U_2578)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2576,U_2580)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2580,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2576),U_2577),U_2578),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2576),U_2579),U_2580)) ),
    inference(clausify,[status(thm)],[f_790_3]) ).

fof(f_791_1,plain,
    ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg__lemma]) ).

fof(f_791_2,plain,
    ! [U_2586,U_2585,U_2584,U_2583,U_2582,U_2581] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2585,U_2582)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2584,U_2581)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2584)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2586)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2583,U_2581)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2584),U_2585),U_2586),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2581),U_2582),U_2583) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2584),U_2585),U_2586) ),
    inference(variable_rename,[status(thm)],[f_791_1]) ).

fof(f_791_3,plain,
    ! [U_2582,U_2581,U_2583,U_2584,U_2585,U_2586] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2585,U_2582)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2584,U_2581)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2584)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2586)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2583,U_2581)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2584),U_2585),U_2586),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2581),U_2582),U_2583) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2584),U_2585),U_2586) ),
    inference(definitional_conversion,[status(esa)],[f_791_2]) ).

cnf(f_791_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2585,U_2582)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2584,U_2581)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2584)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2586)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2583,U_2581)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2584),U_2585),U_2586),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2581),U_2582),U_2583) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2584),U_2585),U_2586) ),
    inference(clausify,[status(thm)],[f_791_3]) ).

fof(f_792_1,plain,
    ! [V_n,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J]) ).

fof(f_792_2,plain,
    ! [U_2588,U_2587] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2587),U_2588))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2587) ),
    inference(variable_rename,[status(thm)],[f_792_1]) ).

fof(f_792_3,plain,
    ! [U_2587,U_2588] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2587),U_2588))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2587) ),
    inference(definitional_conversion,[status(esa)],[f_792_2]) ).

cnf(f_792_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2587),U_2588))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2587) ),
    inference(clausify,[status(thm)],[f_792_3]) ).

fof(f_793_1,plain,
    ! [V_y,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J]) ).

fof(f_793_2,plain,
    ! [U_2590,U_2589] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2589),U_2590))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2590)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2589) ),
    inference(variable_rename,[status(thm)],[f_793_1]) ).

fof(f_793_3,plain,
    ! [U_2590,U_2589] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2589),U_2590))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2590)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2589) ),
    inference(definitional_conversion,[status(esa)],[f_793_2]) ).

cnf(f_793_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2589),U_2590))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2590)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2589) ),
    inference(clausify,[status(thm)],[f_793_3]) ).

fof(f_794_1,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J]) ).

fof(f_794_2,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_794_1]) ).

cnf(f_794_3,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_794_2]) ).

fof(f_795_1,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J]) ).

fof(f_795_2,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_795_1]) ).

cnf(f_795_3,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_795_2]) ).

fof(f_796_1,plain,
    ! [V_y,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_y))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J]) ).

fof(f_796_2,plain,
    ! [U_2592,U_2591] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2591,U_2592))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2592)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2591) ),
    inference(variable_rename,[status(thm)],[f_796_1]) ).

fof(f_796_3,plain,
    ! [U_2592,U_2591] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2591,U_2592))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2592)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2591) ),
    inference(definitional_conversion,[status(esa)],[f_796_2]) ).

cnf(f_796_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2591,U_2592))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2592)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2591) ),
    inference(clausify,[status(thm)],[f_796_3]) ).

fof(f_797_1,plain,
    ! [V_x] :
      ( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
    inference(fof_nnf,[status(thm)],[fact_natceiling__add__one]) ).

fof(f_797_2,plain,
    ! [U_2593] :
      ( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2593,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_2593),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2593) ),
    inference(variable_rename,[status(thm)],[f_797_1]) ).

fof(f_797_3,plain,
    ! [U_2593] :
      ( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2593,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_2593),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2593) ),
    inference(definitional_conversion,[status(esa)],[f_797_2]) ).

cnf(f_797_4,plain,
    ( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2593,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_2593),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2593) ),
    inference(clausify,[status(thm)],[f_797_3]) ).

fof(f_798_1,plain,
    ! [T_a] :
      ( c_Power_Opower__class_Opower(T_a) = c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a))
      | ~ class_Power_Opower(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__power__power]) ).

fof(f_798_2,plain,
    ! [U_2594] :
      ( c_Power_Opower__class_Opower(U_2594) = c_Power_Opower_Opower(U_2594,c_Groups_Oone__class_Oone(U_2594),c_Groups_Otimes__class_Otimes(U_2594))
      | ~ class_Power_Opower(U_2594) ),
    inference(variable_rename,[status(thm)],[f_798_1]) ).

fof(f_798_3,plain,
    ! [U_2594] :
      ( c_Power_Opower__class_Opower(U_2594) = c_Power_Opower_Opower(U_2594,c_Groups_Oone__class_Oone(U_2594),c_Groups_Otimes__class_Otimes(U_2594))
      | ~ class_Power_Opower(U_2594) ),
    inference(definitional_conversion,[status(esa)],[f_798_2]) ).

cnf(f_798_4,plain,
    ( c_Power_Opower__class_Opower(U_2594) = c_Power_Opower_Opower(U_2594,c_Groups_Oone__class_Oone(U_2594),c_Groups_Otimes__class_Otimes(U_2594))
    | ~ class_Power_Opower(U_2594) ),
    inference(clausify,[status(thm)],[f_798_3]) ).

fof(f_799_1,plain,
    c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_natceiling__zero]) ).

fof(f_799_2,plain,
    c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_799_1]) ).

cnf(f_799_3,plain,
    c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_799_2]) ).

fof(f_800_1,plain,
    ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),
    inference(fof_nnf,[status(thm)],[fact_zero__le__natceiling]) ).

fof(f_800_2,plain,
    ! [U_2595] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(U_2595)),
    inference(variable_rename,[status(thm)],[f_800_1]) ).

fof(f_800_3,plain,
    ! [U_2595] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(U_2595)),
    inference(definitional_conversion,[status(esa)],[f_800_2]) ).

cnf(f_800_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(U_2595)),
    inference(clausify,[status(thm)],[f_800_3]) ).

fof(f_801_1,plain,
    ! [V_y,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y) ),
    inference(fof_nnf,[status(thm)],[fact_natceiling__mono]) ).

fof(f_801_2,plain,
    ! [U_2597,U_2596] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2596),c_RComplete_Onatceiling(U_2597))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2596,U_2597) ),
    inference(variable_rename,[status(thm)],[f_801_1]) ).

fof(f_801_3,plain,
    ! [U_2596,U_2597] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2596),c_RComplete_Onatceiling(U_2597))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2596,U_2597) ),
    inference(definitional_conversion,[status(esa)],[f_801_2]) ).

cnf(f_801_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2596),c_RComplete_Onatceiling(U_2597))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2596,U_2597) ),
    inference(clausify,[status(thm)],[f_801_3]) ).

fof(f_802_1,plain,
    c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[fact_natceiling__one]) ).

fof(f_802_2,plain,
    c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_802_1]) ).

cnf(f_802_3,plain,
    c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_802_2]) ).

fof(f_803_1,plain,
    ! [V_ab_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_ab_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2,
    inference(fof_nnf,[status(thm)],[fact_power_Opower_Opower__0]) ).

fof(f_803_2,plain,
    ! [U_2601,U_2600,U_2599,U_2598] : hAPP(hAPP(c_Power_Opower_Opower(U_2598,U_2599,U_2600),U_2601),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2599,
    inference(variable_rename,[status(thm)],[f_803_1]) ).

fof(f_803_3,plain,
    ! [U_2598,U_2599,U_2600,U_2601] : hAPP(hAPP(c_Power_Opower_Opower(U_2598,U_2599,U_2600),U_2601),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2599,
    inference(definitional_conversion,[status(esa)],[f_803_2]) ).

cnf(f_803_4,plain,
    hAPP(hAPP(c_Power_Opower_Opower(U_2598,U_2599,U_2600),U_2601),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2599,
    inference(clausify,[status(thm)],[f_803_3]) ).

fof(f_804_1,plain,
    ! [V_n_2,V_ab_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_ab_2),c_Nat_OSuc(V_n_2)) = hAPP(hAPP(V_times_2,V_ab_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_ab_2),V_n_2)),
    inference(fof_nnf,[status(thm)],[fact_power_Opower_Opower__Suc]) ).

fof(f_804_2,plain,
    ! [U_2606,U_2605,U_2604,U_2603,U_2602] : hAPP(hAPP(c_Power_Opower_Opower(U_2602,U_2603,U_2604),U_2605),c_Nat_OSuc(U_2606)) = hAPP(hAPP(U_2604,U_2605),hAPP(hAPP(c_Power_Opower_Opower(U_2602,U_2603,U_2604),U_2605),U_2606)),
    inference(variable_rename,[status(thm)],[f_804_1]) ).

fof(f_804_3,plain,
    ! [U_2605,U_2606,U_2604,U_2602,U_2603] : hAPP(hAPP(c_Power_Opower_Opower(U_2602,U_2603,U_2604),U_2605),c_Nat_OSuc(U_2606)) = hAPP(hAPP(U_2604,U_2605),hAPP(hAPP(c_Power_Opower_Opower(U_2602,U_2603,U_2604),U_2605),U_2606)),
    inference(definitional_conversion,[status(esa)],[f_804_2]) ).

cnf(f_804_4,plain,
    hAPP(hAPP(c_Power_Opower_Opower(U_2602,U_2603,U_2604),U_2605),c_Nat_OSuc(U_2606)) = hAPP(hAPP(U_2604,U_2605),hAPP(hAPP(c_Power_Opower_Opower(U_2602,U_2603,U_2604),U_2605),U_2606)),
    inference(clausify,[status(thm)],[f_804_3]) ).

fof(f_805_1,plain,
    ! [V_x] :
      ( c_RComplete_Onatceiling(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(fof_nnf,[status(thm)],[fact_natceiling__neg]) ).

fof(f_805_2,plain,
    ! [U_2607] :
      ( c_RComplete_Onatceiling(U_2607) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2607,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(variable_rename,[status(thm)],[f_805_1]) ).

fof(f_805_3,plain,
    ! [U_2607] :
      ( c_RComplete_Onatceiling(U_2607) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2607,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(definitional_conversion,[status(esa)],[f_805_2]) ).

cnf(f_805_4,plain,
    ( c_RComplete_Onatceiling(U_2607) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2607,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(clausify,[status(thm)],[f_805_3]) ).

fof(f_806_1,plain,
    ! [V_x_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(fof_nnf,[status(thm)],[fact_natceiling__le__eq__one]) ).

fof(f_806_2,plain,
    ! [U_2608] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2608),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2608,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2608,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2608),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_806_1]) ).

fof(f_806_3,plain,
    ( ! [U_2610] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2610),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2610,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
    & ! [U_2609] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2609,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2609),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_806_2]) ).

fof(f_806_4,plain,
    ( ! [U_2610] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2610),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2610,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
    & ! [U_2609] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2609,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2609),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa)],[f_806_3]) ).

cnf(f_806_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2609,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2609),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_806_4]) ).

cnf(f_806_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2610),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2610,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
    inference(clausify,[status(thm)],[f_806_4]) ).

fof(f_807_1,plain,
    ! [V_z] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_z,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    inference(fof_nnf,[status(thm)],[fact_unimodular__reduce__norm]) ).

fof(f_807_2,plain,
    ! [U_2611] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2611,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_2611,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2611,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_2611,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2611) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    inference(variable_rename,[status(thm)],[f_807_1]) ).

fof(f_807_3,plain,
    ! [U_2611] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2611,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_2611,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2611,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_2611,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2611) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    inference(definitional_conversion,[status(esa)],[f_807_2]) ).

cnf(f_807_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2611,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_2611,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2611,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_2611,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_2611) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
    inference(clausify,[status(thm)],[f_807_3]) ).

fof(f_808_1,plain,
    ! [V_a,V_p,T_a] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Nat_OSuc(c_Polynomial_Oorder(T_a,V_a,V_p))),V_p)
      | V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
      | ~ class_Rings_Oidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__2]) ).

fof(f_808_2,plain,
    ! [U_2614,U_2613,U_2612] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2612),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_2612)),c_Polynomial_OpCons(U_2612,c_Groups_Ouminus__class_Ouminus(U_2612,U_2614),c_Polynomial_OpCons(U_2612,c_Groups_Oone__class_Oone(U_2612),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2612))))),c_Nat_OSuc(c_Polynomial_Oorder(U_2612,U_2614,U_2613))),U_2613)
      | U_2613 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2612))
      | ~ class_Rings_Oidom(U_2612) ),
    inference(variable_rename,[status(thm)],[f_808_1]) ).

fof(f_808_3,plain,
    ! [U_2614,U_2612,U_2613] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2612),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_2612)),c_Polynomial_OpCons(U_2612,c_Groups_Ouminus__class_Ouminus(U_2612,U_2614),c_Polynomial_OpCons(U_2612,c_Groups_Oone__class_Oone(U_2612),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2612))))),c_Nat_OSuc(c_Polynomial_Oorder(U_2612,U_2614,U_2613))),U_2613)
      | U_2613 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2612))
      | ~ class_Rings_Oidom(U_2612) ),
    inference(definitional_conversion,[status(esa)],[f_808_2]) ).

cnf(f_808_4,plain,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2612),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_2612)),c_Polynomial_OpCons(U_2612,c_Groups_Ouminus__class_Ouminus(U_2612,U_2614),c_Polynomial_OpCons(U_2612,c_Groups_Oone__class_Oone(U_2612),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2612))))),c_Nat_OSuc(c_Polynomial_Oorder(U_2612,U_2614,U_2613))),U_2613)
    | U_2613 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2612))
    | ~ class_Rings_Oidom(U_2612) ),
    inference(clausify,[status(thm)],[f_808_3]) ).

fof(f_809_1,plain,
    ! [V_a,T_a] :
      ( c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__0__right]) ).

fof(f_809_2,plain,
    ! [U_2616,U_2615] :
      ( c_Rings_Odvd__class_Odvd(U_2615,U_2616,c_Groups_Ozero__class_Ozero(U_2615))
      | ~ class_Rings_Ocomm__semiring__1(U_2615) ),
    inference(variable_rename,[status(thm)],[f_809_1]) ).

fof(f_809_3,plain,
    ! [U_2616,U_2615] :
      ( c_Rings_Odvd__class_Odvd(U_2615,U_2616,c_Groups_Ozero__class_Ozero(U_2615))
      | ~ class_Rings_Ocomm__semiring__1(U_2615) ),
    inference(definitional_conversion,[status(esa)],[f_809_2]) ).

cnf(f_809_4,plain,
    ( c_Rings_Odvd__class_Odvd(U_2615,U_2616,c_Groups_Ozero__class_Ozero(U_2615))
    | ~ class_Rings_Ocomm__semiring__1(U_2615) ),
    inference(clausify,[status(thm)],[f_809_3]) ).

fof(f_810_1,plain,
    ! [V_m,V_b,V_n,V_a,T_a] :
      ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),V_b)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
      | ~ c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),V_b)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_power__le__dvd]) ).

fof(f_810_2,plain,
    ! [U_2621,U_2620,U_2619,U_2618,U_2617] :
      ( c_Rings_Odvd__class_Odvd(U_2617,hAPP(hAPP(c_Power_Opower__class_Opower(U_2617),U_2618),U_2621),U_2620)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2621,U_2619)
      | ~ c_Rings_Odvd__class_Odvd(U_2617,hAPP(hAPP(c_Power_Opower__class_Opower(U_2617),U_2618),U_2619),U_2620)
      | ~ class_Rings_Ocomm__semiring__1(U_2617) ),
    inference(variable_rename,[status(thm)],[f_810_1]) ).

fof(f_810_3,plain,
    ! [U_2617,U_2618,U_2619,U_2620,U_2621] :
      ( c_Rings_Odvd__class_Odvd(U_2617,hAPP(hAPP(c_Power_Opower__class_Opower(U_2617),U_2618),U_2621),U_2620)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2621,U_2619)
      | ~ c_Rings_Odvd__class_Odvd(U_2617,hAPP(hAPP(c_Power_Opower__class_Opower(U_2617),U_2618),U_2619),U_2620)
      | ~ class_Rings_Ocomm__semiring__1(U_2617) ),
    inference(definitional_conversion,[status(esa)],[f_810_2]) ).

cnf(f_810_4,plain,
    ( c_Rings_Odvd__class_Odvd(U_2617,hAPP(hAPP(c_Power_Opower__class_Opower(U_2617),U_2618),U_2621),U_2620)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2621,U_2619)
    | ~ c_Rings_Odvd__class_Odvd(U_2617,hAPP(hAPP(c_Power_Opower__class_Opower(U_2617),U_2618),U_2619),U_2620)
    | ~ class_Rings_Ocomm__semiring__1(U_2617) ),
    inference(clausify,[status(thm)],[f_810_3]) ).

fof(f_811_1,plain,
    ! [V_m,V_n,V_y,V_x,T_a] :
      ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_m))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__power__le]) ).

fof(f_811_2,plain,
    ! [U_2626,U_2625,U_2624,U_2623,U_2622] :
      ( c_Rings_Odvd__class_Odvd(U_2622,hAPP(hAPP(c_Power_Opower__class_Opower(U_2622),U_2623),U_2625),hAPP(hAPP(c_Power_Opower__class_Opower(U_2622),U_2624),U_2626))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2625,U_2626)
      | ~ c_Rings_Odvd__class_Odvd(U_2622,U_2623,U_2624)
      | ~ class_Rings_Ocomm__semiring__1(U_2622) ),
    inference(variable_rename,[status(thm)],[f_811_1]) ).

fof(f_811_3,plain,
    ! [U_2624,U_2622,U_2623,U_2625,U_2626] :
      ( c_Rings_Odvd__class_Odvd(U_2622,hAPP(hAPP(c_Power_Opower__class_Opower(U_2622),U_2623),U_2625),hAPP(hAPP(c_Power_Opower__class_Opower(U_2622),U_2624),U_2626))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2625,U_2626)
      | ~ c_Rings_Odvd__class_Odvd(U_2622,U_2623,U_2624)
      | ~ class_Rings_Ocomm__semiring__1(U_2622) ),
    inference(definitional_conversion,[status(esa)],[f_811_2]) ).

cnf(f_811_4,plain,
    ( c_Rings_Odvd__class_Odvd(U_2622,hAPP(hAPP(c_Power_Opower__class_Opower(U_2622),U_2623),U_2625),hAPP(hAPP(c_Power_Opower__class_Opower(U_2622),U_2624),U_2626))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2625,U_2626)
    | ~ c_Rings_Odvd__class_Odvd(U_2622,U_2623,U_2624)
    | ~ class_Rings_Ocomm__semiring__1(U_2622) ),
    inference(clausify,[status(thm)],[f_811_3]) ).

fof(f_812_1,plain,
    ! [V_a,V_n,V_m,T_a] :
      ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__imp__power__dvd]) ).

fof(f_812_2,plain,
    ! [U_2630,U_2629,U_2628,U_2627] :
      ( c_Rings_Odvd__class_Odvd(U_2627,hAPP(hAPP(c_Power_Opower__class_Opower(U_2627),U_2630),U_2628),hAPP(hAPP(c_Power_Opower__class_Opower(U_2627),U_2630),U_2629))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2628,U_2629)
      | ~ class_Rings_Ocomm__semiring__1(U_2627) ),
    inference(variable_rename,[status(thm)],[f_812_1]) ).

fof(f_812_3,plain,
    ! [U_2627,U_2628,U_2629,U_2630] :
      ( c_Rings_Odvd__class_Odvd(U_2627,hAPP(hAPP(c_Power_Opower__class_Opower(U_2627),U_2630),U_2628),hAPP(hAPP(c_Power_Opower__class_Opower(U_2627),U_2630),U_2629))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2628,U_2629)
      | ~ class_Rings_Ocomm__semiring__1(U_2627) ),
    inference(definitional_conversion,[status(esa)],[f_812_2]) ).

cnf(f_812_4,plain,
    ( c_Rings_Odvd__class_Odvd(U_2627,hAPP(hAPP(c_Power_Opower__class_Opower(U_2627),U_2630),U_2628),hAPP(hAPP(c_Power_Opower__class_Opower(U_2627),U_2630),U_2629))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2628,U_2629)
    | ~ class_Rings_Ocomm__semiring__1(U_2627) ),
    inference(clausify,[status(thm)],[f_812_3]) ).

fof(f_813_1,plain,
    ! [V_n,V_y,V_x,T_a] :
      ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n))
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__power__same]) ).

fof(f_813_2,plain,
    ! [U_2634,U_2633,U_2632,U_2631] :
      ( c_Rings_Odvd__class_Odvd(U_2631,hAPP(hAPP(c_Power_Opower__class_Opower(U_2631),U_2632),U_2634),hAPP(hAPP(c_Power_Opower__class_Opower(U_2631),U_2633),U_2634))
      | ~ c_Rings_Odvd__class_Odvd(U_2631,U_2632,U_2633)
      | ~ class_Rings_Ocomm__semiring__1(U_2631) ),
    inference(variable_rename,[status(thm)],[f_813_1]) ).

fof(f_813_3,plain,
    ! [U_2631,U_2632,U_2633,U_2634] :
      ( c_Rings_Odvd__class_Odvd(U_2631,hAPP(hAPP(c_Power_Opower__class_Opower(U_2631),U_2632),U_2634),hAPP(hAPP(c_Power_Opower__class_Opower(U_2631),U_2633),U_2634))
      | ~ c_Rings_Odvd__class_Odvd(U_2631,U_2632,U_2633)
      | ~ class_Rings_Ocomm__semiring__1(U_2631) ),
    inference(definitional_conversion,[status(esa)],[f_813_2]) ).

cnf(f_813_4,plain,
    ( c_Rings_Odvd__class_Odvd(U_2631,hAPP(hAPP(c_Power_Opower__class_Opower(U_2631),U_2632),U_2634),hAPP(hAPP(c_Power_Opower__class_Opower(U_2631),U_2633),U_2634))
    | ~ c_Rings_Odvd__class_Odvd(U_2631,U_2632,U_2633)
    | ~ class_Rings_Ocomm__semiring__1(U_2631) ),
    inference(clausify,[status(thm)],[f_813_3]) ).

fof(f_814_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__triv__left]) ).

fof(f_814_2,plain,
    ! [U_2637,U_2636,U_2635] :
      ( c_Rings_Odvd__class_Odvd(U_2635,U_2636,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2635),U_2636),U_2637))
      | ~ class_Rings_Ocomm__semiring__1(U_2635) ),
    inference(variable_rename,[status(thm)],[f_814_1]) ).

fof(f_814_3,plain,
    ! [U_2636,U_2637,U_2635] :
      ( c_Rings_Odvd__class_Odvd(U_2635,U_2636,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2635),U_2636),U_2637))
      | ~ class_Rings_Ocomm__semiring__1(U_2635) ),
    inference(definitional_conversion,[status(esa)],[f_814_2]) ).

cnf(f_814_4,plain,
    ( c_Rings_Odvd__class_Odvd(U_2635,U_2636,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2635),U_2636),U_2637))
    | ~ class_Rings_Ocomm__semiring__1(U_2635) ),
    inference(clausify,[status(thm)],[f_814_3]) ).

fof(f_815_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__triv__right]) ).

fof(f_815_2,plain,
    ! [U_2640,U_2639,U_2638] :
      ( c_Rings_Odvd__class_Odvd(U_2638,U_2639,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2638),U_2640),U_2639))
      | ~ class_Rings_Ocomm__semiring__1(U_2638) ),
    inference(variable_rename,[status(thm)],[f_815_1]) ).

fof(f_815_3,plain,
    ! [U_2638,U_2639,U_2640] :
      ( c_Rings_Odvd__class_Odvd(U_2638,U_2639,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2638),U_2640),U_2639))
      | ~ class_Rings_Ocomm__semiring__1(U_2638) ),
    inference(definitional_conversion,[status(esa)],[f_815_2]) ).

cnf(f_815_4,plain,
    ( c_Rings_Odvd__class_Odvd(U_2638,U_2639,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2638),U_2640),U_2639))
    | ~ class_Rings_Ocomm__semiring__1(U_2638) ),
    inference(clausify,[status(thm)],[f_815_3]) ).

fof(f_816_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mult2]) ).

fof(f_816_2,plain,
    ! [U_2644,U_2643,U_2642,U_2641] :
      ( c_Rings_Odvd__class_Odvd(U_2641,U_2642,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2641),U_2643),U_2644))
      | ~ c_Rings_Odvd__class_Odvd(U_2641,U_2642,U_2643)
      | ~ class_Rings_Ocomm__semiring__1(U_2641) ),
    inference(variable_rename,[status(thm)],[f_816_1]) ).

fof(f_816_3,plain,
    ! [U_2641,U_2642,U_2643,U_2644] :
      ( c_Rings_Odvd__class_Odvd(U_2641,U_2642,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2641),U_2643),U_2644))
      | ~ c_Rings_Odvd__class_Odvd(U_2641,U_2642,U_2643)
      | ~ class_Rings_Ocomm__semiring__1(U_2641) ),
    inference(definitional_conversion,[status(esa)],[f_816_2]) ).

cnf(f_816_4,plain,
    ( c_Rings_Odvd__class_Odvd(U_2641,U_2642,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2641),U_2643),U_2644))
    | ~ c_Rings_Odvd__class_Odvd(U_2641,U_2642,U_2643)
    | ~ class_Rings_Ocomm__semiring__1(U_2641) ),
    inference(clausify,[status(thm)],[f_816_3]) ).

fof(f_817_1,plain,
    ! [V_b,V_c,V_a,T_a] :
      ( c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mult]) ).

fof(f_817_2,plain,
    ! [U_2648,U_2647,U_2646,U_2645] :
      ( c_Rings_Odvd__class_Odvd(U_2645,U_2646,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2645),U_2648),U_2647))
      | ~ c_Rings_Odvd__class_Odvd(U_2645,U_2646,U_2647)
      | ~ class_Rings_Ocomm__semiring__1(U_2645) ),
    inference(variable_rename,[status(thm)],[f_817_1]) ).

fof(f_817_3,plain,
    ! [U_2645,U_2646,U_2647,U_2648] :
      ( c_Rings_Odvd__class_Odvd(U_2645,U_2646,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2645),U_2648),U_2647))
      | ~ c_Rings_Odvd__class_Odvd(U_2645,U_2646,U_2647)
      | ~ class_Rings_Ocomm__semiring__1(U_2645) ),
    inference(definitional_conversion,[status(esa)],[f_817_2]) ).

cnf(f_817_4,plain,
    ( c_Rings_Odvd__class_Odvd(U_2645,U_2646,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2645),U_2648),U_2647))
    | ~ c_Rings_Odvd__class_Odvd(U_2645,U_2646,U_2647)
    | ~ class_Rings_Ocomm__semiring__1(U_2645) ),
    inference(clausify,[status(thm)],[f_817_3]) ).

fof(f_818_1,plain,
    ! [V_d,V_c,V_b,V_a,T_a] :
      ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_c,V_d)
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__dvd__mono]) ).

fof(f_818_2,plain,
    ! [U_2653,U_2652,U_2651,U_2650,U_2649] :
      ( c_Rings_Odvd__class_Odvd(U_2649,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2649),U_2650),U_2652),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2649),U_2651),U_2653))
      | ~ c_Rings_Odvd__class_Odvd(U_2649,U_2652,U_2653)
      | ~ c_Rings_Odvd__class_Odvd(U_2649,U_2650,U_2651)
      | ~ class_Rings_Ocomm__semiring__1(U_2649) ),
    inference(variable_rename,[status(thm)],[f_818_1]) ).

fof(f_818_3,plain,
    ! [U_2649,U_2650,U_2651,U_2652,U_2653] :
      ( c_Rings_Odvd__class_Odvd(U_2649,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2649),U_2650),U_2652),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2649),U_2651),U_2653))
      | ~ c_Rings_Odvd__class_Odvd(U_2649,U_2652,U_2653)
      | ~ c_Rings_Odvd__class_Odvd(U_2649,U_2650,U_2651)
      | ~ class_Rings_Ocomm__semiring__1(U_2649) ),
    inference(definitional_conversion,[status(esa)],[f_818_2]) ).

cnf(f_818_4,plain,
    ( c_Rings_Odvd__class_Odvd(U_2649,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2649),U_2650),U_2652),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2649),U_2651),U_2653))
    | ~ c_Rings_Odvd__class_Odvd(U_2649,U_2652,U_2653)
    | ~ c_Rings_Odvd__class_Odvd(U_2649,U_2650,U_2651)
    | ~ class_Rings_Ocomm__semiring__1(U_2649) ),
    inference(clausify,[status(thm)],[f_818_3]) ).

fof(f_819_1,plain,
    ! [V_k,V_b,V_a,T_a] :
      ( c_Rings_Odvd__class_Odvd(T_a,V_b,V_a)
      | V_a != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
      | ~ class_Rings_Odvd(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvdI]) ).

fof(f_819_2,plain,
    ! [U_2657,U_2656,U_2655,U_2654] :
      ( c_Rings_Odvd__class_Odvd(U_2654,U_2656,U_2655)
      | U_2655 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2654),U_2656),U_2657)
      | ~ class_Rings_Odvd(U_2654) ),
    inference(variable_rename,[status(thm)],[f_819_1]) ).

fof(f_819_3,plain,
    ! [U_2655,U_2657,U_2654,U_2656] :
      ( c_Rings_Odvd__class_Odvd(U_2654,U_2656,U_2655)
      | U_2655 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2654),U_2656),U_2657)
      | ~ class_Rings_Odvd(U_2654) ),
    inference(definitional_conversion,[status(esa)],[f_819_2]) ).

cnf(f_819_4,plain,
    ( c_Rings_Odvd__class_Odvd(U_2654,U_2656,U_2655)
    | U_2655 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2654),U_2656),U_2657)
    | ~ class_Rings_Odvd(U_2654) ),
    inference(clausify,[status(thm)],[f_819_3]) ).

fof(f_820_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)
      | ~ c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mult__left]) ).

fof(f_820_2,plain,
    ! [U_2661,U_2660,U_2659,U_2658] :
      ( c_Rings_Odvd__class_Odvd(U_2658,U_2659,U_2661)
      | ~ c_Rings_Odvd__class_Odvd(U_2658,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2658),U_2659),U_2660),U_2661)
      | ~ class_Rings_Ocomm__semiring__1(U_2658) ),
    inference(variable_rename,[status(thm)],[f_820_1]) ).

fof(f_820_3,plain,
    ! [U_2658,U_2659,U_2660,U_2661] :
      ( c_Rings_Odvd__class_Odvd(U_2658,U_2659,U_2661)
      | ~ c_Rings_Odvd__class_Odvd(U_2658,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2658),U_2659),U_2660),U_2661)
      | ~ class_Rings_Ocomm__semiring__1(U_2658) ),
    inference(definitional_conversion,[status(esa)],[f_820_2]) ).

cnf(f_820_4,plain,
    ( c_Rings_Odvd__class_Odvd(U_2658,U_2659,U_2661)
    | ~ c_Rings_Odvd__class_Odvd(U_2658,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2658),U_2659),U_2660),U_2661)
    | ~ class_Rings_Ocomm__semiring__1(U_2658) ),
    inference(clausify,[status(thm)],[f_820_3]) ).

fof(f_821_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Rings_Odvd__class_Odvd(T_a,V_b,V_c)
      | ~ c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mult__right]) ).

fof(f_821_2,plain,
    ! [U_2665,U_2664,U_2663,U_2662] :
      ( c_Rings_Odvd__class_Odvd(U_2662,U_2664,U_2665)
      | ~ c_Rings_Odvd__class_Odvd(U_2662,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2662),U_2663),U_2664),U_2665)
      | ~ class_Rings_Ocomm__semiring__1(U_2662) ),
    inference(variable_rename,[status(thm)],[f_821_1]) ).

fof(f_821_3,plain,
    ! [U_2662,U_2663,U_2664,U_2665] :
      ( c_Rings_Odvd__class_Odvd(U_2662,U_2664,U_2665)
      | ~ c_Rings_Odvd__class_Odvd(U_2662,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2662),U_2663),U_2664),U_2665)
      | ~ class_Rings_Ocomm__semiring__1(U_2662) ),
    inference(definitional_conversion,[status(esa)],[f_821_2]) ).

cnf(f_821_4,plain,
    ( c_Rings_Odvd__class_Odvd(U_2662,U_2664,U_2665)
    | ~ c_Rings_Odvd__class_Odvd(U_2662,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2662),U_2663),U_2664),U_2665)
    | ~ class_Rings_Ocomm__semiring__1(U_2662) ),
    inference(clausify,[status(thm)],[f_821_3]) ).

fof(f_822_1,plain,
    ! [V_a,T_a] :
      ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_a)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__refl]) ).

fof(f_822_2,plain,
    ! [U_2667,U_2666] :
      ( c_Rings_Odvd__class_Odvd(U_2666,U_2667,U_2667)
      | ~ class_Rings_Ocomm__semiring__1(U_2666) ),
    inference(variable_rename,[status(thm)],[f_822_1]) ).

fof(f_822_3,plain,
    ! [U_2667,U_2666] :
      ( c_Rings_Odvd__class_Odvd(U_2666,U_2667,U_2667)
      | ~ class_Rings_Ocomm__semiring__1(U_2666) ),
    inference(definitional_conversion,[status(esa)],[f_822_2]) ).

cnf(f_822_4,plain,
    ( c_Rings_Odvd__class_Odvd(U_2666,U_2667,U_2667)
    | ~ class_Rings_Ocomm__semiring__1(U_2666) ),
    inference(clausify,[status(thm)],[f_822_3]) ).

fof(f_823_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_b,V_c)
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__trans]) ).

fof(f_823_2,plain,
    ! [U_2671,U_2670,U_2669,U_2668] :
      ( c_Rings_Odvd__class_Odvd(U_2668,U_2669,U_2671)
      | ~ c_Rings_Odvd__class_Odvd(U_2668,U_2670,U_2671)
      | ~ c_Rings_Odvd__class_Odvd(U_2668,U_2669,U_2670)
      | ~ class_Rings_Ocomm__semiring__1(U_2668) ),
    inference(variable_rename,[status(thm)],[f_823_1]) ).

fof(f_823_3,plain,
    ! [U_2669,U_2668,U_2670,U_2671] :
      ( c_Rings_Odvd__class_Odvd(U_2668,U_2669,U_2671)
      | ~ c_Rings_Odvd__class_Odvd(U_2668,U_2670,U_2671)
      | ~ c_Rings_Odvd__class_Odvd(U_2668,U_2669,U_2670)
      | ~ class_Rings_Ocomm__semiring__1(U_2668) ),
    inference(definitional_conversion,[status(esa)],[f_823_2]) ).

cnf(f_823_4,plain,
    ( c_Rings_Odvd__class_Odvd(U_2668,U_2669,U_2671)
    | ~ c_Rings_Odvd__class_Odvd(U_2668,U_2670,U_2671)
    | ~ c_Rings_Odvd__class_Odvd(U_2668,U_2669,U_2670)
    | ~ class_Rings_Ocomm__semiring__1(U_2668) ),
    inference(clausify,[status(thm)],[f_823_3]) ).

fof(f_824_1,plain,
    ! [V_q,V_p,V_a,T_a] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q)
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),V_q)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_smult__dvd__cancel]) ).

fof(f_824_2,plain,
    ! [U_2675,U_2674,U_2673,U_2672] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2672),U_2674,U_2675)
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2672),c_Polynomial_Osmult(U_2672,U_2673,U_2674),U_2675)
      | ~ class_Rings_Ocomm__semiring__1(U_2672) ),
    inference(variable_rename,[status(thm)],[f_824_1]) ).

fof(f_824_3,plain,
    ! [U_2675,U_2673,U_2672,U_2674] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2672),U_2674,U_2675)
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2672),c_Polynomial_Osmult(U_2672,U_2673,U_2674),U_2675)
      | ~ class_Rings_Ocomm__semiring__1(U_2672) ),
    inference(definitional_conversion,[status(esa)],[f_824_2]) ).

cnf(f_824_4,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2672),U_2674,U_2675)
    | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2672),c_Polynomial_Osmult(U_2672,U_2673,U_2674),U_2675)
    | ~ class_Rings_Ocomm__semiring__1(U_2672) ),
    inference(clausify,[status(thm)],[f_824_3]) ).

fof(f_825_1,plain,
    ! [V_a,V_q,V_p,T_a] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_a,V_q))
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__smult]) ).

fof(f_825_2,plain,
    ! [U_2679,U_2678,U_2677,U_2676] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2676),U_2677,c_Polynomial_Osmult(U_2676,U_2679,U_2678))
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2676),U_2677,U_2678)
      | ~ class_Rings_Ocomm__semiring__1(U_2676) ),
    inference(variable_rename,[status(thm)],[f_825_1]) ).

fof(f_825_3,plain,
    ! [U_2676,U_2677,U_2678,U_2679] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2676),U_2677,c_Polynomial_Osmult(U_2676,U_2679,U_2678))
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2676),U_2677,U_2678)
      | ~ class_Rings_Ocomm__semiring__1(U_2676) ),
    inference(definitional_conversion,[status(esa)],[f_825_2]) ).

cnf(f_825_4,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2676),U_2677,c_Polynomial_Osmult(U_2676,U_2679,U_2678))
    | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2676),U_2677,U_2678)
    | ~ class_Rings_Ocomm__semiring__1(U_2676) ),
    inference(clausify,[status(thm)],[f_825_3]) ).

fof(f_826_1,plain,
    c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[fact_complex__i__not__one]) ).

fof(f_826_2,plain,
    c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_826_1]) ).

cnf(f_826_3,plain,
    c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_826_2]) ).

fof(f_827_1,plain,
    ! [V_a,T_a] :
      ( V_a = c_Groups_Ozero__class_Ozero(T_a)
      | ~ c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__0__left]) ).

fof(f_827_2,plain,
    ! [U_2681,U_2680] :
      ( U_2681 = c_Groups_Ozero__class_Ozero(U_2680)
      | ~ c_Rings_Odvd__class_Odvd(U_2680,c_Groups_Ozero__class_Ozero(U_2680),U_2681)
      | ~ class_Rings_Ocomm__semiring__1(U_2680) ),
    inference(variable_rename,[status(thm)],[f_827_1]) ).

fof(f_827_3,plain,
    ! [U_2681,U_2680] :
      ( U_2681 = c_Groups_Ozero__class_Ozero(U_2680)
      | ~ c_Rings_Odvd__class_Odvd(U_2680,c_Groups_Ozero__class_Ozero(U_2680),U_2681)
      | ~ class_Rings_Ocomm__semiring__1(U_2680) ),
    inference(definitional_conversion,[status(esa)],[f_827_2]) ).

cnf(f_827_4,plain,
    ( U_2681 = c_Groups_Ozero__class_Ozero(U_2680)
    | ~ c_Rings_Odvd__class_Odvd(U_2680,c_Groups_Ozero__class_Ozero(U_2680),U_2681)
    | ~ class_Rings_Ocomm__semiring__1(U_2680) ),
    inference(clausify,[status(thm)],[f_827_3]) ).

fof(f_828_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__add]) ).

fof(f_828_2,plain,
    ! [U_2685,U_2684,U_2683,U_2682] :
      ( c_Rings_Odvd__class_Odvd(U_2682,U_2683,c_Groups_Oplus__class_Oplus(U_2682,U_2684,U_2685))
      | ~ c_Rings_Odvd__class_Odvd(U_2682,U_2683,U_2685)
      | ~ c_Rings_Odvd__class_Odvd(U_2682,U_2683,U_2684)
      | ~ class_Rings_Ocomm__semiring__1(U_2682) ),
    inference(variable_rename,[status(thm)],[f_828_1]) ).

fof(f_828_3,plain,
    ! [U_2682,U_2683,U_2684,U_2685] :
      ( c_Rings_Odvd__class_Odvd(U_2682,U_2683,c_Groups_Oplus__class_Oplus(U_2682,U_2684,U_2685))
      | ~ c_Rings_Odvd__class_Odvd(U_2682,U_2683,U_2685)
      | ~ c_Rings_Odvd__class_Odvd(U_2682,U_2683,U_2684)
      | ~ class_Rings_Ocomm__semiring__1(U_2682) ),
    inference(definitional_conversion,[status(esa)],[f_828_2]) ).

cnf(f_828_4,plain,
    ( c_Rings_Odvd__class_Odvd(U_2682,U_2683,c_Groups_Oplus__class_Oplus(U_2682,U_2684,U_2685))
    | ~ c_Rings_Odvd__class_Odvd(U_2682,U_2683,U_2685)
    | ~ c_Rings_Odvd__class_Odvd(U_2682,U_2683,U_2684)
    | ~ class_Rings_Ocomm__semiring__1(U_2682) ),
    inference(clausify,[status(thm)],[f_828_3]) ).

fof(f_829_1,plain,
    ! [V_a,T_a] :
      ( c_Rings_Odvd__class_Odvd(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_one__dvd]) ).

fof(f_829_2,plain,
    ! [U_2687,U_2686] :
      ( c_Rings_Odvd__class_Odvd(U_2686,c_Groups_Oone__class_Oone(U_2686),U_2687)
      | ~ class_Rings_Ocomm__semiring__1(U_2686) ),
    inference(variable_rename,[status(thm)],[f_829_1]) ).

fof(f_829_3,plain,
    ! [U_2686,U_2687] :
      ( c_Rings_Odvd__class_Odvd(U_2686,c_Groups_Oone__class_Oone(U_2686),U_2687)
      | ~ class_Rings_Ocomm__semiring__1(U_2686) ),
    inference(definitional_conversion,[status(esa)],[f_829_2]) ).

cnf(f_829_4,plain,
    ( c_Rings_Odvd__class_Odvd(U_2686,c_Groups_Oone__class_Oone(U_2686),U_2687)
    | ~ class_Rings_Ocomm__semiring__1(U_2686) ),
    inference(clausify,[status(thm)],[f_829_3]) ).

fof(f_830_1,plain,
    c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[fact_complex__i__not__zero]) ).

fof(f_830_2,plain,
    c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_830_1]) ).

cnf(f_830_3,plain,
    c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_830_2]) ).

fof(f_831_1,plain,
    ! [V_q_2,V_pa_2,V_ab_2,T_a] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,c_Polynomial_Osmult(T_a,V_ab_2,V_q_2))
          | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,V_q_2) )
        & ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,V_q_2)
          | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,c_Polynomial_Osmult(T_a,V_ab_2,V_q_2)) ) )
      | V_ab_2 = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__smult__iff]) ).

fof(f_831_2,plain,
    ! [U_2691,U_2690,U_2689,U_2688] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2688),U_2690,c_Polynomial_Osmult(U_2688,U_2689,U_2691))
          | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2688),U_2690,U_2691) )
        & ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2688),U_2690,U_2691)
          | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2688),U_2690,c_Polynomial_Osmult(U_2688,U_2689,U_2691)) ) )
      | U_2689 = c_Groups_Ozero__class_Ozero(U_2688)
      | ~ class_Fields_Ofield(U_2688) ),
    inference(variable_rename,[status(thm)],[f_831_1]) ).

fof(f_831_3,plain,
    ( ! [U_2688,U_2689,U_2690,U_2691] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2688),U_2690,c_Polynomial_Osmult(U_2688,U_2689,U_2691))
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2688),U_2690,U_2691)
        | ~ sP220(U_2688,U_2689,U_2690,U_2691) )
    & ! [U_2688,U_2689,U_2690,U_2691] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2688),U_2690,U_2691)
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2688),U_2690,c_Polynomial_Osmult(U_2688,U_2689,U_2691))
        | ~ sP220(U_2688,U_2689,U_2690,U_2691) )
    & ! [U_2688,U_2689,U_2690,U_2691] :
        ( sP220(U_2688,U_2689,U_2690,U_2691)
        | U_2689 = c_Groups_Ozero__class_Ozero(U_2688)
        | ~ class_Fields_Ofield(U_2688) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP220])],[f_831_2]) ).

cnf(f_831_4,plain,
    ( sP220(U_2688,U_2689,U_2690,U_2691)
    | U_2689 = c_Groups_Ozero__class_Ozero(U_2688)
    | ~ class_Fields_Ofield(U_2688) ),
    inference(clausify,[status(thm)],[f_831_3]) ).

cnf(f_831_5,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2688),U_2690,U_2691)
    | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2688),U_2690,c_Polynomial_Osmult(U_2688,U_2689,U_2691))
    | ~ sP220(U_2688,U_2689,U_2690,U_2691) ),
    inference(clausify,[status(thm)],[f_831_3]) ).

cnf(f_831_6,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2688),U_2690,c_Polynomial_Osmult(U_2688,U_2689,U_2691))
    | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2688),U_2690,U_2691)
    | ~ sP220(U_2688,U_2689,U_2690,U_2691) ),
    inference(clausify,[status(thm)],[f_831_3]) ).

fof(f_832_1,plain,
    ! [V_a,V_q,V_p,T_a] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),V_q)
      | V_a = c_Groups_Ozero__class_Ozero(T_a)
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q)
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_smult__dvd]) ).

fof(f_832_2,plain,
    ! [U_2695,U_2694,U_2693,U_2692] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2692),c_Polynomial_Osmult(U_2692,U_2695,U_2693),U_2694)
      | U_2695 = c_Groups_Ozero__class_Ozero(U_2692)
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2692),U_2693,U_2694)
      | ~ class_Fields_Ofield(U_2692) ),
    inference(variable_rename,[status(thm)],[f_832_1]) ).

fof(f_832_3,plain,
    ! [U_2695,U_2694,U_2692,U_2693] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2692),c_Polynomial_Osmult(U_2692,U_2695,U_2693),U_2694)
      | U_2695 = c_Groups_Ozero__class_Ozero(U_2692)
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2692),U_2693,U_2694)
      | ~ class_Fields_Ofield(U_2692) ),
    inference(definitional_conversion,[status(esa)],[f_832_2]) ).

cnf(f_832_4,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2692),c_Polynomial_Osmult(U_2692,U_2695,U_2693),U_2694)
    | U_2695 = c_Groups_Ozero__class_Ozero(U_2692)
    | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2692),U_2693,U_2694)
    | ~ class_Fields_Ofield(U_2692) ),
    inference(clausify,[status(thm)],[f_832_3]) ).

fof(f_833_1,plain,
    ! [V_q,V_a,V_p,T_a] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q)
      | V_a = c_Groups_Ozero__class_Ozero(T_a)
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_a,V_q))
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__smult__cancel]) ).

fof(f_833_2,plain,
    ! [U_2699,U_2698,U_2697,U_2696] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2696),U_2697,U_2699)
      | U_2698 = c_Groups_Ozero__class_Ozero(U_2696)
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2696),U_2697,c_Polynomial_Osmult(U_2696,U_2698,U_2699))
      | ~ class_Fields_Ofield(U_2696) ),
    inference(variable_rename,[status(thm)],[f_833_1]) ).

fof(f_833_3,plain,
    ! [U_2696,U_2697,U_2698,U_2699] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2696),U_2697,U_2699)
      | U_2698 = c_Groups_Ozero__class_Ozero(U_2696)
      | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2696),U_2697,c_Polynomial_Osmult(U_2696,U_2698,U_2699))
      | ~ class_Fields_Ofield(U_2696) ),
    inference(definitional_conversion,[status(esa)],[f_833_2]) ).

cnf(f_833_4,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2696),U_2697,U_2699)
    | U_2698 = c_Groups_Ozero__class_Ozero(U_2696)
    | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2696),U_2697,c_Polynomial_Osmult(U_2696,U_2698,U_2699))
    | ~ class_Fields_Ofield(U_2696) ),
    inference(clausify,[status(thm)],[f_833_3]) ).

fof(f_834_1,plain,
    ! [V_b_2,V_ab_2,V_ca_2,T_a] :
      ( ( ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
          | ( ~ c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_b_2)
            & V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
        & ( c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_b_2)
          | V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
          | ~ c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)) ) )
      | ~ class_Rings_Oidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__left]) ).

fof(f_834_2,plain,
    ! [U_2703,U_2702,U_2701,U_2700] :
      ( ( ( c_Rings_Odvd__class_Odvd(U_2700,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2700),U_2701),U_2702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2700),U_2701),U_2703))
          | ( ~ c_Rings_Odvd__class_Odvd(U_2700,U_2702,U_2703)
            & U_2701 != c_Groups_Ozero__class_Ozero(U_2700) ) )
        & ( c_Rings_Odvd__class_Odvd(U_2700,U_2702,U_2703)
          | U_2701 = c_Groups_Ozero__class_Ozero(U_2700)
          | ~ c_Rings_Odvd__class_Odvd(U_2700,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2700),U_2701),U_2702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2700),U_2701),U_2703)) ) )
      | ~ class_Rings_Oidom(U_2700) ),
    inference(variable_rename,[status(thm)],[f_834_1]) ).

fof(f_834_3,plain,
    ( ! [U_2700,U_2701,U_2702,U_2703] :
        ( ~ c_Rings_Odvd__class_Odvd(U_2700,U_2702,U_2703)
        | ~ sP221(U_2700,U_2701,U_2702,U_2703) )
    & ! [U_2700,U_2701,U_2702,U_2703] :
        ( U_2701 != c_Groups_Ozero__class_Ozero(U_2700)
        | ~ sP221(U_2700,U_2701,U_2702,U_2703) )
    & ! [U_2700,U_2701,U_2702,U_2703] :
        ( c_Rings_Odvd__class_Odvd(U_2700,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2700),U_2701),U_2702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2700),U_2701),U_2703))
        | sP221(U_2700,U_2701,U_2702,U_2703)
        | ~ sP222(U_2700,U_2701,U_2702,U_2703) )
    & ! [U_2700,U_2701,U_2702,U_2703] :
        ( c_Rings_Odvd__class_Odvd(U_2700,U_2702,U_2703)
        | U_2701 = c_Groups_Ozero__class_Ozero(U_2700)
        | ~ c_Rings_Odvd__class_Odvd(U_2700,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2700),U_2701),U_2702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2700),U_2701),U_2703))
        | ~ sP222(U_2700,U_2701,U_2702,U_2703) )
    & ! [U_2700,U_2701,U_2702,U_2703] :
        ( sP222(U_2700,U_2701,U_2702,U_2703)
        | ~ class_Rings_Oidom(U_2700) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP221,sP222])],[f_834_2]) ).

cnf(f_834_4,plain,
    ( sP222(U_2700,U_2701,U_2702,U_2703)
    | ~ class_Rings_Oidom(U_2700) ),
    inference(clausify,[status(thm)],[f_834_3]) ).

cnf(f_834_5,plain,
    ( c_Rings_Odvd__class_Odvd(U_2700,U_2702,U_2703)
    | U_2701 = c_Groups_Ozero__class_Ozero(U_2700)
    | ~ c_Rings_Odvd__class_Odvd(U_2700,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2700),U_2701),U_2702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2700),U_2701),U_2703))
    | ~ sP222(U_2700,U_2701,U_2702,U_2703) ),
    inference(clausify,[status(thm)],[f_834_3]) ).

cnf(f_834_6,plain,
    ( c_Rings_Odvd__class_Odvd(U_2700,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2700),U_2701),U_2702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2700),U_2701),U_2703))
    | sP221(U_2700,U_2701,U_2702,U_2703)
    | ~ sP222(U_2700,U_2701,U_2702,U_2703) ),
    inference(clausify,[status(thm)],[f_834_3]) ).

cnf(f_834_7,plain,
    ( U_2701 != c_Groups_Ozero__class_Ozero(U_2700)
    | ~ sP221(U_2700,U_2701,U_2702,U_2703) ),
    inference(clausify,[status(thm)],[f_834_3]) ).

cnf(f_834_8,plain,
    ( ~ c_Rings_Odvd__class_Odvd(U_2700,U_2702,U_2703)
    | ~ sP221(U_2700,U_2701,U_2702,U_2703) ),
    inference(clausify,[status(thm)],[f_834_3]) ).

fof(f_835_1,plain,
    ! [V_b_2,V_ca_2,V_ab_2,T_a] :
      ( ( ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))
          | ( ~ c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_b_2)
            & V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
        & ( c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_b_2)
          | V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
          | ~ c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)) ) )
      | ~ class_Rings_Oidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__right]) ).

fof(f_835_2,plain,
    ! [U_2707,U_2706,U_2705,U_2704] :
      ( ( ( c_Rings_Odvd__class_Odvd(U_2704,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2704),U_2705),U_2706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2704),U_2707),U_2706))
          | ( ~ c_Rings_Odvd__class_Odvd(U_2704,U_2705,U_2707)
            & U_2706 != c_Groups_Ozero__class_Ozero(U_2704) ) )
        & ( c_Rings_Odvd__class_Odvd(U_2704,U_2705,U_2707)
          | U_2706 = c_Groups_Ozero__class_Ozero(U_2704)
          | ~ c_Rings_Odvd__class_Odvd(U_2704,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2704),U_2705),U_2706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2704),U_2707),U_2706)) ) )
      | ~ class_Rings_Oidom(U_2704) ),
    inference(variable_rename,[status(thm)],[f_835_1]) ).

fof(f_835_3,plain,
    ( ! [U_2706,U_2707,U_2705,U_2704] :
        ( ~ c_Rings_Odvd__class_Odvd(U_2704,U_2705,U_2707)
        | ~ sP223(U_2706,U_2707,U_2705,U_2704) )
    & ! [U_2706,U_2707,U_2705,U_2704] :
        ( U_2706 != c_Groups_Ozero__class_Ozero(U_2704)
        | ~ sP223(U_2706,U_2707,U_2705,U_2704) )
    & ! [U_2706,U_2707,U_2705,U_2704] :
        ( c_Rings_Odvd__class_Odvd(U_2704,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2704),U_2705),U_2706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2704),U_2707),U_2706))
        | sP223(U_2706,U_2707,U_2705,U_2704)
        | ~ sP224(U_2706,U_2707,U_2705,U_2704) )
    & ! [U_2706,U_2707,U_2705,U_2704] :
        ( c_Rings_Odvd__class_Odvd(U_2704,U_2705,U_2707)
        | U_2706 = c_Groups_Ozero__class_Ozero(U_2704)
        | ~ c_Rings_Odvd__class_Odvd(U_2704,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2704),U_2705),U_2706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2704),U_2707),U_2706))
        | ~ sP224(U_2706,U_2707,U_2705,U_2704) )
    & ! [U_2706,U_2707,U_2705,U_2704] :
        ( sP224(U_2706,U_2707,U_2705,U_2704)
        | ~ class_Rings_Oidom(U_2704) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP223,sP224])],[f_835_2]) ).

cnf(f_835_4,plain,
    ( sP224(U_2706,U_2707,U_2705,U_2704)
    | ~ class_Rings_Oidom(U_2704) ),
    inference(clausify,[status(thm)],[f_835_3]) ).

cnf(f_835_5,plain,
    ( c_Rings_Odvd__class_Odvd(U_2704,U_2705,U_2707)
    | U_2706 = c_Groups_Ozero__class_Ozero(U_2704)
    | ~ c_Rings_Odvd__class_Odvd(U_2704,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2704),U_2705),U_2706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2704),U_2707),U_2706))
    | ~ sP224(U_2706,U_2707,U_2705,U_2704) ),
    inference(clausify,[status(thm)],[f_835_3]) ).

cnf(f_835_6,plain,
    ( c_Rings_Odvd__class_Odvd(U_2704,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2704),U_2705),U_2706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2704),U_2707),U_2706))
    | sP223(U_2706,U_2707,U_2705,U_2704)
    | ~ sP224(U_2706,U_2707,U_2705,U_2704) ),
    inference(clausify,[status(thm)],[f_835_3]) ).

cnf(f_835_7,plain,
    ( U_2706 != c_Groups_Ozero__class_Ozero(U_2704)
    | ~ sP223(U_2706,U_2707,U_2705,U_2704) ),
    inference(clausify,[status(thm)],[f_835_3]) ).

cnf(f_835_8,plain,
    ( ~ c_Rings_Odvd__class_Odvd(U_2704,U_2705,U_2707)
    | ~ sP223(U_2706,U_2707,U_2705,U_2704) ),
    inference(clausify,[status(thm)],[f_835_3]) ).

fof(f_836_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( c_Rings_Odvd__class_Odvd(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_z))
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_x,V_z)
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)
      | ~ class_Rings_Ocomm__ring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__diff]) ).

fof(f_836_2,plain,
    ! [U_2711,U_2710,U_2709,U_2708] :
      ( c_Rings_Odvd__class_Odvd(U_2708,U_2709,c_Groups_Ominus__class_Ominus(U_2708,U_2710,U_2711))
      | ~ c_Rings_Odvd__class_Odvd(U_2708,U_2709,U_2711)
      | ~ c_Rings_Odvd__class_Odvd(U_2708,U_2709,U_2710)
      | ~ class_Rings_Ocomm__ring__1(U_2708) ),
    inference(variable_rename,[status(thm)],[f_836_1]) ).

fof(f_836_3,plain,
    ! [U_2709,U_2710,U_2708,U_2711] :
      ( c_Rings_Odvd__class_Odvd(U_2708,U_2709,c_Groups_Ominus__class_Ominus(U_2708,U_2710,U_2711))
      | ~ c_Rings_Odvd__class_Odvd(U_2708,U_2709,U_2711)
      | ~ c_Rings_Odvd__class_Odvd(U_2708,U_2709,U_2710)
      | ~ class_Rings_Ocomm__ring__1(U_2708) ),
    inference(definitional_conversion,[status(esa)],[f_836_2]) ).

cnf(f_836_4,plain,
    ( c_Rings_Odvd__class_Odvd(U_2708,U_2709,c_Groups_Ominus__class_Ominus(U_2708,U_2710,U_2711))
    | ~ c_Rings_Odvd__class_Odvd(U_2708,U_2709,U_2711)
    | ~ c_Rings_Odvd__class_Odvd(U_2708,U_2709,U_2710)
    | ~ class_Rings_Ocomm__ring__1(U_2708) ),
    inference(clausify,[status(thm)],[f_836_3]) ).

fof(f_837_1,plain,
    ! [V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),V_x)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,V_x),
    inference(fof_nnf,[status(thm)],[fact_complex__i__mult__minus]) ).

fof(f_837_2,plain,
    ! [U_2712] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),U_2712)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,U_2712),
    inference(variable_rename,[status(thm)],[f_837_1]) ).

fof(f_837_3,plain,
    ! [U_2712] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),U_2712)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,U_2712),
    inference(definitional_conversion,[status(esa)],[f_837_2]) ).

cnf(f_837_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),U_2712)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,U_2712),
    inference(clausify,[status(thm)],[f_837_3]) ).

fof(f_838_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),V_y_2)
          | ~ c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2) )
        & ( c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2)
          | ~ c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),V_y_2) ) )
      | ~ class_Rings_Ocomm__ring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_minus__dvd__iff]) ).

fof(f_838_2,plain,
    ! [U_2715,U_2714,U_2713] :
      ( ( ( c_Rings_Odvd__class_Odvd(U_2713,c_Groups_Ouminus__class_Ouminus(U_2713,U_2714),U_2715)
          | ~ c_Rings_Odvd__class_Odvd(U_2713,U_2714,U_2715) )
        & ( c_Rings_Odvd__class_Odvd(U_2713,U_2714,U_2715)
          | ~ c_Rings_Odvd__class_Odvd(U_2713,c_Groups_Ouminus__class_Ouminus(U_2713,U_2714),U_2715) ) )
      | ~ class_Rings_Ocomm__ring__1(U_2713) ),
    inference(variable_rename,[status(thm)],[f_838_1]) ).

fof(f_838_3,plain,
    ( ! [U_2713,U_2714,U_2715] :
        ( c_Rings_Odvd__class_Odvd(U_2713,c_Groups_Ouminus__class_Ouminus(U_2713,U_2714),U_2715)
        | ~ c_Rings_Odvd__class_Odvd(U_2713,U_2714,U_2715)
        | ~ sP225(U_2713,U_2714,U_2715) )
    & ! [U_2713,U_2714,U_2715] :
        ( c_Rings_Odvd__class_Odvd(U_2713,U_2714,U_2715)
        | ~ c_Rings_Odvd__class_Odvd(U_2713,c_Groups_Ouminus__class_Ouminus(U_2713,U_2714),U_2715)
        | ~ sP225(U_2713,U_2714,U_2715) )
    & ! [U_2713,U_2714,U_2715] :
        ( sP225(U_2713,U_2714,U_2715)
        | ~ class_Rings_Ocomm__ring__1(U_2713) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP225])],[f_838_2]) ).

cnf(f_838_4,plain,
    ( sP225(U_2713,U_2714,U_2715)
    | ~ class_Rings_Ocomm__ring__1(U_2713) ),
    inference(clausify,[status(thm)],[f_838_3]) ).

cnf(f_838_5,plain,
    ( c_Rings_Odvd__class_Odvd(U_2713,U_2714,U_2715)
    | ~ c_Rings_Odvd__class_Odvd(U_2713,c_Groups_Ouminus__class_Ouminus(U_2713,U_2714),U_2715)
    | ~ sP225(U_2713,U_2714,U_2715) ),
    inference(clausify,[status(thm)],[f_838_3]) ).

cnf(f_838_6,plain,
    ( c_Rings_Odvd__class_Odvd(U_2713,c_Groups_Ouminus__class_Ouminus(U_2713,U_2714),U_2715)
    | ~ c_Rings_Odvd__class_Odvd(U_2713,U_2714,U_2715)
    | ~ sP225(U_2713,U_2714,U_2715) ),
    inference(clausify,[status(thm)],[f_838_3]) ).

fof(f_839_1,plain,
    ! [V_y_2,V_x_2,T_a] :
      ( ( ( c_Rings_Odvd__class_Odvd(T_a,V_x_2,c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))
          | ~ c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2) )
        & ( c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2)
          | ~ c_Rings_Odvd__class_Odvd(T_a,V_x_2,c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)) ) )
      | ~ class_Rings_Ocomm__ring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__minus__iff]) ).

fof(f_839_2,plain,
    ! [U_2718,U_2717,U_2716] :
      ( ( ( c_Rings_Odvd__class_Odvd(U_2716,U_2717,c_Groups_Ouminus__class_Ouminus(U_2716,U_2718))
          | ~ c_Rings_Odvd__class_Odvd(U_2716,U_2717,U_2718) )
        & ( c_Rings_Odvd__class_Odvd(U_2716,U_2717,U_2718)
          | ~ c_Rings_Odvd__class_Odvd(U_2716,U_2717,c_Groups_Ouminus__class_Ouminus(U_2716,U_2718)) ) )
      | ~ class_Rings_Ocomm__ring__1(U_2716) ),
    inference(variable_rename,[status(thm)],[f_839_1]) ).

fof(f_839_3,plain,
    ( ! [U_2718,U_2717,U_2716] :
        ( c_Rings_Odvd__class_Odvd(U_2716,U_2717,c_Groups_Ouminus__class_Ouminus(U_2716,U_2718))
        | ~ c_Rings_Odvd__class_Odvd(U_2716,U_2717,U_2718)
        | ~ sP226(U_2718,U_2717,U_2716) )
    & ! [U_2718,U_2717,U_2716] :
        ( c_Rings_Odvd__class_Odvd(U_2716,U_2717,U_2718)
        | ~ c_Rings_Odvd__class_Odvd(U_2716,U_2717,c_Groups_Ouminus__class_Ouminus(U_2716,U_2718))
        | ~ sP226(U_2718,U_2717,U_2716) )
    & ! [U_2718,U_2717,U_2716] :
        ( sP226(U_2718,U_2717,U_2716)
        | ~ class_Rings_Ocomm__ring__1(U_2716) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP226])],[f_839_2]) ).

cnf(f_839_4,plain,
    ( sP226(U_2718,U_2717,U_2716)
    | ~ class_Rings_Ocomm__ring__1(U_2716) ),
    inference(clausify,[status(thm)],[f_839_3]) ).

cnf(f_839_5,plain,
    ( c_Rings_Odvd__class_Odvd(U_2716,U_2717,U_2718)
    | ~ c_Rings_Odvd__class_Odvd(U_2716,U_2717,c_Groups_Ouminus__class_Ouminus(U_2716,U_2718))
    | ~ sP226(U_2718,U_2717,U_2716) ),
    inference(clausify,[status(thm)],[f_839_3]) ).

cnf(f_839_6,plain,
    ( c_Rings_Odvd__class_Odvd(U_2716,U_2717,c_Groups_Ouminus__class_Ouminus(U_2716,U_2718))
    | ~ c_Rings_Odvd__class_Odvd(U_2716,U_2717,U_2718)
    | ~ sP226(U_2718,U_2717,U_2716) ),
    inference(clausify,[status(thm)],[f_839_3]) ).

fof(f_840_1,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
    inference(fof_nnf,[status(thm)],[fact_i__mult__eq2]) ).

fof(f_840_2,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
    inference(definitional_conversion,[status(esa)],[f_840_1]) ).

cnf(f_840_3,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
    inference(clausify,[status(thm)],[f_840_2]) ).

fof(f_841_1,plain,
    ! [V_q_2,V_pa_2,V_ab_2,T_a] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_ab_2,V_pa_2),V_q_2)
          | ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,V_q_2)
            & V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) )
          | ( V_q_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
            & V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) ) )
        & ( ( ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,V_q_2)
              | V_ab_2 = c_Groups_Ozero__class_Ozero(T_a) )
            & ( V_q_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
              | V_ab_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
          | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_ab_2,V_pa_2),V_q_2) ) )
      | ~ class_Fields_Ofield(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_smult__dvd__iff]) ).

fof(f_841_2,plain,
    ! [U_2722,U_2721,U_2720,U_2719] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2719),c_Polynomial_Osmult(U_2719,U_2720,U_2721),U_2722)
          | ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2719),U_2721,U_2722)
            & U_2720 != c_Groups_Ozero__class_Ozero(U_2719) )
          | ( U_2722 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2719))
            & U_2720 = c_Groups_Ozero__class_Ozero(U_2719) ) )
        & ( ( ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2719),U_2721,U_2722)
              | U_2720 = c_Groups_Ozero__class_Ozero(U_2719) )
            & ( U_2722 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2719))
              | U_2720 != c_Groups_Ozero__class_Ozero(U_2719) ) )
          | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2719),c_Polynomial_Osmult(U_2719,U_2720,U_2721),U_2722) ) )
      | ~ class_Fields_Ofield(U_2719) ),
    inference(variable_rename,[status(thm)],[f_841_1]) ).

fof(f_841_3,plain,
    ( ! [U_2721,U_2720,U_2722,U_2719] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2719),U_2721,U_2722)
        | ~ sP229(U_2721,U_2720,U_2722,U_2719) )
    & ! [U_2721,U_2720,U_2722,U_2719] :
        ( U_2720 != c_Groups_Ozero__class_Ozero(U_2719)
        | ~ sP229(U_2721,U_2720,U_2722,U_2719) )
    & ! [U_2720,U_2722,U_2719] :
        ( U_2722 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2719))
        | ~ sP228(U_2720,U_2722,U_2719) )
    & ! [U_2720,U_2722,U_2719] :
        ( U_2720 = c_Groups_Ozero__class_Ozero(U_2719)
        | ~ sP228(U_2720,U_2722,U_2719) )
    & ! [U_2721,U_2720,U_2722,U_2719] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2719),U_2721,U_2722)
        | U_2720 = c_Groups_Ozero__class_Ozero(U_2719)
        | ~ sP227(U_2721,U_2720,U_2722,U_2719) )
    & ! [U_2721,U_2720,U_2722,U_2719] :
        ( U_2722 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2719))
        | U_2720 != c_Groups_Ozero__class_Ozero(U_2719)
        | ~ sP227(U_2721,U_2720,U_2722,U_2719) )
    & ! [U_2721,U_2720,U_2722,U_2719] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2719),c_Polynomial_Osmult(U_2719,U_2720,U_2721),U_2722)
        | sP229(U_2721,U_2720,U_2722,U_2719)
        | sP228(U_2720,U_2722,U_2719)
        | ~ sP230(U_2721,U_2720,U_2722,U_2719) )
    & ! [U_2721,U_2720,U_2722,U_2719] :
        ( sP227(U_2721,U_2720,U_2722,U_2719)
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2719),c_Polynomial_Osmult(U_2719,U_2720,U_2721),U_2722)
        | ~ sP230(U_2721,U_2720,U_2722,U_2719) )
    & ! [U_2721,U_2720,U_2722,U_2719] :
        ( sP230(U_2721,U_2720,U_2722,U_2719)
        | ~ class_Fields_Ofield(U_2719) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP227,sP228,sP229,sP230])],[f_841_2]) ).

cnf(f_841_4,plain,
    ( sP230(U_2721,U_2720,U_2722,U_2719)
    | ~ class_Fields_Ofield(U_2719) ),
    inference(clausify,[status(thm)],[f_841_3]) ).

cnf(f_841_5,plain,
    ( sP227(U_2721,U_2720,U_2722,U_2719)
    | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2719),c_Polynomial_Osmult(U_2719,U_2720,U_2721),U_2722)
    | ~ sP230(U_2721,U_2720,U_2722,U_2719) ),
    inference(clausify,[status(thm)],[f_841_3]) ).

cnf(f_841_6,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2719),c_Polynomial_Osmult(U_2719,U_2720,U_2721),U_2722)
    | sP229(U_2721,U_2720,U_2722,U_2719)
    | sP228(U_2720,U_2722,U_2719)
    | ~ sP230(U_2721,U_2720,U_2722,U_2719) ),
    inference(clausify,[status(thm)],[f_841_3]) ).

cnf(f_841_7,plain,
    ( U_2722 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2719))
    | U_2720 != c_Groups_Ozero__class_Ozero(U_2719)
    | ~ sP227(U_2721,U_2720,U_2722,U_2719) ),
    inference(clausify,[status(thm)],[f_841_3]) ).

cnf(f_841_8,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2719),U_2721,U_2722)
    | U_2720 = c_Groups_Ozero__class_Ozero(U_2719)
    | ~ sP227(U_2721,U_2720,U_2722,U_2719) ),
    inference(clausify,[status(thm)],[f_841_3]) ).

cnf(f_841_9,plain,
    ( U_2720 = c_Groups_Ozero__class_Ozero(U_2719)
    | ~ sP228(U_2720,U_2722,U_2719) ),
    inference(clausify,[status(thm)],[f_841_3]) ).

cnf(f_841_10,plain,
    ( U_2722 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2719))
    | ~ sP228(U_2720,U_2722,U_2719) ),
    inference(clausify,[status(thm)],[f_841_3]) ).

cnf(f_841_11,plain,
    ( U_2720 != c_Groups_Ozero__class_Ozero(U_2719)
    | ~ sP229(U_2721,U_2720,U_2722,U_2719) ),
    inference(clausify,[status(thm)],[f_841_3]) ).

cnf(f_841_12,plain,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2719),U_2721,U_2722)
    | ~ sP229(U_2721,U_2720,U_2722,U_2719) ),
    inference(clausify,[status(thm)],[f_841_3]) ).

fof(f_842_1,plain,
    ! [V_x,V_n,T_a] :
      ( c_Rings_Odvd__class_Odvd(T_a,V_x,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))
      | ( V_x != c_Groups_Oone__class_Oone(T_a)
        & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) )
      | ~ class_Rings_Ocomm__semiring__1(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__power]) ).

fof(f_842_2,plain,
    ! [U_2725,U_2724,U_2723] :
      ( c_Rings_Odvd__class_Odvd(U_2723,U_2725,hAPP(hAPP(c_Power_Opower__class_Opower(U_2723),U_2725),U_2724))
      | ( U_2725 != c_Groups_Oone__class_Oone(U_2723)
        & ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2724) )
      | ~ class_Rings_Ocomm__semiring__1(U_2723) ),
    inference(variable_rename,[status(thm)],[f_842_1]) ).

fof(f_842_3,plain,
    ( ! [U_2725,U_2723,U_2724] :
        ( U_2725 != c_Groups_Oone__class_Oone(U_2723)
        | ~ sP231(U_2725,U_2723,U_2724) )
    & ! [U_2725,U_2723,U_2724] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2724)
        | ~ sP231(U_2725,U_2723,U_2724) )
    & ! [U_2725,U_2723,U_2724] :
        ( c_Rings_Odvd__class_Odvd(U_2723,U_2725,hAPP(hAPP(c_Power_Opower__class_Opower(U_2723),U_2725),U_2724))
        | sP231(U_2725,U_2723,U_2724)
        | ~ class_Rings_Ocomm__semiring__1(U_2723) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP231])],[f_842_2]) ).

cnf(f_842_4,plain,
    ( c_Rings_Odvd__class_Odvd(U_2723,U_2725,hAPP(hAPP(c_Power_Opower__class_Opower(U_2723),U_2725),U_2724))
    | sP231(U_2725,U_2723,U_2724)
    | ~ class_Rings_Ocomm__semiring__1(U_2723) ),
    inference(clausify,[status(thm)],[f_842_3]) ).

cnf(f_842_5,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2724)
    | ~ sP231(U_2725,U_2723,U_2724) ),
    inference(clausify,[status(thm)],[f_842_3]) ).

cnf(f_842_6,plain,
    ( U_2725 != c_Groups_Oone__class_Oone(U_2723)
    | ~ sP231(U_2725,U_2723,U_2724) ),
    inference(clausify,[status(thm)],[f_842_3]) ).

fof(f_843_1,plain,
    ! [V_pa_2,V_ca_2,T_a] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_ca_2,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2)
          | hAPP(c_Polynomial_Opoly(T_a,V_pa_2),c_Groups_Ouminus__class_Ouminus(T_a,V_ca_2)) != c_Groups_Ozero__class_Ozero(T_a) )
        & ( hAPP(c_Polynomial_Opoly(T_a,V_pa_2),c_Groups_Ouminus__class_Ouminus(T_a,V_ca_2)) = c_Groups_Ozero__class_Ozero(T_a)
          | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_ca_2,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2) ) )
      | ~ class_Rings_Oidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__iff__poly__eq__0]) ).

fof(f_843_2,plain,
    ! [U_2728,U_2727,U_2726] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2726),c_Polynomial_OpCons(U_2726,U_2727,c_Polynomial_OpCons(U_2726,c_Groups_Oone__class_Oone(U_2726),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2726)))),U_2728)
          | hAPP(c_Polynomial_Opoly(U_2726,U_2728),c_Groups_Ouminus__class_Ouminus(U_2726,U_2727)) != c_Groups_Ozero__class_Ozero(U_2726) )
        & ( hAPP(c_Polynomial_Opoly(U_2726,U_2728),c_Groups_Ouminus__class_Ouminus(U_2726,U_2727)) = c_Groups_Ozero__class_Ozero(U_2726)
          | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2726),c_Polynomial_OpCons(U_2726,U_2727,c_Polynomial_OpCons(U_2726,c_Groups_Oone__class_Oone(U_2726),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2726)))),U_2728) ) )
      | ~ class_Rings_Oidom(U_2726) ),
    inference(variable_rename,[status(thm)],[f_843_1]) ).

fof(f_843_3,plain,
    ( ! [U_2728,U_2727,U_2726] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2726),c_Polynomial_OpCons(U_2726,U_2727,c_Polynomial_OpCons(U_2726,c_Groups_Oone__class_Oone(U_2726),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2726)))),U_2728)
        | hAPP(c_Polynomial_Opoly(U_2726,U_2728),c_Groups_Ouminus__class_Ouminus(U_2726,U_2727)) != c_Groups_Ozero__class_Ozero(U_2726)
        | ~ sP232(U_2728,U_2727,U_2726) )
    & ! [U_2728,U_2727,U_2726] :
        ( hAPP(c_Polynomial_Opoly(U_2726,U_2728),c_Groups_Ouminus__class_Ouminus(U_2726,U_2727)) = c_Groups_Ozero__class_Ozero(U_2726)
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2726),c_Polynomial_OpCons(U_2726,U_2727,c_Polynomial_OpCons(U_2726,c_Groups_Oone__class_Oone(U_2726),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2726)))),U_2728)
        | ~ sP232(U_2728,U_2727,U_2726) )
    & ! [U_2728,U_2727,U_2726] :
        ( sP232(U_2728,U_2727,U_2726)
        | ~ class_Rings_Oidom(U_2726) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP232])],[f_843_2]) ).

cnf(f_843_4,plain,
    ( sP232(U_2728,U_2727,U_2726)
    | ~ class_Rings_Oidom(U_2726) ),
    inference(clausify,[status(thm)],[f_843_3]) ).

cnf(f_843_5,plain,
    ( hAPP(c_Polynomial_Opoly(U_2726,U_2728),c_Groups_Ouminus__class_Ouminus(U_2726,U_2727)) = c_Groups_Ozero__class_Ozero(U_2726)
    | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2726),c_Polynomial_OpCons(U_2726,U_2727,c_Polynomial_OpCons(U_2726,c_Groups_Oone__class_Oone(U_2726),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2726)))),U_2728)
    | ~ sP232(U_2728,U_2727,U_2726) ),
    inference(clausify,[status(thm)],[f_843_3]) ).

cnf(f_843_6,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2726),c_Polynomial_OpCons(U_2726,U_2727,c_Polynomial_OpCons(U_2726,c_Groups_Oone__class_Oone(U_2726),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2726)))),U_2728)
    | hAPP(c_Polynomial_Opoly(U_2726,U_2728),c_Groups_Ouminus__class_Ouminus(U_2726,U_2727)) != c_Groups_Ozero__class_Ozero(U_2726)
    | ~ sP232(U_2728,U_2727,U_2726) ),
    inference(clausify,[status(thm)],[f_843_3]) ).

fof(f_844_1,plain,
    ! [V_ca_2,V_pa_2,T_a] :
      ( ( ( hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_ca_2) = c_Groups_Ozero__class_Ozero(T_a)
          | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ca_2),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2) )
        & ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ca_2),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2)
          | hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_ca_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
      | ~ class_Rings_Oidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_poly__eq__0__iff__dvd]) ).

fof(f_844_2,plain,
    ! [U_2731,U_2730,U_2729] :
      ( ( ( hAPP(c_Polynomial_Opoly(U_2729,U_2730),U_2731) = c_Groups_Ozero__class_Ozero(U_2729)
          | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2729),c_Polynomial_OpCons(U_2729,c_Groups_Ouminus__class_Ouminus(U_2729,U_2731),c_Polynomial_OpCons(U_2729,c_Groups_Oone__class_Oone(U_2729),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2729)))),U_2730) )
        & ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2729),c_Polynomial_OpCons(U_2729,c_Groups_Ouminus__class_Ouminus(U_2729,U_2731),c_Polynomial_OpCons(U_2729,c_Groups_Oone__class_Oone(U_2729),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2729)))),U_2730)
          | hAPP(c_Polynomial_Opoly(U_2729,U_2730),U_2731) != c_Groups_Ozero__class_Ozero(U_2729) ) )
      | ~ class_Rings_Oidom(U_2729) ),
    inference(variable_rename,[status(thm)],[f_844_1]) ).

fof(f_844_3,plain,
    ( ! [U_2731,U_2730,U_2729] :
        ( hAPP(c_Polynomial_Opoly(U_2729,U_2730),U_2731) = c_Groups_Ozero__class_Ozero(U_2729)
        | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2729),c_Polynomial_OpCons(U_2729,c_Groups_Ouminus__class_Ouminus(U_2729,U_2731),c_Polynomial_OpCons(U_2729,c_Groups_Oone__class_Oone(U_2729),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2729)))),U_2730)
        | ~ sP233(U_2731,U_2730,U_2729) )
    & ! [U_2731,U_2730,U_2729] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2729),c_Polynomial_OpCons(U_2729,c_Groups_Ouminus__class_Ouminus(U_2729,U_2731),c_Polynomial_OpCons(U_2729,c_Groups_Oone__class_Oone(U_2729),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2729)))),U_2730)
        | hAPP(c_Polynomial_Opoly(U_2729,U_2730),U_2731) != c_Groups_Ozero__class_Ozero(U_2729)
        | ~ sP233(U_2731,U_2730,U_2729) )
    & ! [U_2731,U_2730,U_2729] :
        ( sP233(U_2731,U_2730,U_2729)
        | ~ class_Rings_Oidom(U_2729) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP233])],[f_844_2]) ).

cnf(f_844_4,plain,
    ( sP233(U_2731,U_2730,U_2729)
    | ~ class_Rings_Oidom(U_2729) ),
    inference(clausify,[status(thm)],[f_844_3]) ).

cnf(f_844_5,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2729),c_Polynomial_OpCons(U_2729,c_Groups_Ouminus__class_Ouminus(U_2729,U_2731),c_Polynomial_OpCons(U_2729,c_Groups_Oone__class_Oone(U_2729),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2729)))),U_2730)
    | hAPP(c_Polynomial_Opoly(U_2729,U_2730),U_2731) != c_Groups_Ozero__class_Ozero(U_2729)
    | ~ sP233(U_2731,U_2730,U_2729) ),
    inference(clausify,[status(thm)],[f_844_3]) ).

cnf(f_844_6,plain,
    ( hAPP(c_Polynomial_Opoly(U_2729,U_2730),U_2731) = c_Groups_Ozero__class_Ozero(U_2729)
    | ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2729),c_Polynomial_OpCons(U_2729,c_Groups_Ouminus__class_Ouminus(U_2729,U_2731),c_Polynomial_OpCons(U_2729,c_Groups_Oone__class_Oone(U_2729),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2729)))),U_2730)
    | ~ sP233(U_2731,U_2730,U_2729) ),
    inference(clausify,[status(thm)],[f_844_3]) ).

fof(f_845_1,plain,
    ! [V_p,V_a,T_a] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p)),V_p)
      | ~ class_Rings_Oidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order__1]) ).

fof(f_845_2,plain,
    ! [U_2734,U_2733,U_2732] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2732),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_2732)),c_Polynomial_OpCons(U_2732,c_Groups_Ouminus__class_Ouminus(U_2732,U_2733),c_Polynomial_OpCons(U_2732,c_Groups_Oone__class_Oone(U_2732),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2732))))),c_Polynomial_Oorder(U_2732,U_2733,U_2734)),U_2734)
      | ~ class_Rings_Oidom(U_2732) ),
    inference(variable_rename,[status(thm)],[f_845_1]) ).

fof(f_845_3,plain,
    ! [U_2734,U_2733,U_2732] :
      ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2732),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_2732)),c_Polynomial_OpCons(U_2732,c_Groups_Ouminus__class_Ouminus(U_2732,U_2733),c_Polynomial_OpCons(U_2732,c_Groups_Oone__class_Oone(U_2732),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2732))))),c_Polynomial_Oorder(U_2732,U_2733,U_2734)),U_2734)
      | ~ class_Rings_Oidom(U_2732) ),
    inference(definitional_conversion,[status(esa)],[f_845_2]) ).

cnf(f_845_4,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2732),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_2732)),c_Polynomial_OpCons(U_2732,c_Groups_Ouminus__class_Ouminus(U_2732,U_2733),c_Polynomial_OpCons(U_2732,c_Groups_Oone__class_Oone(U_2732),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2732))))),c_Polynomial_Oorder(U_2732,U_2733,U_2734)),U_2734)
    | ~ class_Rings_Oidom(U_2732) ),
    inference(clausify,[status(thm)],[f_845_3]) ).

fof(f_846_1,plain,
    ! [V_a,V_p,T_a] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Nat_OSuc(c_Polynomial_Oorder(T_a,V_a,V_p))),V_p)
        & c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p)),V_p) )
      | V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
      | ~ class_Rings_Oidom(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_order]) ).

fof(f_846_2,plain,
    ! [U_2737,U_2736,U_2735] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2735),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_2735)),c_Polynomial_OpCons(U_2735,c_Groups_Ouminus__class_Ouminus(U_2735,U_2737),c_Polynomial_OpCons(U_2735,c_Groups_Oone__class_Oone(U_2735),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2735))))),c_Nat_OSuc(c_Polynomial_Oorder(U_2735,U_2737,U_2736))),U_2736)
        & c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2735),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_2735)),c_Polynomial_OpCons(U_2735,c_Groups_Ouminus__class_Ouminus(U_2735,U_2737),c_Polynomial_OpCons(U_2735,c_Groups_Oone__class_Oone(U_2735),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2735))))),c_Polynomial_Oorder(U_2735,U_2737,U_2736)),U_2736) )
      | U_2736 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2735))
      | ~ class_Rings_Oidom(U_2735) ),
    inference(variable_rename,[status(thm)],[f_846_1]) ).

fof(f_846_3,plain,
    ( ! [U_2735,U_2736,U_2737] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2735),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_2735)),c_Polynomial_OpCons(U_2735,c_Groups_Ouminus__class_Ouminus(U_2735,U_2737),c_Polynomial_OpCons(U_2735,c_Groups_Oone__class_Oone(U_2735),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2735))))),c_Nat_OSuc(c_Polynomial_Oorder(U_2735,U_2737,U_2736))),U_2736)
        | ~ sP234(U_2735,U_2736,U_2737) )
    & ! [U_2735,U_2736,U_2737] :
        ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2735),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_2735)),c_Polynomial_OpCons(U_2735,c_Groups_Ouminus__class_Ouminus(U_2735,U_2737),c_Polynomial_OpCons(U_2735,c_Groups_Oone__class_Oone(U_2735),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2735))))),c_Polynomial_Oorder(U_2735,U_2737,U_2736)),U_2736)
        | ~ sP234(U_2735,U_2736,U_2737) )
    & ! [U_2735,U_2736,U_2737] :
        ( sP234(U_2735,U_2736,U_2737)
        | U_2736 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2735))
        | ~ class_Rings_Oidom(U_2735) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP234])],[f_846_2]) ).

cnf(f_846_4,plain,
    ( sP234(U_2735,U_2736,U_2737)
    | U_2736 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2735))
    | ~ class_Rings_Oidom(U_2735) ),
    inference(clausify,[status(thm)],[f_846_3]) ).

cnf(f_846_5,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2735),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_2735)),c_Polynomial_OpCons(U_2735,c_Groups_Ouminus__class_Ouminus(U_2735,U_2737),c_Polynomial_OpCons(U_2735,c_Groups_Oone__class_Oone(U_2735),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2735))))),c_Polynomial_Oorder(U_2735,U_2737,U_2736)),U_2736)
    | ~ sP234(U_2735,U_2736,U_2737) ),
    inference(clausify,[status(thm)],[f_846_3]) ).

cnf(f_846_6,plain,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2735),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_2735)),c_Polynomial_OpCons(U_2735,c_Groups_Ouminus__class_Ouminus(U_2735,U_2737),c_Polynomial_OpCons(U_2735,c_Groups_Oone__class_Oone(U_2735),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2735))))),c_Nat_OSuc(c_Polynomial_Oorder(U_2735,U_2737,U_2736))),U_2736)
    | ~ sP234(U_2735,U_2736,U_2737) ),
    inference(clausify,[status(thm)],[f_846_3]) ).

fof(f_847_1,plain,
    ! [V_t_2,V_D_2,V_db_2,T_a] :
      ( ! [B_x,B_k] :
          ( ( c_Rings_Odvd__class_Odvd(T_a,V_db_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))
            | ~ c_Rings_Odvd__class_Odvd(T_a,V_db_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2)) )
          & ( c_Rings_Odvd__class_Odvd(T_a,V_db_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2))
            | ~ c_Rings_Odvd__class_Odvd(T_a,V_db_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2)) ) )
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_db_2,V_D_2)
      | ~ class_Rings_Odvd(T_a)
      | ~ class_Rings_Ocomm__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__period_I3_J]) ).

fof(f_847_2,plain,
    ! [U_2743,U_2742,U_2741,U_2740] :
      ( ! [U_2739,U_2738] :
          ( ( c_Rings_Odvd__class_Odvd(U_2740,U_2741,c_Groups_Oplus__class_Oplus(U_2740,U_2739,U_2743))
            | ~ c_Rings_Odvd__class_Odvd(U_2740,U_2741,c_Groups_Oplus__class_Oplus(U_2740,c_Groups_Ominus__class_Ominus(U_2740,U_2739,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2740),U_2738),U_2742)),U_2743)) )
          & ( c_Rings_Odvd__class_Odvd(U_2740,U_2741,c_Groups_Oplus__class_Oplus(U_2740,c_Groups_Ominus__class_Ominus(U_2740,U_2739,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2740),U_2738),U_2742)),U_2743))
            | ~ c_Rings_Odvd__class_Odvd(U_2740,U_2741,c_Groups_Oplus__class_Oplus(U_2740,U_2739,U_2743)) ) )
      | ~ c_Rings_Odvd__class_Odvd(U_2740,U_2741,U_2742)
      | ~ class_Rings_Odvd(U_2740)
      | ~ class_Rings_Ocomm__ring(U_2740) ),
    inference(variable_rename,[status(thm)],[f_847_1]) ).

fof(f_847_3,plain,
    ! [U_2743,U_2742,U_2741,U_2740] :
      ( ( ! [U_2747] :
            ( ! [U_2745] : ~ c_Rings_Odvd__class_Odvd(U_2740,U_2741,c_Groups_Oplus__class_Oplus(U_2740,c_Groups_Ominus__class_Ominus(U_2740,U_2747,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2740),U_2745),U_2742)),U_2743))
            | c_Rings_Odvd__class_Odvd(U_2740,U_2741,c_Groups_Oplus__class_Oplus(U_2740,U_2747,U_2743)) )
        & ! [U_2746] :
            ( ! [U_2744] : c_Rings_Odvd__class_Odvd(U_2740,U_2741,c_Groups_Oplus__class_Oplus(U_2740,c_Groups_Ominus__class_Ominus(U_2740,U_2746,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2740),U_2744),U_2742)),U_2743))
            | ~ c_Rings_Odvd__class_Odvd(U_2740,U_2741,c_Groups_Oplus__class_Oplus(U_2740,U_2746,U_2743)) ) )
      | ~ c_Rings_Odvd__class_Odvd(U_2740,U_2741,U_2742)
      | ~ class_Rings_Odvd(U_2740)
      | ~ class_Rings_Ocomm__ring(U_2740) ),
    inference(miniscope,[status(thm)],[f_847_2]) ).

fof(f_847_4,plain,
    ( ! [U_2742,U_2747,U_2741,U_2740,U_2743,U_2744,U_2745,U_2746] :
        ( ~ c_Rings_Odvd__class_Odvd(U_2740,U_2741,c_Groups_Oplus__class_Oplus(U_2740,c_Groups_Ominus__class_Ominus(U_2740,U_2747,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2740),U_2745),U_2742)),U_2743))
        | c_Rings_Odvd__class_Odvd(U_2740,U_2741,c_Groups_Oplus__class_Oplus(U_2740,U_2747,U_2743))
        | ~ sP235(U_2742,U_2747,U_2741,U_2740,U_2743,U_2744,U_2745,U_2746) )
    & ! [U_2742,U_2747,U_2741,U_2740,U_2743,U_2744,U_2745,U_2746] :
        ( c_Rings_Odvd__class_Odvd(U_2740,U_2741,c_Groups_Oplus__class_Oplus(U_2740,c_Groups_Ominus__class_Ominus(U_2740,U_2746,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2740),U_2744),U_2742)),U_2743))
        | ~ c_Rings_Odvd__class_Odvd(U_2740,U_2741,c_Groups_Oplus__class_Oplus(U_2740,U_2746,U_2743))
        | ~ sP235(U_2742,U_2747,U_2741,U_2740,U_2743,U_2744,U_2745,U_2746) )
    & ! [U_2742,U_2747,U_2741,U_2740,U_2743,U_2744,U_2745,U_2746] :
        ( sP235(U_2742,U_2747,U_2741,U_2740,U_2743,U_2744,U_2745,U_2746)
        | ~ c_Rings_Odvd__class_Odvd(U_2740,U_2741,U_2742)
        | ~ class_Rings_Odvd(U_2740)
        | ~ class_Rings_Ocomm__ring(U_2740) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP235])],[f_847_3]) ).

cnf(f_847_5,plain,
    ( sP235(U_2742,U_2747,U_2741,U_2740,U_2743,U_2744,U_2745,U_2746)
    | ~ c_Rings_Odvd__class_Odvd(U_2740,U_2741,U_2742)
    | ~ class_Rings_Odvd(U_2740)
    | ~ class_Rings_Ocomm__ring(U_2740) ),
    inference(clausify,[status(thm)],[f_847_4]) ).

cnf(f_847_6,plain,
    ( c_Rings_Odvd__class_Odvd(U_2740,U_2741,c_Groups_Oplus__class_Oplus(U_2740,c_Groups_Ominus__class_Ominus(U_2740,U_2746,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2740),U_2744),U_2742)),U_2743))
    | ~ c_Rings_Odvd__class_Odvd(U_2740,U_2741,c_Groups_Oplus__class_Oplus(U_2740,U_2746,U_2743))
    | ~ sP235(U_2742,U_2747,U_2741,U_2740,U_2743,U_2744,U_2745,U_2746) ),
    inference(clausify,[status(thm)],[f_847_4]) ).

cnf(f_847_7,plain,
    ( ~ c_Rings_Odvd__class_Odvd(U_2740,U_2741,c_Groups_Oplus__class_Oplus(U_2740,c_Groups_Ominus__class_Ominus(U_2740,U_2747,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2740),U_2745),U_2742)),U_2743))
    | c_Rings_Odvd__class_Odvd(U_2740,U_2741,c_Groups_Oplus__class_Oplus(U_2740,U_2747,U_2743))
    | ~ sP235(U_2742,U_2747,U_2741,U_2740,U_2743,U_2744,U_2745,U_2746) ),
    inference(clausify,[status(thm)],[f_847_4]) ).

fof(f_848_1,plain,
    ! [V_t_2,V_D_2,V_db_2,T_a] :
      ( ! [B_x,B_k] :
          ( ( c_Rings_Odvd__class_Odvd(T_a,V_db_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))
            | ~ c_Rings_Odvd__class_Odvd(T_a,V_db_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2)) )
          & ( c_Rings_Odvd__class_Odvd(T_a,V_db_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2))
            | ~ c_Rings_Odvd__class_Odvd(T_a,V_db_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2)) ) )
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_db_2,V_D_2)
      | ~ class_Rings_Odvd(T_a)
      | ~ class_Rings_Ocomm__ring(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_inf__period_I4_J]) ).

fof(f_848_2,plain,
    ! [U_2753,U_2752,U_2751,U_2750] :
      ( ! [U_2749,U_2748] :
          ( ( c_Rings_Odvd__class_Odvd(U_2750,U_2751,c_Groups_Oplus__class_Oplus(U_2750,U_2749,U_2753))
            | ~ c_Rings_Odvd__class_Odvd(U_2750,U_2751,c_Groups_Oplus__class_Oplus(U_2750,c_Groups_Ominus__class_Ominus(U_2750,U_2749,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2750),U_2748),U_2752)),U_2753)) )
          & ( c_Rings_Odvd__class_Odvd(U_2750,U_2751,c_Groups_Oplus__class_Oplus(U_2750,c_Groups_Ominus__class_Ominus(U_2750,U_2749,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2750),U_2748),U_2752)),U_2753))
            | ~ c_Rings_Odvd__class_Odvd(U_2750,U_2751,c_Groups_Oplus__class_Oplus(U_2750,U_2749,U_2753)) ) )
      | ~ c_Rings_Odvd__class_Odvd(U_2750,U_2751,U_2752)
      | ~ class_Rings_Odvd(U_2750)
      | ~ class_Rings_Ocomm__ring(U_2750) ),
    inference(variable_rename,[status(thm)],[f_848_1]) ).

fof(f_848_3,plain,
    ! [U_2753,U_2752,U_2751,U_2750] :
      ( ( ! [U_2757] :
            ( ! [U_2755] : ~ c_Rings_Odvd__class_Odvd(U_2750,U_2751,c_Groups_Oplus__class_Oplus(U_2750,c_Groups_Ominus__class_Ominus(U_2750,U_2757,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2750),U_2755),U_2752)),U_2753))
            | c_Rings_Odvd__class_Odvd(U_2750,U_2751,c_Groups_Oplus__class_Oplus(U_2750,U_2757,U_2753)) )
        & ! [U_2756] :
            ( ! [U_2754] : c_Rings_Odvd__class_Odvd(U_2750,U_2751,c_Groups_Oplus__class_Oplus(U_2750,c_Groups_Ominus__class_Ominus(U_2750,U_2756,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2750),U_2754),U_2752)),U_2753))
            | ~ c_Rings_Odvd__class_Odvd(U_2750,U_2751,c_Groups_Oplus__class_Oplus(U_2750,U_2756,U_2753)) ) )
      | ~ c_Rings_Odvd__class_Odvd(U_2750,U_2751,U_2752)
      | ~ class_Rings_Odvd(U_2750)
      | ~ class_Rings_Ocomm__ring(U_2750) ),
    inference(miniscope,[status(thm)],[f_848_2]) ).

fof(f_848_4,plain,
    ( ! [U_2751,U_2752,U_2757,U_2754,U_2750,U_2753,U_2755,U_2756] :
        ( ~ c_Rings_Odvd__class_Odvd(U_2750,U_2751,c_Groups_Oplus__class_Oplus(U_2750,c_Groups_Ominus__class_Ominus(U_2750,U_2757,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2750),U_2755),U_2752)),U_2753))
        | c_Rings_Odvd__class_Odvd(U_2750,U_2751,c_Groups_Oplus__class_Oplus(U_2750,U_2757,U_2753))
        | ~ sP236(U_2751,U_2752,U_2757,U_2754,U_2750,U_2753,U_2755,U_2756) )
    & ! [U_2751,U_2752,U_2757,U_2754,U_2750,U_2753,U_2755,U_2756] :
        ( c_Rings_Odvd__class_Odvd(U_2750,U_2751,c_Groups_Oplus__class_Oplus(U_2750,c_Groups_Ominus__class_Ominus(U_2750,U_2756,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2750),U_2754),U_2752)),U_2753))
        | ~ c_Rings_Odvd__class_Odvd(U_2750,U_2751,c_Groups_Oplus__class_Oplus(U_2750,U_2756,U_2753))
        | ~ sP236(U_2751,U_2752,U_2757,U_2754,U_2750,U_2753,U_2755,U_2756) )
    & ! [U_2751,U_2752,U_2757,U_2754,U_2750,U_2753,U_2755,U_2756] :
        ( sP236(U_2751,U_2752,U_2757,U_2754,U_2750,U_2753,U_2755,U_2756)
        | ~ c_Rings_Odvd__class_Odvd(U_2750,U_2751,U_2752)
        | ~ class_Rings_Odvd(U_2750)
        | ~ class_Rings_Ocomm__ring(U_2750) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP236])],[f_848_3]) ).

cnf(f_848_5,plain,
    ( sP236(U_2751,U_2752,U_2757,U_2754,U_2750,U_2753,U_2755,U_2756)
    | ~ c_Rings_Odvd__class_Odvd(U_2750,U_2751,U_2752)
    | ~ class_Rings_Odvd(U_2750)
    | ~ class_Rings_Ocomm__ring(U_2750) ),
    inference(clausify,[status(thm)],[f_848_4]) ).

cnf(f_848_6,plain,
    ( c_Rings_Odvd__class_Odvd(U_2750,U_2751,c_Groups_Oplus__class_Oplus(U_2750,c_Groups_Ominus__class_Ominus(U_2750,U_2756,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2750),U_2754),U_2752)),U_2753))
    | ~ c_Rings_Odvd__class_Odvd(U_2750,U_2751,c_Groups_Oplus__class_Oplus(U_2750,U_2756,U_2753))
    | ~ sP236(U_2751,U_2752,U_2757,U_2754,U_2750,U_2753,U_2755,U_2756) ),
    inference(clausify,[status(thm)],[f_848_4]) ).

cnf(f_848_7,plain,
    ( ~ c_Rings_Odvd__class_Odvd(U_2750,U_2751,c_Groups_Oplus__class_Oplus(U_2750,c_Groups_Ominus__class_Ominus(U_2750,U_2757,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2750),U_2755),U_2752)),U_2753))
    | c_Rings_Odvd__class_Odvd(U_2750,U_2751,c_Groups_Oplus__class_Oplus(U_2750,U_2757,U_2753))
    | ~ sP236(U_2751,U_2752,U_2757,U_2754,U_2750,U_2753,U_2755,U_2756) ),
    inference(clausify,[status(thm)],[f_848_4]) ).

fof(f_849_1,plain,
    ! [V_k] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k),
    inference(fof_nnf,[status(thm)],[fact_dvd__1__left]) ).

fof(f_849_2,plain,
    ! [U_2758] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2758),
    inference(variable_rename,[status(thm)],[f_849_1]) ).

fof(f_849_3,plain,
    ! [U_2758] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2758),
    inference(definitional_conversion,[status(esa)],[f_849_2]) ).

cnf(f_849_4,plain,
    c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2758),
    inference(clausify,[status(thm)],[f_849_3]) ).

fof(f_850_1,plain,
    ! [V_n,V_m] :
      ( V_m = V_n
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m,V_n)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m) ),
    inference(fof_nnf,[status(thm)],[fact_zdvd__antisym__nonneg]) ).

fof(f_850_2,plain,
    ! [U_2760,U_2759] :
      ( U_2759 = U_2760
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2760,U_2759)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2759,U_2760)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2760)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2759) ),
    inference(variable_rename,[status(thm)],[f_850_1]) ).

fof(f_850_3,plain,
    ! [U_2760,U_2759] :
      ( U_2759 = U_2760
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2760,U_2759)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2759,U_2760)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2760)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2759) ),
    inference(definitional_conversion,[status(esa)],[f_850_2]) ).

cnf(f_850_4,plain,
    ( U_2759 = U_2760
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2760,U_2759)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2759,U_2760)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2760)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2759) ),
    inference(clausify,[status(thm)],[f_850_3]) ).

fof(f_851_1,plain,
    ! [V_n,V_m,V_k] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__diffD1]) ).

fof(f_851_2,plain,
    ! [U_2763,U_2762,U_2761] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2761,U_2763)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2763,U_2762)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2761,U_2762)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2761,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2762,U_2763)) ),
    inference(variable_rename,[status(thm)],[f_851_1]) ).

fof(f_851_3,plain,
    ! [U_2762,U_2761,U_2763] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2761,U_2763)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2763,U_2762)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2761,U_2762)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2761,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2762,U_2763)) ),
    inference(definitional_conversion,[status(esa)],[f_851_2]) ).

cnf(f_851_4,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2761,U_2763)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2763,U_2762)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2761,U_2762)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2761,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2762,U_2763)) ),
    inference(clausify,[status(thm)],[f_851_3]) ).

fof(f_852_1,plain,
    ! [V_n,V_m,V_k] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__diffD]) ).

fof(f_852_2,plain,
    ! [U_2766,U_2765,U_2764] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2764,U_2765)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2766,U_2765)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2764,U_2766)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2764,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2765,U_2766)) ),
    inference(variable_rename,[status(thm)],[f_852_1]) ).

fof(f_852_3,plain,
    ! [U_2765,U_2764,U_2766] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2764,U_2765)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2766,U_2765)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2764,U_2766)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2764,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2765,U_2766)) ),
    inference(definitional_conversion,[status(esa)],[f_852_2]) ).

cnf(f_852_4,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2764,U_2765)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2766,U_2765)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2764,U_2766)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2764,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2765,U_2766)) ),
    inference(clausify,[status(thm)],[f_852_3]) ).

fof(f_853_1,plain,
    ! [V_n_2,V_k_2] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,V_n_2) )
      & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,V_n_2)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__reduce]) ).

fof(f_853_2,plain,
    ! [U_2768,U_2767] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2767,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2768,U_2767))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2767,U_2768) )
      & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2767,U_2768)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2767,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2768,U_2767)) ) ),
    inference(variable_rename,[status(thm)],[f_853_1]) ).

fof(f_853_3,plain,
    ( ! [U_2772,U_2770] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2770,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2772,U_2770))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2770,U_2772) )
    & ! [U_2771,U_2769] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2769,U_2771)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2769,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2771,U_2769)) ) ),
    inference(miniscope,[status(thm)],[f_853_2]) ).

fof(f_853_4,plain,
    ( ! [U_2770,U_2772] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2770,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2772,U_2770))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2770,U_2772) )
    & ! [U_2771,U_2769] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2769,U_2771)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2769,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2771,U_2769)) ) ),
    inference(definitional_conversion,[status(esa)],[f_853_3]) ).

cnf(f_853_5,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2769,U_2771)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2769,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2771,U_2769)) ),
    inference(clausify,[status(thm)],[f_853_4]) ).

cnf(f_853_6,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2770,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2772,U_2770))
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2770,U_2772) ),
    inference(clausify,[status(thm)],[f_853_4]) ).

fof(f_854_1,plain,
    ! [V_m_2] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | V_m_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__dvd__1__iff__1]) ).

fof(f_854_2,plain,
    ! [U_2773] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2773,c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | U_2773 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( U_2773 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2773,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_854_1]) ).

fof(f_854_3,plain,
    ( ! [U_2775] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2775,c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | U_2775 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_2774] :
        ( U_2774 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2774,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_854_2]) ).

fof(f_854_4,plain,
    ( ! [U_2775] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2775,c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | U_2775 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_2774] :
        ( U_2774 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2774,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa)],[f_854_3]) ).

cnf(f_854_5,plain,
    ( U_2774 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2774,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_854_4]) ).

cnf(f_854_6,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2775,c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | U_2775 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_854_4]) ).

fof(f_855_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
        | ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,V_n_2)
          & V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,V_n_2)
        | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__dvd__cancel__disj]) ).

fof(f_855_2,plain,
    ! [U_2778,U_2777,U_2776] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2776),U_2777),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2776),U_2778))
        | ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2777,U_2778)
          & U_2776 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2777,U_2778)
        | U_2776 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2776),U_2777),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2776),U_2778)) ) ),
    inference(variable_rename,[status(thm)],[f_855_1]) ).

fof(f_855_3,plain,
    ( ! [U_2784,U_2782,U_2780] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2780),U_2782),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2780),U_2784))
        | ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2782,U_2784)
          & U_2780 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_2783,U_2781,U_2779] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2781,U_2783)
        | U_2779 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2779),U_2781),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2779),U_2783)) ) ),
    inference(miniscope,[status(thm)],[f_855_2]) ).

fof(f_855_4,plain,
    ( ! [U_2784,U_2780,U_2782] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2782,U_2784)
        | ~ sP237(U_2784,U_2780,U_2782) )
    & ! [U_2784,U_2780,U_2782] :
        ( U_2780 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP237(U_2784,U_2780,U_2782) )
    & ! [U_2784,U_2780,U_2782] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2780),U_2782),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2780),U_2784))
        | sP237(U_2784,U_2780,U_2782) )
    & ! [U_2779,U_2781,U_2783] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2781,U_2783)
        | U_2779 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2779),U_2781),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2779),U_2783)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP237])],[f_855_3]) ).

cnf(f_855_5,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2781,U_2783)
    | U_2779 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2779),U_2781),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2779),U_2783)) ),
    inference(clausify,[status(thm)],[f_855_4]) ).

cnf(f_855_6,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2780),U_2782),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2780),U_2784))
    | sP237(U_2784,U_2780,U_2782) ),
    inference(clausify,[status(thm)],[f_855_4]) ).

cnf(f_855_7,plain,
    ( U_2780 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP237(U_2784,U_2780,U_2782) ),
    inference(clausify,[status(thm)],[f_855_4]) ).

cnf(f_855_8,plain,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2782,U_2784)
    | ~ sP237(U_2784,U_2780,U_2782) ),
    inference(clausify,[status(thm)],[f_855_4]) ).

fof(f_856_1,plain,
    ! [V_n,V_m] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_n,V_m)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) ),
    inference(fof_nnf,[status(thm)],[fact_nat__dvd__not__less]) ).

fof(f_856_2,plain,
    ! [U_2786,U_2785] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2786,U_2785)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2785,U_2786)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2785) ),
    inference(variable_rename,[status(thm)],[f_856_1]) ).

fof(f_856_3,plain,
    ! [U_2786,U_2785] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2786,U_2785)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2785,U_2786)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2785) ),
    inference(definitional_conversion,[status(esa)],[f_856_2]) ).

cnf(f_856_4,plain,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2786,U_2785)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2785,U_2786)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2785) ),
    inference(clausify,[status(thm)],[f_856_3]) ).

fof(f_857_1,plain,
    ! [V_m_2] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | V_m_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( V_m_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__1__iff__1]) ).

fof(f_857_2,plain,
    ! [U_2787] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2787,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_2787 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( U_2787 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2787,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(variable_rename,[status(thm)],[f_857_1]) ).

fof(f_857_3,plain,
    ( ! [U_2789] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2789,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_2789 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    & ! [U_2788] :
        ( U_2788 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2788,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(miniscope,[status(thm)],[f_857_2]) ).

fof(f_857_4,plain,
    ( ! [U_2789] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2789,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_2789 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    & ! [U_2788] :
        ( U_2788 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2788,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(definitional_conversion,[status(esa)],[f_857_3]) ).

cnf(f_857_5,plain,
    ( U_2788 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2788,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_857_4]) ).

cnf(f_857_6,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2789,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_2789 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_857_4]) ).

fof(f_858_1,plain,
    ! [V_n,V_m,V_k] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_m)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_n)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_zdvd__zdiffD]) ).

fof(f_858_2,plain,
    ! [U_2792,U_2791,U_2790] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2790,U_2791)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2790,U_2792)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2790,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2791,U_2792)) ),
    inference(variable_rename,[status(thm)],[f_858_1]) ).

fof(f_858_3,plain,
    ! [U_2790,U_2791,U_2792] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2790,U_2791)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2790,U_2792)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2790,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2791,U_2792)) ),
    inference(definitional_conversion,[status(esa)],[f_858_2]) ).

cnf(f_858_4,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2790,U_2791)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2790,U_2792)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2790,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2791,U_2792)) ),
    inference(clausify,[status(thm)],[f_858_3]) ).

fof(f_859_1,plain,
    ! [V_n,V_m,V_k] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m,V_n)
      | V_k = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_zdvd__mult__cancel]) ).

fof(f_859_2,plain,
    ! [U_2795,U_2794,U_2793] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2794,U_2795)
      | U_2793 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2793),U_2794),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2793),U_2795)) ),
    inference(variable_rename,[status(thm)],[f_859_1]) ).

fof(f_859_3,plain,
    ! [U_2793,U_2794,U_2795] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2794,U_2795)
      | U_2793 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2793),U_2794),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2793),U_2795)) ),
    inference(definitional_conversion,[status(esa)],[f_859_2]) ).

cnf(f_859_4,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2794,U_2795)
    | U_2793 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2793),U_2794),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2793),U_2795)) ),
    inference(clausify,[status(thm)],[f_859_3]) ).

fof(f_860_1,plain,
    ! [V_ca_2,V_t_2,V_x_2,V_db_2,V_ab_2] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ab_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,V_t_2))
          | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ab_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ca_2),V_db_2)),V_t_2)) )
        & ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ab_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ca_2),V_db_2)),V_t_2))
          | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ab_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,V_t_2)) ) )
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ab_2,V_db_2) ),
    inference(fof_nnf,[status(thm)],[fact_zdvd__period]) ).

fof(f_860_2,plain,
    ! [U_2800,U_2799,U_2798,U_2797,U_2796] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2796,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2798,U_2799))
          | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2796,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2798,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2800),U_2797)),U_2799)) )
        & ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2796,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2798,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2800),U_2797)),U_2799))
          | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2796,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2798,U_2799)) ) )
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2796,U_2797) ),
    inference(variable_rename,[status(thm)],[f_860_1]) ).

fof(f_860_3,plain,
    ( ! [U_2798,U_2799,U_2796,U_2797,U_2800] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2796,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2798,U_2799))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2796,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2798,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2800),U_2797)),U_2799))
        | ~ sP238(U_2798,U_2799,U_2796,U_2797,U_2800) )
    & ! [U_2798,U_2799,U_2796,U_2797,U_2800] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2796,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2798,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2800),U_2797)),U_2799))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2796,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2798,U_2799))
        | ~ sP238(U_2798,U_2799,U_2796,U_2797,U_2800) )
    & ! [U_2798,U_2799,U_2796,U_2797,U_2800] :
        ( sP238(U_2798,U_2799,U_2796,U_2797,U_2800)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2796,U_2797) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP238])],[f_860_2]) ).

cnf(f_860_4,plain,
    ( sP238(U_2798,U_2799,U_2796,U_2797,U_2800)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2796,U_2797) ),
    inference(clausify,[status(thm)],[f_860_3]) ).

cnf(f_860_5,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2796,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2798,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2800),U_2797)),U_2799))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2796,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2798,U_2799))
    | ~ sP238(U_2798,U_2799,U_2796,U_2797,U_2800) ),
    inference(clausify,[status(thm)],[f_860_3]) ).

cnf(f_860_6,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2796,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2798,U_2799))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2796,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2798,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2800),U_2797)),U_2799))
    | ~ sP238(U_2798,U_2799,U_2796,U_2797,U_2800) ),
    inference(clausify,[status(thm)],[f_860_3]) ).

fof(f_861_1,plain,
    ! [V_t_2,V_m_2,V_k_2] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m_2,V_t_2)
          | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2)) )
        & ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2))
          | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m_2,V_t_2) ) )
      | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(fof_nnf,[status(thm)],[fact_zdvd__mono]) ).

fof(f_861_2,plain,
    ! [U_2803,U_2802,U_2801] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2802,U_2803)
          | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2801),U_2802),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2801),U_2803)) )
        & ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2801),U_2802),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2801),U_2803))
          | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2802,U_2803) ) )
      | U_2801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_861_1]) ).

fof(f_861_3,plain,
    ( ! [U_2802,U_2801,U_2803] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2802,U_2803)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2801),U_2802),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2801),U_2803))
        | ~ sP239(U_2802,U_2801,U_2803) )
    & ! [U_2802,U_2801,U_2803] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2801),U_2802),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2801),U_2803))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2802,U_2803)
        | ~ sP239(U_2802,U_2801,U_2803) )
    & ! [U_2802,U_2801,U_2803] :
        ( sP239(U_2802,U_2801,U_2803)
        | U_2801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP239])],[f_861_2]) ).

cnf(f_861_4,plain,
    ( sP239(U_2802,U_2801,U_2803)
    | U_2801 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_861_3]) ).

cnf(f_861_5,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2801),U_2802),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2801),U_2803))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2802,U_2803)
    | ~ sP239(U_2802,U_2801,U_2803) ),
    inference(clausify,[status(thm)],[f_861_3]) ).

cnf(f_861_6,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2802,U_2803)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2801),U_2802),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2801),U_2803))
    | ~ sP239(U_2802,U_2801,U_2803) ),
    inference(clausify,[status(thm)],[f_861_3]) ).

fof(f_862_1,plain,
    ! [V_m_2,V_n_2,V_k_2] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_n_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2)))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,V_n_2) )
      & ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,V_n_2)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_n_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_zdvd__reduce]) ).

fof(f_862_2,plain,
    ! [U_2806,U_2805,U_2804] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2804,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2805,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2804),U_2806)))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2804,U_2805) )
      & ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2804,U_2805)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2804,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2805,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2804),U_2806))) ) ),
    inference(variable_rename,[status(thm)],[f_862_1]) ).

fof(f_862_3,plain,
    ( ! [U_2812,U_2810,U_2808] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2808,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2808),U_2812)))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2808,U_2810) )
    & ! [U_2811,U_2809,U_2807] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2807,U_2809)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2807,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2809,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2807),U_2811))) ) ),
    inference(miniscope,[status(thm)],[f_862_2]) ).

fof(f_862_4,plain,
    ( ! [U_2812,U_2810,U_2808] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2808,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2808),U_2812)))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2808,U_2810) )
    & ! [U_2811,U_2807,U_2809] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2807,U_2809)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2807,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2809,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2807),U_2811))) ) ),
    inference(definitional_conversion,[status(esa)],[f_862_3]) ).

cnf(f_862_5,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2807,U_2809)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2807,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2809,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2807),U_2811))) ),
    inference(clausify,[status(thm)],[f_862_4]) ).

cnf(f_862_6,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2808,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2808),U_2812)))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2808,U_2810) ),
    inference(clausify,[status(thm)],[f_862_4]) ).

fof(f_863_1,plain,
    ! [V_n,V_m,V_k] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__diff__nat]) ).

fof(f_863_2,plain,
    ! [U_2815,U_2814,U_2813] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2813,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2814,U_2815))
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2813,U_2815)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2813,U_2814) ),
    inference(variable_rename,[status(thm)],[f_863_1]) ).

fof(f_863_3,plain,
    ! [U_2814,U_2815,U_2813] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2813,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2814,U_2815))
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2813,U_2815)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2813,U_2814) ),
    inference(definitional_conversion,[status(esa)],[f_863_2]) ).

cnf(f_863_4,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2813,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2814,U_2815))
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2813,U_2815)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2813,U_2814) ),
    inference(clausify,[status(thm)],[f_863_3]) ).

fof(f_864_1,plain,
    ! [V_t_2,V_db_2] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_db_2,V_t_2)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_db_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_t_2)) )
      & ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_db_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_t_2))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_db_2,V_t_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_uminus__dvd__conv_I2_J]) ).

fof(f_864_2,plain,
    ! [U_2817,U_2816] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2816,U_2817)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2816,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2817)) )
      & ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2816,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2817))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2816,U_2817) ) ),
    inference(variable_rename,[status(thm)],[f_864_1]) ).

fof(f_864_3,plain,
    ( ! [U_2821,U_2819] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2819,U_2821)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2819,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2821)) )
    & ! [U_2820,U_2818] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2818,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2820))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2818,U_2820) ) ),
    inference(miniscope,[status(thm)],[f_864_2]) ).

fof(f_864_4,plain,
    ( ! [U_2821,U_2819] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2819,U_2821)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2819,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2821)) )
    & ! [U_2818,U_2820] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2818,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2820))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2818,U_2820) ) ),
    inference(definitional_conversion,[status(esa)],[f_864_3]) ).

cnf(f_864_5,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2818,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2820))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2818,U_2820) ),
    inference(clausify,[status(thm)],[f_864_4]) ).

cnf(f_864_6,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2819,U_2821)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2819,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2821)) ),
    inference(clausify,[status(thm)],[f_864_4]) ).

fof(f_865_1,plain,
    ! [V_t_2,V_db_2] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_db_2,V_t_2)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_db_2),V_t_2) )
      & ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_db_2),V_t_2)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_db_2,V_t_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_uminus__dvd__conv_I1_J]) ).

fof(f_865_2,plain,
    ! [U_2823,U_2822] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2822,U_2823)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2822),U_2823) )
      & ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2822),U_2823)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2822,U_2823) ) ),
    inference(variable_rename,[status(thm)],[f_865_1]) ).

fof(f_865_3,plain,
    ( ! [U_2827,U_2825] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2825,U_2827)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2825),U_2827) )
    & ! [U_2826,U_2824] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2824),U_2826)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2824,U_2826) ) ),
    inference(miniscope,[status(thm)],[f_865_2]) ).

fof(f_865_4,plain,
    ( ! [U_2827,U_2825] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2825,U_2827)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2825),U_2827) )
    & ! [U_2826,U_2824] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2824),U_2826)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2824,U_2826) ) ),
    inference(definitional_conversion,[status(esa)],[f_865_3]) ).

cnf(f_865_5,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2824),U_2826)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2824,U_2826) ),
    inference(clausify,[status(thm)],[f_865_4]) ).

cnf(f_865_6,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2825,U_2827)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2825),U_2827) ),
    inference(clausify,[status(thm)],[f_865_4]) ).

fof(f_866_1,plain,
    ! [V_n,V_m] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_m,V_n)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m) ),
    inference(fof_nnf,[status(thm)],[fact_zdvd__not__zless]) ).

fof(f_866_2,plain,
    ! [U_2829,U_2828] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2829,U_2828)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2828,U_2829)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2828) ),
    inference(variable_rename,[status(thm)],[f_866_1]) ).

fof(f_866_3,plain,
    ! [U_2828,U_2829] :
      ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2829,U_2828)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2828,U_2829)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2828) ),
    inference(definitional_conversion,[status(esa)],[f_866_2]) ).

cnf(f_866_4,plain,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2829,U_2828)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2828,U_2829)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2828) ),
    inference(clausify,[status(thm)],[f_866_3]) ).

fof(f_867_1,plain,
    ! [V_n,V_z] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_n)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_z,V_n) ),
    inference(fof_nnf,[status(thm)],[fact_zdvd__imp__le]) ).

fof(f_867_2,plain,
    ! [U_2831,U_2830] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2830,U_2831)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2831)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2830,U_2831) ),
    inference(variable_rename,[status(thm)],[f_867_1]) ).

fof(f_867_3,plain,
    ! [U_2831,U_2830] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2830,U_2831)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2831)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2830,U_2831) ),
    inference(definitional_conversion,[status(esa)],[f_867_2]) ).

cnf(f_867_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2830,U_2831)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2831)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2830,U_2831) ),
    inference(clausify,[status(thm)],[f_867_3]) ).

fof(f_868_1,plain,
    ! [V_n,V_k] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__imp__le]) ).

fof(f_868_2,plain,
    ! [U_2833,U_2832] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2832,U_2833)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2833)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2832,U_2833) ),
    inference(variable_rename,[status(thm)],[f_868_1]) ).

fof(f_868_3,plain,
    ! [U_2832,U_2833] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2832,U_2833)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2833)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2832,U_2833) ),
    inference(definitional_conversion,[status(esa)],[f_868_2]) ).

cnf(f_868_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2832,U_2833)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2833)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2832,U_2833) ),
    inference(clausify,[status(thm)],[f_868_3]) ).

fof(f_869_1,plain,
    ! [V_n_2,V_m_2,V_k_2] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,V_n_2) )
        & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,V_n_2)
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) ),
    inference(fof_nnf,[status(thm)],[fact_nat__mult__dvd__cancel1]) ).

fof(f_869_2,plain,
    ! [U_2836,U_2835,U_2834] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2834),U_2835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2834),U_2836))
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2835,U_2836) )
        & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2835,U_2836)
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2834),U_2835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2834),U_2836)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2834) ),
    inference(variable_rename,[status(thm)],[f_869_1]) ).

fof(f_869_3,plain,
    ( ! [U_2835,U_2836,U_2834] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2834),U_2835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2834),U_2836))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2835,U_2836)
        | ~ sP240(U_2835,U_2836,U_2834) )
    & ! [U_2835,U_2836,U_2834] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2835,U_2836)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2834),U_2835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2834),U_2836))
        | ~ sP240(U_2835,U_2836,U_2834) )
    & ! [U_2835,U_2836,U_2834] :
        ( sP240(U_2835,U_2836,U_2834)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2834) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP240])],[f_869_2]) ).

cnf(f_869_4,plain,
    ( sP240(U_2835,U_2836,U_2834)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2834) ),
    inference(clausify,[status(thm)],[f_869_3]) ).

cnf(f_869_5,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2835,U_2836)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2834),U_2835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2834),U_2836))
    | ~ sP240(U_2835,U_2836,U_2834) ),
    inference(clausify,[status(thm)],[f_869_3]) ).

cnf(f_869_6,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2834),U_2835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2834),U_2836))
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2835,U_2836)
    | ~ sP240(U_2835,U_2836,U_2834) ),
    inference(clausify,[status(thm)],[f_869_3]) ).

fof(f_870_1,plain,
    ! [V_n,V_m,V_k] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel]) ).

fof(f_870_2,plain,
    ! [U_2839,U_2838,U_2837] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2838,U_2839)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2837)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2837),U_2838),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2837),U_2839)) ),
    inference(variable_rename,[status(thm)],[f_870_1]) ).

fof(f_870_3,plain,
    ! [U_2839,U_2838,U_2837] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2838,U_2839)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2837)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2837),U_2838),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2837),U_2839)) ),
    inference(definitional_conversion,[status(esa)],[f_870_2]) ).

cnf(f_870_4,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2838,U_2839)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2837)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2837),U_2838),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2837),U_2839)) ),
    inference(clausify,[status(thm)],[f_870_3]) ).

fof(f_871_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2),V_m_2)
          | V_n_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        & ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2),V_m_2) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel1]) ).

fof(f_871_2,plain,
    ! [U_2841,U_2840] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2840),U_2841),U_2840)
          | U_2841 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        & ( U_2841 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2840),U_2841),U_2840) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2840) ),
    inference(variable_rename,[status(thm)],[f_871_1]) ).

fof(f_871_3,plain,
    ( ! [U_2840,U_2841] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2840),U_2841),U_2840)
        | U_2841 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP241(U_2840,U_2841) )
    & ! [U_2840,U_2841] :
        ( U_2841 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2840),U_2841),U_2840)
        | ~ sP241(U_2840,U_2841) )
    & ! [U_2840,U_2841] :
        ( sP241(U_2840,U_2841)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2840) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP241])],[f_871_2]) ).

cnf(f_871_4,plain,
    ( sP241(U_2840,U_2841)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2840) ),
    inference(clausify,[status(thm)],[f_871_3]) ).

cnf(f_871_5,plain,
    ( U_2841 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2840),U_2841),U_2840)
    | ~ sP241(U_2840,U_2841) ),
    inference(clausify,[status(thm)],[f_871_3]) ).

cnf(f_871_6,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2840),U_2841),U_2840)
    | U_2841 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP241(U_2840,U_2841) ),
    inference(clausify,[status(thm)],[f_871_3]) ).

fof(f_872_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_m_2),V_m_2)
          | V_n_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        & ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_m_2),V_m_2) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel2]) ).

fof(f_872_2,plain,
    ! [U_2843,U_2842] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2843),U_2842),U_2842)
          | U_2843 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        & ( U_2843 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2843),U_2842),U_2842) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2842) ),
    inference(variable_rename,[status(thm)],[f_872_1]) ).

fof(f_872_3,plain,
    ( ! [U_2843,U_2842] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2843),U_2842),U_2842)
        | U_2843 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP242(U_2843,U_2842) )
    & ! [U_2843,U_2842] :
        ( U_2843 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2843),U_2842),U_2842)
        | ~ sP242(U_2843,U_2842) )
    & ! [U_2843,U_2842] :
        ( sP242(U_2843,U_2842)
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2842) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP242])],[f_872_2]) ).

cnf(f_872_4,plain,
    ( sP242(U_2843,U_2842)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2842) ),
    inference(clausify,[status(thm)],[f_872_3]) ).

cnf(f_872_5,plain,
    ( U_2843 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2843),U_2842),U_2842)
    | ~ sP242(U_2843,U_2842) ),
    inference(clausify,[status(thm)],[f_872_3]) ).

cnf(f_872_6,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2843),U_2842),U_2842)
    | U_2843 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP242(U_2843,U_2842) ),
    inference(clausify,[status(thm)],[f_872_3]) ).

fof(f_873_1,plain,
    ! [V_n,V_m,V_i] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_i)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_power__dvd__imp__le]) ).

fof(f_873_2,plain,
    ! [U_2846,U_2845,U_2844] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2845,U_2846)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_2844)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2844),U_2845),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2844),U_2846)) ),
    inference(variable_rename,[status(thm)],[f_873_1]) ).

fof(f_873_3,plain,
    ! [U_2845,U_2846,U_2844] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2845,U_2846)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_2844)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2844),U_2845),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2844),U_2846)) ),
    inference(definitional_conversion,[status(esa)],[f_873_2]) ).

cnf(f_873_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2845,U_2846)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_2844)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2844),U_2845),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2844),U_2846)) ),
    inference(clausify,[status(thm)],[f_873_3]) ).

fof(f_874_1,plain,
    ! [V_l_2,V_P_2,T_a] :
      ( ( ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_l_2),B_x)))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(V_P_2,B_x))
              | ~ c_Rings_Odvd__class_Odvd(T_a,V_l_2,c_Groups_Oplus__class_Oplus(T_a,B_x,c_Groups_Ozero__class_Ozero(T_a))) ) )
        & ( ? [B_x] :
              ( hBOOL(hAPP(V_P_2,B_x))
              & c_Rings_Odvd__class_Odvd(T_a,V_l_2,c_Groups_Oplus__class_Oplus(T_a,B_x,c_Groups_Ozero__class_Ozero(T_a))) )
          | ! [B_x] : ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_l_2),B_x))) ) )
      | ~ class_Rings_Osemiring__0(T_a)
      | ~ class_Rings_Odvd(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_unity__coeff__ex]) ).

fof(f_874_2,plain,
    ! [U_2853,U_2852,U_2851] :
      ( ( ( ? [U_2850] : hBOOL(hAPP(U_2852,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2851),U_2853),U_2850)))
          | ! [U_2849] :
              ( ~ hBOOL(hAPP(U_2852,U_2849))
              | ~ c_Rings_Odvd__class_Odvd(U_2851,U_2853,c_Groups_Oplus__class_Oplus(U_2851,U_2849,c_Groups_Ozero__class_Ozero(U_2851))) ) )
        & ( ? [U_2848] :
              ( hBOOL(hAPP(U_2852,U_2848))
              & c_Rings_Odvd__class_Odvd(U_2851,U_2853,c_Groups_Oplus__class_Oplus(U_2851,U_2848,c_Groups_Ozero__class_Ozero(U_2851))) )
          | ! [U_2847] : ~ hBOOL(hAPP(U_2852,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2851),U_2853),U_2847))) ) )
      | ~ class_Rings_Osemiring__0(U_2851)
      | ~ class_Rings_Odvd(U_2851) ),
    inference(variable_rename,[status(thm)],[f_874_1]) ).

fof(f_874_3,plain,
    ! [U_2853,U_2852,U_2851] :
      ( ( ( ? [U_2850] : hBOOL(hAPP(U_2852,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2851),U_2853),U_2850)))
          | ! [U_2849] :
              ( ~ hBOOL(hAPP(U_2852,U_2849))
              | ~ c_Rings_Odvd__class_Odvd(U_2851,U_2853,c_Groups_Oplus__class_Oplus(U_2851,U_2849,c_Groups_Ozero__class_Ozero(U_2851))) ) )
        & ( ( hBOOL(hAPP(U_2852,sK19(U_2853,U_2852,U_2851)))
            & c_Rings_Odvd__class_Odvd(U_2851,U_2853,c_Groups_Oplus__class_Oplus(U_2851,sK19(U_2853,U_2852,U_2851),c_Groups_Ozero__class_Ozero(U_2851))) )
          | ! [U_2847] : ~ hBOOL(hAPP(U_2852,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2851),U_2853),U_2847))) ) )
      | ~ class_Rings_Osemiring__0(U_2851)
      | ~ class_Rings_Odvd(U_2851) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_2848,sK19(U_2853,U_2852,U_2851))],[f_874_2]) ).

fof(f_874_4,plain,
    ! [U_2853,U_2852,U_2851] :
      ( ( ( hBOOL(hAPP(U_2852,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2851),U_2853),sK20(U_2853,U_2852,U_2851))))
          | ! [U_2849] :
              ( ~ hBOOL(hAPP(U_2852,U_2849))
              | ~ c_Rings_Odvd__class_Odvd(U_2851,U_2853,c_Groups_Oplus__class_Oplus(U_2851,U_2849,c_Groups_Ozero__class_Ozero(U_2851))) ) )
        & ( ( hBOOL(hAPP(U_2852,sK19(U_2853,U_2852,U_2851)))
            & c_Rings_Odvd__class_Odvd(U_2851,U_2853,c_Groups_Oplus__class_Oplus(U_2851,sK19(U_2853,U_2852,U_2851),c_Groups_Ozero__class_Ozero(U_2851))) )
          | ! [U_2847] : ~ hBOOL(hAPP(U_2852,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2851),U_2853),U_2847))) ) )
      | ~ class_Rings_Osemiring__0(U_2851)
      | ~ class_Rings_Odvd(U_2851) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_2850,sK20(U_2853,U_2852,U_2851))],[f_874_3]) ).

fof(f_874_5,plain,
    ( ! [U_2851,U_2852,U_2853] :
        ( hBOOL(hAPP(U_2852,sK19(U_2853,U_2852,U_2851)))
        | ~ sP243(U_2851,U_2852,U_2853) )
    & ! [U_2851,U_2852,U_2853] :
        ( c_Rings_Odvd__class_Odvd(U_2851,U_2853,c_Groups_Oplus__class_Oplus(U_2851,sK19(U_2853,U_2852,U_2851),c_Groups_Ozero__class_Ozero(U_2851)))
        | ~ sP243(U_2851,U_2852,U_2853) )
    & ! [U_2849,U_2847,U_2851,U_2852,U_2853] :
        ( hBOOL(hAPP(U_2852,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2851),U_2853),sK20(U_2853,U_2852,U_2851))))
        | ~ hBOOL(hAPP(U_2852,U_2849))
        | ~ c_Rings_Odvd__class_Odvd(U_2851,U_2853,c_Groups_Oplus__class_Oplus(U_2851,U_2849,c_Groups_Ozero__class_Ozero(U_2851)))
        | ~ sP244(U_2849,U_2847,U_2851,U_2852,U_2853) )
    & ! [U_2849,U_2847,U_2851,U_2852,U_2853] :
        ( sP243(U_2851,U_2852,U_2853)
        | ~ hBOOL(hAPP(U_2852,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2851),U_2853),U_2847)))
        | ~ sP244(U_2849,U_2847,U_2851,U_2852,U_2853) )
    & ! [U_2849,U_2847,U_2851,U_2852,U_2853] :
        ( sP244(U_2849,U_2847,U_2851,U_2852,U_2853)
        | ~ class_Rings_Osemiring__0(U_2851)
        | ~ class_Rings_Odvd(U_2851) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP243,sP244])],[f_874_4]) ).

cnf(f_874_6,plain,
    ( sP244(U_2849,U_2847,U_2851,U_2852,U_2853)
    | ~ class_Rings_Osemiring__0(U_2851)
    | ~ class_Rings_Odvd(U_2851) ),
    inference(clausify,[status(thm)],[f_874_5]) ).

cnf(f_874_7,plain,
    ( sP243(U_2851,U_2852,U_2853)
    | ~ hBOOL(hAPP(U_2852,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2851),U_2853),U_2847)))
    | ~ sP244(U_2849,U_2847,U_2851,U_2852,U_2853) ),
    inference(clausify,[status(thm)],[f_874_5]) ).

cnf(f_874_8,plain,
    ( hBOOL(hAPP(U_2852,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2851),U_2853),sK20(U_2853,U_2852,U_2851))))
    | ~ hBOOL(hAPP(U_2852,U_2849))
    | ~ c_Rings_Odvd__class_Odvd(U_2851,U_2853,c_Groups_Oplus__class_Oplus(U_2851,U_2849,c_Groups_Ozero__class_Ozero(U_2851)))
    | ~ sP244(U_2849,U_2847,U_2851,U_2852,U_2853) ),
    inference(clausify,[status(thm)],[f_874_5]) ).

cnf(f_874_9,plain,
    ( c_Rings_Odvd__class_Odvd(U_2851,U_2853,c_Groups_Oplus__class_Oplus(U_2851,sK19(U_2853,U_2852,U_2851),c_Groups_Ozero__class_Ozero(U_2851)))
    | ~ sP243(U_2851,U_2852,U_2853) ),
    inference(clausify,[status(thm)],[f_874_5]) ).

cnf(f_874_10,plain,
    ( hBOOL(hAPP(U_2852,sK19(U_2853,U_2852,U_2851)))
    | ~ sP243(U_2851,U_2852,U_2853) ),
    inference(clausify,[status(thm)],[f_874_5]) ).

fof(f_875_1,plain,
    ! [V_n,V_b] :
      ( ? [B_z] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),V_b),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),B_z),V_n)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | V_b = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    inference(fof_nnf,[status(thm)],[fact_reduce__poly__simple]) ).

fof(f_875_2,plain,
    ! [U_2856,U_2855] :
      ( ? [U_2854] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),U_2855),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),U_2854),U_2856)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | U_2856 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | U_2855 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    inference(variable_rename,[status(thm)],[f_875_1]) ).

fof(f_875_3,plain,
    ! [U_2856,U_2855] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),U_2855),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),sK21(U_2856,U_2855)),U_2856)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | U_2856 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | U_2855 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_2854,sK21(U_2856,U_2855))],[f_875_2]) ).

fof(f_875_4,plain,
    ! [U_2855,U_2856] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),U_2855),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),sK21(U_2856,U_2855)),U_2856)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
      | U_2856 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | U_2855 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    inference(definitional_conversion,[status(esa)],[f_875_3]) ).

cnf(f_875_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),U_2855),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),sK21(U_2856,U_2855)),U_2856)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | U_2856 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2855 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    inference(clausify,[status(thm)],[f_875_4]) ).

fof(f_876_1,plain,
    ! [V_b_2,V_ab_2,V_n_2] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_ab_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b_2),V_n_2))
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ab_2,V_b_2) )
        & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ab_2,V_b_2)
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_ab_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b_2),V_n_2)) ) )
      | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_nnf,[status(thm)],[fact_pow__divides__eq__nat]) ).

fof(f_876_2,plain,
    ! [U_2859,U_2858,U_2857] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2858),U_2857),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2859),U_2857))
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2858,U_2859) )
        & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2858,U_2859)
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2858),U_2857),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2859),U_2857)) ) )
      | U_2857 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_876_1]) ).

fof(f_876_3,plain,
    ( ! [U_2859,U_2857,U_2858] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2858),U_2857),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2859),U_2857))
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2858,U_2859)
        | ~ sP245(U_2859,U_2857,U_2858) )
    & ! [U_2859,U_2857,U_2858] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2858,U_2859)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2858),U_2857),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2859),U_2857))
        | ~ sP245(U_2859,U_2857,U_2858) )
    & ! [U_2859,U_2857,U_2858] :
        ( sP245(U_2859,U_2857,U_2858)
        | U_2857 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP245])],[f_876_2]) ).

cnf(f_876_4,plain,
    ( sP245(U_2859,U_2857,U_2858)
    | U_2857 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_876_3]) ).

cnf(f_876_5,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2858,U_2859)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2858),U_2857),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2859),U_2857))
    | ~ sP245(U_2859,U_2857,U_2858) ),
    inference(clausify,[status(thm)],[f_876_3]) ).

cnf(f_876_6,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2858),U_2857),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2859),U_2857))
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2858,U_2859)
    | ~ sP245(U_2859,U_2857,U_2858) ),
    inference(clausify,[status(thm)],[f_876_3]) ).

fof(f_877_1,plain,
    ! [V_x] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_x),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oorder__refl]) ).

fof(f_877_2,plain,
    ! [U_2860] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2860,U_2860),
    inference(variable_rename,[status(thm)],[f_877_1]) ).

fof(f_877_3,plain,
    ! [U_2860] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2860,U_2860),
    inference(definitional_conversion,[status(esa)],[f_877_2]) ).

cnf(f_877_4,plain,
    c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2860,U_2860),
    inference(clausify,[status(thm)],[f_877_3]) ).

fof(f_878_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( V_x_2 = V_y_2
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) )
      & ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) )
        | V_x_2 != V_y_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oeq__iff]) ).

fof(f_878_2,plain,
    ! [U_2862,U_2861] :
      ( ( U_2861 = U_2862
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2862,U_2861)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2861,U_2862) )
      & ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2862,U_2861)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2861,U_2862) )
        | U_2861 != U_2862 ) ),
    inference(variable_rename,[status(thm)],[f_878_1]) ).

fof(f_878_3,plain,
    ( ! [U_2866,U_2864] :
        ( U_2864 = U_2866
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2866,U_2864)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2864,U_2866) )
    & ! [U_2865,U_2863] :
        ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2865,U_2863)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2863,U_2865) )
        | U_2863 != U_2865 ) ),
    inference(miniscope,[status(thm)],[f_878_2]) ).

fof(f_878_4,plain,
    ( ! [U_2865,U_2863] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2865,U_2863)
        | ~ sP246(U_2865,U_2863) )
    & ! [U_2865,U_2863] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2863,U_2865)
        | ~ sP246(U_2865,U_2863) )
    & ! [U_2864,U_2866] :
        ( U_2864 = U_2866
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2866,U_2864)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2864,U_2866) )
    & ! [U_2865,U_2863] :
        ( sP246(U_2865,U_2863)
        | U_2863 != U_2865 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP246])],[f_878_3]) ).

cnf(f_878_5,plain,
    ( sP246(U_2865,U_2863)
    | U_2863 != U_2865 ),
    inference(clausify,[status(thm)],[f_878_4]) ).

cnf(f_878_6,plain,
    ( U_2864 = U_2866
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2866,U_2864)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2864,U_2866) ),
    inference(clausify,[status(thm)],[f_878_4]) ).

cnf(f_878_7,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2863,U_2865)
    | ~ sP246(U_2865,U_2863) ),
    inference(clausify,[status(thm)],[f_878_4]) ).

cnf(f_878_8,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2865,U_2863)
    | ~ sP246(U_2865,U_2863) ),
    inference(clausify,[status(thm)],[f_878_4]) ).

fof(f_879_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
        | ( V_x_2 != V_y_2
          & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)
            | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) ) ) )
      & ( V_x_2 = V_y_2
        | ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) )
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Ole__less]) ).

fof(f_879_2,plain,
    ! [U_2868,U_2867] :
      ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2867,U_2868)
        | ( U_2867 != U_2868
          & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2868,U_2867)
            | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2867,U_2868) ) ) )
      & ( U_2867 = U_2868
        | ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2868,U_2867)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2867,U_2868) )
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2867,U_2868) ) ),
    inference(variable_rename,[status(thm)],[f_879_1]) ).

fof(f_879_3,plain,
    ( ! [U_2872,U_2870] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2870,U_2872)
        | ( U_2870 != U_2872
          & ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2872,U_2870)
            | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2870,U_2872) ) ) )
    & ! [U_2871,U_2869] :
        ( U_2869 = U_2871
        | ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2871,U_2869)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2869,U_2871) )
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2869,U_2871) ) ),
    inference(miniscope,[status(thm)],[f_879_2]) ).

fof(f_879_4,plain,
    ( ! [U_2870,U_2872] :
        ( U_2870 != U_2872
        | ~ sP248(U_2870,U_2872) )
    & ! [U_2870,U_2872] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2872,U_2870)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2870,U_2872)
        | ~ sP248(U_2870,U_2872) )
    & ! [U_2871,U_2869] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2871,U_2869)
        | ~ sP247(U_2871,U_2869) )
    & ! [U_2871,U_2869] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2869,U_2871)
        | ~ sP247(U_2871,U_2869) )
    & ! [U_2870,U_2872] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2870,U_2872)
        | sP248(U_2870,U_2872) )
    & ! [U_2871,U_2869] :
        ( U_2869 = U_2871
        | sP247(U_2871,U_2869)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2869,U_2871) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP247,sP248])],[f_879_3]) ).

cnf(f_879_5,plain,
    ( U_2869 = U_2871
    | sP247(U_2871,U_2869)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2869,U_2871) ),
    inference(clausify,[status(thm)],[f_879_4]) ).

cnf(f_879_6,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2870,U_2872)
    | sP248(U_2870,U_2872) ),
    inference(clausify,[status(thm)],[f_879_4]) ).

cnf(f_879_7,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2869,U_2871)
    | ~ sP247(U_2871,U_2869) ),
    inference(clausify,[status(thm)],[f_879_4]) ).

cnf(f_879_8,plain,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2871,U_2869)
    | ~ sP247(U_2871,U_2869) ),
    inference(clausify,[status(thm)],[f_879_4]) ).

cnf(f_879_9,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2872,U_2870)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2870,U_2872)
    | ~ sP248(U_2870,U_2872) ),
    inference(clausify,[status(thm)],[f_879_4]) ).

cnf(f_879_10,plain,
    ( U_2870 != U_2872
    | ~ sP248(U_2870,U_2872) ),
    inference(clausify,[status(thm)],[f_879_4]) ).

fof(f_880_1,plain,
    ! [V_y_2,V_x_2] :
      ( ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) )
        | V_x_2 = V_y_2
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) )
      & ( ( V_x_2 != V_y_2
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) )
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__le]) ).

fof(f_880_2,plain,
    ! [U_2874,U_2873] :
      ( ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2874,U_2873)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2873,U_2874) )
        | U_2873 = U_2874
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2873,U_2874) )
      & ( ( U_2873 != U_2874
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2873,U_2874) )
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2874,U_2873)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2873,U_2874) ) ),
    inference(variable_rename,[status(thm)],[f_880_1]) ).

fof(f_880_3,plain,
    ( ! [U_2878,U_2876] :
        ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2878,U_2876)
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2876,U_2878) )
        | U_2876 = U_2878
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2876,U_2878) )
    & ! [U_2877,U_2875] :
        ( ( U_2875 != U_2877
          & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2875,U_2877) )
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2877,U_2875)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2875,U_2877) ) ),
    inference(miniscope,[status(thm)],[f_880_2]) ).

fof(f_880_4,plain,
    ( ! [U_2876,U_2878] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2878,U_2876)
        | ~ sP250(U_2876,U_2878) )
    & ! [U_2876,U_2878] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2876,U_2878)
        | ~ sP250(U_2876,U_2878) )
    & ! [U_2875,U_2877] :
        ( U_2875 != U_2877
        | ~ sP249(U_2875,U_2877) )
    & ! [U_2875,U_2877] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2875,U_2877)
        | ~ sP249(U_2875,U_2877) )
    & ! [U_2876,U_2878] :
        ( sP250(U_2876,U_2878)
        | U_2876 = U_2878
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2876,U_2878) )
    & ! [U_2875,U_2877] :
        ( sP249(U_2875,U_2877)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2877,U_2875)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2875,U_2877) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP249,sP250])],[f_880_3]) ).

cnf(f_880_5,plain,
    ( sP249(U_2875,U_2877)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2877,U_2875)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2875,U_2877) ),
    inference(clausify,[status(thm)],[f_880_4]) ).

cnf(f_880_6,plain,
    ( sP250(U_2876,U_2878)
    | U_2876 = U_2878
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2876,U_2878) ),
    inference(clausify,[status(thm)],[f_880_4]) ).

cnf(f_880_7,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2875,U_2877)
    | ~ sP249(U_2875,U_2877) ),
    inference(clausify,[status(thm)],[f_880_4]) ).

cnf(f_880_8,plain,
    ( U_2875 != U_2877
    | ~ sP249(U_2875,U_2877) ),
    inference(clausify,[status(thm)],[f_880_4]) ).

cnf(f_880_9,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2876,U_2878)
    | ~ sP250(U_2876,U_2878) ),
    inference(clausify,[status(thm)],[f_880_4]) ).

cnf(f_880_10,plain,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2878,U_2876)
    | ~ sP250(U_2876,U_2878) ),
    inference(clausify,[status(thm)],[f_880_4]) ).

fof(f_881_1,plain,
    ! [V_b,V_a] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) )
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
      | V_a = V_b ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oneq__le__trans]) ).

fof(f_881_2,plain,
    ! [U_2880,U_2879] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2880,U_2879)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2879,U_2880) )
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2879,U_2880)
      | U_2879 = U_2880 ),
    inference(variable_rename,[status(thm)],[f_881_1]) ).

fof(f_881_3,plain,
    ( ! [U_2880,U_2879] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2880,U_2879)
        | ~ sP251(U_2880,U_2879) )
    & ! [U_2880,U_2879] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2879,U_2880)
        | ~ sP251(U_2880,U_2879) )
    & ! [U_2880,U_2879] :
        ( sP251(U_2880,U_2879)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2879,U_2880)
        | U_2879 = U_2880 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP251])],[f_881_2]) ).

cnf(f_881_4,plain,
    ( sP251(U_2880,U_2879)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2879,U_2880)
    | U_2879 = U_2880 ),
    inference(clausify,[status(thm)],[f_881_3]) ).

cnf(f_881_5,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2879,U_2880)
    | ~ sP251(U_2880,U_2879) ),
    inference(clausify,[status(thm)],[f_881_3]) ).

cnf(f_881_6,plain,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2880,U_2879)
    | ~ sP251(U_2880,U_2879) ),
    inference(clausify,[status(thm)],[f_881_3]) ).

fof(f_882_1,plain,
    ! [V_y,V_x] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
      | V_x != V_y ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oeq__refl]) ).

fof(f_882_2,plain,
    ! [U_2882,U_2881] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2881,U_2882)
      | U_2881 != U_2882 ),
    inference(variable_rename,[status(thm)],[f_882_1]) ).

fof(f_882_3,plain,
    ! [U_2882,U_2881] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2881,U_2882)
      | U_2881 != U_2882 ),
    inference(definitional_conversion,[status(esa)],[f_882_2]) ).

cnf(f_882_4,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2881,U_2882)
    | U_2881 != U_2882 ),
    inference(clausify,[status(thm)],[f_882_3]) ).

fof(f_883_1,plain,
    ! [V_x_2,V_y_2] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
          | V_x_2 != V_y_2 )
        & ( V_x_2 = V_y_2
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) ) )
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oantisym__conv]) ).

fof(f_883_2,plain,
    ! [U_2884,U_2883] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2884,U_2883)
          | U_2884 != U_2883 )
        & ( U_2884 = U_2883
          | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2884,U_2883) ) )
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2883,U_2884) ),
    inference(variable_rename,[status(thm)],[f_883_1]) ).

fof(f_883_3,plain,
    ( ! [U_2884,U_2883] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2884,U_2883)
        | U_2884 != U_2883
        | ~ sP252(U_2884,U_2883) )
    & ! [U_2884,U_2883] :
        ( U_2884 = U_2883
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2884,U_2883)
        | ~ sP252(U_2884,U_2883) )
    & ! [U_2884,U_2883] :
        ( sP252(U_2884,U_2883)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2883,U_2884) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP252])],[f_883_2]) ).

cnf(f_883_4,plain,
    ( sP252(U_2884,U_2883)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2883,U_2884) ),
    inference(clausify,[status(thm)],[f_883_3]) ).

cnf(f_883_5,plain,
    ( U_2884 = U_2883
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2884,U_2883)
    | ~ sP252(U_2884,U_2883) ),
    inference(clausify,[status(thm)],[f_883_3]) ).

cnf(f_883_6,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2884,U_2883)
    | U_2884 != U_2883
    | ~ sP252(U_2884,U_2883) ),
    inference(clausify,[status(thm)],[f_883_3]) ).

fof(f_884_1,plain,
    ! [V_y,V_x] :
      ( V_x = V_y
      | ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) )
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Ole__imp__less__or__eq]) ).

fof(f_884_2,plain,
    ! [U_2886,U_2885] :
      ( U_2885 = U_2886
      | ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2886,U_2885)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2885,U_2886) )
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2885,U_2886) ),
    inference(variable_rename,[status(thm)],[f_884_1]) ).

fof(f_884_3,plain,
    ( ! [U_2885,U_2886] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2886,U_2885)
        | ~ sP253(U_2885,U_2886) )
    & ! [U_2885,U_2886] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2885,U_2886)
        | ~ sP253(U_2885,U_2886) )
    & ! [U_2885,U_2886] :
        ( U_2885 = U_2886
        | sP253(U_2885,U_2886)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2885,U_2886) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP253])],[f_884_2]) ).

cnf(f_884_4,plain,
    ( U_2885 = U_2886
    | sP253(U_2885,U_2886)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2885,U_2886) ),
    inference(clausify,[status(thm)],[f_884_3]) ).

cnf(f_884_5,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2885,U_2886)
    | ~ sP253(U_2885,U_2886) ),
    inference(clausify,[status(thm)],[f_884_3]) ).

cnf(f_884_6,plain,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2886,U_2885)
    | ~ sP253(U_2885,U_2886) ),
    inference(clausify,[status(thm)],[f_884_3]) ).

fof(f_885_1,plain,
    ! [V_b,V_a] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) )
      | V_a = V_b
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Ole__neq__trans]) ).

fof(f_885_2,plain,
    ! [U_2888,U_2887] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2888,U_2887)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2887,U_2888) )
      | U_2887 = U_2888
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2887,U_2888) ),
    inference(variable_rename,[status(thm)],[f_885_1]) ).

fof(f_885_3,plain,
    ( ! [U_2888,U_2887] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2888,U_2887)
        | ~ sP254(U_2888,U_2887) )
    & ! [U_2888,U_2887] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2887,U_2888)
        | ~ sP254(U_2888,U_2887) )
    & ! [U_2888,U_2887] :
        ( sP254(U_2888,U_2887)
        | U_2887 = U_2888
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2887,U_2888) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP254])],[f_885_2]) ).

cnf(f_885_4,plain,
    ( sP254(U_2888,U_2887)
    | U_2887 = U_2888
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2887,U_2888) ),
    inference(clausify,[status(thm)],[f_885_3]) ).

cnf(f_885_5,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2887,U_2888)
    | ~ sP254(U_2888,U_2887) ),
    inference(clausify,[status(thm)],[f_885_3]) ).

cnf(f_885_6,plain,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2888,U_2887)
    | ~ sP254(U_2888,U_2887) ),
    inference(clausify,[status(thm)],[f_885_3]) ).

fof(f_886_1,plain,
    ! [V_c,V_b,V_a] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c)
      | V_a != V_b ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oord__eq__le__trans]) ).

fof(f_886_2,plain,
    ! [U_2891,U_2890,U_2889] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2889,U_2891)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2890,U_2891)
      | U_2889 != U_2890 ),
    inference(variable_rename,[status(thm)],[f_886_1]) ).

fof(f_886_3,plain,
    ! [U_2891,U_2889,U_2890] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2889,U_2891)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2890,U_2891)
      | U_2889 != U_2890 ),
    inference(definitional_conversion,[status(esa)],[f_886_2]) ).

cnf(f_886_4,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2889,U_2891)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2890,U_2891)
    | U_2889 != U_2890 ),
    inference(clausify,[status(thm)],[f_886_3]) ).

fof(f_887_1,plain,
    ! [V_c,V_b,V_a] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c)
      | V_b != V_c
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oord__le__eq__trans]) ).

fof(f_887_2,plain,
    ! [U_2894,U_2893,U_2892] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2892,U_2894)
      | U_2893 != U_2894
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2892,U_2893) ),
    inference(variable_rename,[status(thm)],[f_887_1]) ).

fof(f_887_3,plain,
    ! [U_2894,U_2893,U_2892] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2892,U_2894)
      | U_2893 != U_2894
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2892,U_2893) ),
    inference(definitional_conversion,[status(esa)],[f_887_2]) ).

cnf(f_887_4,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2892,U_2894)
    | U_2893 != U_2894
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2892,U_2893) ),
    inference(clausify,[status(thm)],[f_887_3]) ).

fof(f_888_1,plain,
    ! [V_n,V_m] :
      ( V_m = V_n
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_n,V_m)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__antisym]) ).

fof(f_888_2,plain,
    ! [U_2896,U_2895] :
      ( U_2895 = U_2896
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2896,U_2895)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2895,U_2896) ),
    inference(variable_rename,[status(thm)],[f_888_1]) ).

fof(f_888_3,plain,
    ! [U_2896,U_2895] :
      ( U_2895 = U_2896
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2896,U_2895)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2895,U_2896) ),
    inference(definitional_conversion,[status(esa)],[f_888_2]) ).

cnf(f_888_4,plain,
    ( U_2895 = U_2896
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2896,U_2895)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2895,U_2896) ),
    inference(clausify,[status(thm)],[f_888_3]) ).

fof(f_889_1,plain,
    ! [V_y,V_x] :
      ( V_x = V_y
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oantisym]) ).

fof(f_889_2,plain,
    ! [U_2898,U_2897] :
      ( U_2897 = U_2898
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2898,U_2897)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2897,U_2898) ),
    inference(variable_rename,[status(thm)],[f_889_1]) ).

fof(f_889_3,plain,
    ! [U_2897,U_2898] :
      ( U_2897 = U_2898
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2898,U_2897)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2897,U_2898) ),
    inference(definitional_conversion,[status(esa)],[f_889_2]) ).

cnf(f_889_4,plain,
    ( U_2897 = U_2898
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2898,U_2897)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2897,U_2898) ),
    inference(clausify,[status(thm)],[f_889_3]) ).

fof(f_890_1,plain,
    ! [V_z,V_y,V_x] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oorder__trans]) ).

fof(f_890_2,plain,
    ! [U_2901,U_2900,U_2899] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2899,U_2901)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2900,U_2901)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2899,U_2900) ),
    inference(variable_rename,[status(thm)],[f_890_1]) ).

fof(f_890_3,plain,
    ! [U_2899,U_2900,U_2901] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2899,U_2901)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2900,U_2901)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2899,U_2900) ),
    inference(definitional_conversion,[status(esa)],[f_890_2]) ).

cnf(f_890_4,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2899,U_2901)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2900,U_2901)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2899,U_2900) ),
    inference(clausify,[status(thm)],[f_890_3]) ).

fof(f_891_1,plain,
    ! [V_c,V_b,V_a] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_a)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c) )
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_b)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c)
      | V_a != V_b ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oord__eq__less__trans]) ).

fof(f_891_2,plain,
    ! [U_2904,U_2903,U_2902] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2904,U_2902)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2902,U_2904) )
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2904,U_2903)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2903,U_2904)
      | U_2902 != U_2903 ),
    inference(variable_rename,[status(thm)],[f_891_1]) ).

fof(f_891_3,plain,
    ( ! [U_2904,U_2902] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2904,U_2902)
        | ~ sP255(U_2904,U_2902) )
    & ! [U_2904,U_2902] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2902,U_2904)
        | ~ sP255(U_2904,U_2902) )
    & ! [U_2904,U_2902,U_2903] :
        ( sP255(U_2904,U_2902)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2904,U_2903)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2903,U_2904)
        | U_2902 != U_2903 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP255])],[f_891_2]) ).

cnf(f_891_4,plain,
    ( sP255(U_2904,U_2902)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2904,U_2903)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2903,U_2904)
    | U_2902 != U_2903 ),
    inference(clausify,[status(thm)],[f_891_3]) ).

cnf(f_891_5,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2902,U_2904)
    | ~ sP255(U_2904,U_2902) ),
    inference(clausify,[status(thm)],[f_891_3]) ).

cnf(f_891_6,plain,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2904,U_2902)
    | ~ sP255(U_2904,U_2902) ),
    inference(clausify,[status(thm)],[f_891_3]) ).

fof(f_892_1,plain,
    ! [V_z,V_y,V_x] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z) )
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Ole__less__trans]) ).

fof(f_892_2,plain,
    ! [U_2907,U_2906,U_2905] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2907,U_2905)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2905,U_2907) )
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2907,U_2906)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2906,U_2907)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2905,U_2906) ),
    inference(variable_rename,[status(thm)],[f_892_1]) ).

fof(f_892_3,plain,
    ( ! [U_2905,U_2907] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2907,U_2905)
        | ~ sP256(U_2905,U_2907) )
    & ! [U_2905,U_2907] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2905,U_2907)
        | ~ sP256(U_2905,U_2907) )
    & ! [U_2905,U_2906,U_2907] :
        ( sP256(U_2905,U_2907)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2907,U_2906)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2906,U_2907)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2905,U_2906) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP256])],[f_892_2]) ).

cnf(f_892_4,plain,
    ( sP256(U_2905,U_2907)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2907,U_2906)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2906,U_2907)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2905,U_2906) ),
    inference(clausify,[status(thm)],[f_892_3]) ).

cnf(f_892_5,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2905,U_2907)
    | ~ sP256(U_2905,U_2907) ),
    inference(clausify,[status(thm)],[f_892_3]) ).

cnf(f_892_6,plain,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2907,U_2905)
    | ~ sP256(U_2905,U_2907) ),
    inference(clausify,[status(thm)],[f_892_3]) ).

fof(f_893_1,plain,
    ! [V_y,V_x] :
      ( V_x != V_y
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__neq]) ).

fof(f_893_2,plain,
    ! [U_2909,U_2908] :
      ( U_2908 != U_2909
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2909,U_2908)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2908,U_2909) ),
    inference(variable_rename,[status(thm)],[f_893_1]) ).

fof(f_893_3,plain,
    ! [U_2908,U_2909] :
      ( U_2908 != U_2909
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2909,U_2908)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2908,U_2909) ),
    inference(definitional_conversion,[status(esa)],[f_893_2]) ).

cnf(f_893_4,plain,
    ( U_2908 != U_2909
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2909,U_2908)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2908,U_2909) ),
    inference(clausify,[status(thm)],[f_893_3]) ).

fof(f_894_1,plain,
    ! [V_y,V_x] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__not__sym]) ).

fof(f_894_2,plain,
    ! [U_2911,U_2910] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2910,U_2911)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2911,U_2910)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2911,U_2910)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2910,U_2911) ),
    inference(variable_rename,[status(thm)],[f_894_1]) ).

fof(f_894_3,plain,
    ! [U_2910,U_2911] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2910,U_2911)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2911,U_2910)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2911,U_2910)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2910,U_2911) ),
    inference(definitional_conversion,[status(esa)],[f_894_2]) ).

cnf(f_894_4,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2910,U_2911)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2911,U_2910)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2911,U_2910)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2910,U_2911) ),
    inference(clausify,[status(thm)],[f_894_3]) ).

fof(f_895_1,plain,
    ! [V_y,V_x] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__le]) ).

fof(f_895_2,plain,
    ! [U_2913,U_2912] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2912,U_2913)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2913,U_2912)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2912,U_2913) ),
    inference(variable_rename,[status(thm)],[f_895_1]) ).

fof(f_895_3,plain,
    ! [U_2913,U_2912] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2912,U_2913)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2913,U_2912)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2912,U_2913) ),
    inference(definitional_conversion,[status(esa)],[f_895_2]) ).

cnf(f_895_4,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2912,U_2913)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2913,U_2912)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2912,U_2913) ),
    inference(clausify,[status(thm)],[f_895_3]) ).

fof(f_896_1,plain,
    ! [V_y,V_x] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__not__less]) ).

fof(f_896_2,plain,
    ! [U_2915,U_2914] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2914,U_2915)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2915,U_2914)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2915,U_2914)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2914,U_2915) ),
    inference(variable_rename,[status(thm)],[f_896_1]) ).

fof(f_896_3,plain,
    ! [U_2914,U_2915] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2914,U_2915)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2915,U_2914)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2915,U_2914)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2914,U_2915) ),
    inference(definitional_conversion,[status(esa)],[f_896_2]) ).

cnf(f_896_4,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2914,U_2915)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2915,U_2914)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2915,U_2914)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2914,U_2915) ),
    inference(clausify,[status(thm)],[f_896_3]) ).

fof(f_897_1,plain,
    ! [V_y,V_x] :
      ( V_x != V_y
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__not__eq]) ).

fof(f_897_2,plain,
    ! [U_2917,U_2916] :
      ( U_2916 != U_2917
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2917,U_2916)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2916,U_2917) ),
    inference(variable_rename,[status(thm)],[f_897_1]) ).

fof(f_897_3,plain,
    ! [U_2916,U_2917] :
      ( U_2916 != U_2917
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2917,U_2916)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2916,U_2917) ),
    inference(definitional_conversion,[status(esa)],[f_897_2]) ).

cnf(f_897_4,plain,
    ( U_2916 != U_2917
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2917,U_2916)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2916,U_2917) ),
    inference(clausify,[status(thm)],[f_897_3]) ).

fof(f_898_1,plain,
    ! [V_y,V_x] :
      ( V_y != V_x
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__not__eq2]) ).

fof(f_898_2,plain,
    ! [U_2919,U_2918] :
      ( U_2919 != U_2918
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2919,U_2918)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2918,U_2919) ),
    inference(variable_rename,[status(thm)],[f_898_1]) ).

fof(f_898_3,plain,
    ! [U_2919,U_2918] :
      ( U_2919 != U_2918
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2919,U_2918)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2918,U_2919) ),
    inference(definitional_conversion,[status(esa)],[f_898_2]) ).

cnf(f_898_4,plain,
    ( U_2919 != U_2918
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2919,U_2918)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2918,U_2919) ),
    inference(clausify,[status(thm)],[f_898_3]) ).

fof(f_899_1,plain,
    ! [V_c,V_b,V_a] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_a)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c) )
      | V_b != V_c
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oord__less__eq__trans]) ).

fof(f_899_2,plain,
    ! [U_2922,U_2921,U_2920] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2922,U_2920)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2920,U_2922) )
      | U_2921 != U_2922
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2921,U_2920)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2920,U_2921) ),
    inference(variable_rename,[status(thm)],[f_899_1]) ).

fof(f_899_3,plain,
    ( ! [U_2920,U_2922] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2922,U_2920)
        | ~ sP257(U_2920,U_2922) )
    & ! [U_2920,U_2922] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2920,U_2922)
        | ~ sP257(U_2920,U_2922) )
    & ! [U_2920,U_2921,U_2922] :
        ( sP257(U_2920,U_2922)
        | U_2921 != U_2922
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2921,U_2920)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2920,U_2921) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP257])],[f_899_2]) ).

cnf(f_899_4,plain,
    ( sP257(U_2920,U_2922)
    | U_2921 != U_2922
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2921,U_2920)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2920,U_2921) ),
    inference(clausify,[status(thm)],[f_899_3]) ).

cnf(f_899_5,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2920,U_2922)
    | ~ sP257(U_2920,U_2922) ),
    inference(clausify,[status(thm)],[f_899_3]) ).

cnf(f_899_6,plain,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2922,U_2920)
    | ~ sP257(U_2920,U_2922) ),
    inference(clausify,[status(thm)],[f_899_3]) ).

fof(f_900_1,plain,
    ! [V_z,V_y,V_x] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z) )
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__le__trans]) ).

fof(f_900_2,plain,
    ! [U_2925,U_2924,U_2923] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2925,U_2923)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2923,U_2925) )
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2924,U_2925)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2924,U_2923)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2923,U_2924) ),
    inference(variable_rename,[status(thm)],[f_900_1]) ).

fof(f_900_3,plain,
    ( ! [U_2923,U_2925] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2925,U_2923)
        | ~ sP258(U_2923,U_2925) )
    & ! [U_2923,U_2925] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2923,U_2925)
        | ~ sP258(U_2923,U_2925) )
    & ! [U_2924,U_2923,U_2925] :
        ( sP258(U_2923,U_2925)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2924,U_2925)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2924,U_2923)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2923,U_2924) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP258])],[f_900_2]) ).

cnf(f_900_4,plain,
    ( sP258(U_2923,U_2925)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2924,U_2925)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2924,U_2923)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2923,U_2924) ),
    inference(clausify,[status(thm)],[f_900_3]) ).

cnf(f_900_5,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2923,U_2925)
    | ~ sP258(U_2923,U_2925) ),
    inference(clausify,[status(thm)],[f_900_3]) ).

cnf(f_900_6,plain,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2925,U_2923)
    | ~ sP258(U_2923,U_2925) ),
    inference(clausify,[status(thm)],[f_900_3]) ).

fof(f_901_1,plain,
    ! [V_b,V_a] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__asym_H]) ).

fof(f_901_2,plain,
    ! [U_2927,U_2926] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2926,U_2927)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2927,U_2926)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2927,U_2926)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2926,U_2927) ),
    inference(variable_rename,[status(thm)],[f_901_1]) ).

fof(f_901_3,plain,
    ! [U_2926,U_2927] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2926,U_2927)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2927,U_2926)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2927,U_2926)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2926,U_2927) ),
    inference(definitional_conversion,[status(esa)],[f_901_2]) ).

cnf(f_901_4,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2926,U_2927)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2927,U_2926)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2927,U_2926)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2926,U_2927) ),
    inference(clausify,[status(thm)],[f_901_3]) ).

fof(f_902_1,plain,
    ! [V_z,V_y,V_x] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z) )
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__trans]) ).

fof(f_902_2,plain,
    ! [U_2930,U_2929,U_2928] :
      ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2930,U_2928)
        & c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2928,U_2930) )
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2930,U_2929)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2929,U_2930)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2929,U_2928)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2928,U_2929) ),
    inference(variable_rename,[status(thm)],[f_902_1]) ).

fof(f_902_3,plain,
    ( ! [U_2930,U_2928] :
        ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2930,U_2928)
        | ~ sP259(U_2930,U_2928) )
    & ! [U_2930,U_2928] :
        ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2928,U_2930)
        | ~ sP259(U_2930,U_2928) )
    & ! [U_2929,U_2930,U_2928] :
        ( sP259(U_2930,U_2928)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2930,U_2929)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2929,U_2930)
        | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2929,U_2928)
        | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2928,U_2929) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP259])],[f_902_2]) ).

cnf(f_902_4,plain,
    ( sP259(U_2930,U_2928)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2930,U_2929)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2929,U_2930)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2929,U_2928)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2928,U_2929) ),
    inference(clausify,[status(thm)],[f_902_3]) ).

cnf(f_902_5,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2928,U_2930)
    | ~ sP259(U_2930,U_2928) ),
    inference(clausify,[status(thm)],[f_902_3]) ).

cnf(f_902_6,plain,
    ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2930,U_2928)
    | ~ sP259(U_2930,U_2928) ),
    inference(clausify,[status(thm)],[f_902_3]) ).

fof(f_903_1,plain,
    ! [V_y,V_x] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_Oless__asym]) ).

fof(f_903_2,plain,
    ! [U_2932,U_2931] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2931,U_2932)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2932,U_2931)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2932,U_2931)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2931,U_2932) ),
    inference(variable_rename,[status(thm)],[f_903_1]) ).

fof(f_903_3,plain,
    ! [U_2931,U_2932] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2931,U_2932)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2932,U_2931)
      | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2932,U_2931)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2931,U_2932) ),
    inference(definitional_conversion,[status(esa)],[f_903_2]) ).

cnf(f_903_4,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2931,U_2932)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2932,U_2931)
    | c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2932,U_2931)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2931,U_2932) ),
    inference(clausify,[status(thm)],[f_903_3]) ).

fof(f_904_1,plain,
    ! [V_x] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_gcd__lcm__complete__lattice__nat_Otop__greatest]) ).

fof(f_904_2,plain,
    ! [U_2933] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2933,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_904_1]) ).

fof(f_904_3,plain,
    ! [U_2933] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2933,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_904_2]) ).

cnf(f_904_4,plain,
    c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2933,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_904_3]) ).

fof(f_905_1,plain,
    ! [V_x] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_x),
    inference(fof_nnf,[status(thm)],[fact_gcd__lcm__complete__lattice__nat_Obot__least]) ).

fof(f_905_2,plain,
    ! [U_2934] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_2934),
    inference(variable_rename,[status(thm)],[f_905_1]) ).

fof(f_905_3,plain,
    ! [U_2934] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_2934),
    inference(definitional_conversion,[status(esa)],[f_905_2]) ).

cnf(f_905_4,plain,
    c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_2934),
    inference(clausify,[status(thm)],[f_905_3]) ).

fof(f_906_1,plain,
    ! [V_m,V_n] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__pos__nat]) ).

fof(f_906_2,plain,
    ! [U_2936,U_2935] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2936)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2936,U_2935)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2935) ),
    inference(variable_rename,[status(thm)],[f_906_1]) ).

fof(f_906_3,plain,
    ! [U_2936,U_2935] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2936)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2936,U_2935)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2935) ),
    inference(definitional_conversion,[status(esa)],[f_906_2]) ).

cnf(f_906_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2936)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2936,U_2935)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2935) ),
    inference(clausify,[status(thm)],[f_906_3]) ).

fof(f_907_1,plain,
    ! [V_b,V_n,V_a] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a,V_b)
      | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_pow__divides__pow__int]) ).

fof(f_907_2,plain,
    ! [U_2939,U_2938,U_2937] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2937,U_2939)
      | U_2938 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2937),U_2938),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2939),U_2938)) ),
    inference(variable_rename,[status(thm)],[f_907_1]) ).

fof(f_907_3,plain,
    ! [U_2938,U_2937,U_2939] :
      ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2937,U_2939)
      | U_2938 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2937),U_2938),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2939),U_2938)) ),
    inference(definitional_conversion,[status(esa)],[f_907_2]) ).

cnf(f_907_4,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2937,U_2939)
    | U_2938 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2937),U_2938),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2939),U_2938)) ),
    inference(clausify,[status(thm)],[f_907_3]) ).

fof(f_908_1,plain,
    ! [V_b_2,V_ab_2,V_n_2] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_ab_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b_2),V_n_2))
          | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ab_2,V_b_2) )
        & ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ab_2,V_b_2)
          | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_ab_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b_2),V_n_2)) ) )
      | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_nnf,[status(thm)],[fact_pow__divides__eq__int]) ).

fof(f_908_2,plain,
    ! [U_2942,U_2941,U_2940] :
      ( ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2941),U_2940),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2942),U_2940))
          | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2941,U_2942) )
        & ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2941,U_2942)
          | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2941),U_2940),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2942),U_2940)) ) )
      | U_2940 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_908_1]) ).

fof(f_908_3,plain,
    ( ! [U_2941,U_2942,U_2940] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2941),U_2940),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2942),U_2940))
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2941,U_2942)
        | ~ sP260(U_2941,U_2942,U_2940) )
    & ! [U_2941,U_2942,U_2940] :
        ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2941,U_2942)
        | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2941),U_2940),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2942),U_2940))
        | ~ sP260(U_2941,U_2942,U_2940) )
    & ! [U_2941,U_2942,U_2940] :
        ( sP260(U_2941,U_2942,U_2940)
        | U_2940 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP260])],[f_908_2]) ).

cnf(f_908_4,plain,
    ( sP260(U_2941,U_2942,U_2940)
    | U_2940 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_908_3]) ).

cnf(f_908_5,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2941,U_2942)
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2941),U_2940),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2942),U_2940))
    | ~ sP260(U_2941,U_2942,U_2940) ),
    inference(clausify,[status(thm)],[f_908_3]) ).

cnf(f_908_6,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2941),U_2940),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2942),U_2940))
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2941,U_2942)
    | ~ sP260(U_2941,U_2942,U_2940) ),
    inference(clausify,[status(thm)],[f_908_3]) ).

fof(f_909_1,plain,
    ! [V_b,V_n,V_a] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
      | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b),V_n)) ),
    inference(fof_nnf,[status(thm)],[fact_pow__divides__pow__nat]) ).

fof(f_909_2,plain,
    ! [U_2945,U_2944,U_2943] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2943,U_2945)
      | U_2944 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2943),U_2944),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2945),U_2944)) ),
    inference(variable_rename,[status(thm)],[f_909_1]) ).

fof(f_909_3,plain,
    ! [U_2945,U_2943,U_2944] :
      ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2943,U_2945)
      | U_2944 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2943),U_2944),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2945),U_2944)) ),
    inference(definitional_conversion,[status(esa)],[f_909_2]) ).

cnf(f_909_4,plain,
    ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2943,U_2945)
    | U_2944 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2943),U_2944),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2945),U_2944)) ),
    inference(clausify,[status(thm)],[f_909_3]) ).

fof(f_910_1,plain,
    ! [T_a] :
      ( ? [B_K] :
          ( ! [B_a,B_b] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult_Opos__bounded]) ).

fof(f_910_2,plain,
    ! [U_2949] :
      ( ? [U_2948] :
          ( ! [U_2947,U_2946] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2949,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2949),U_2947),U_2946)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2949,U_2947)),c_RealVector_Onorm__class_Onorm(U_2949,U_2946))),U_2948))
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2948) )
      | ~ class_RealVector_Oreal__normed__algebra(U_2949) ),
    inference(variable_rename,[status(thm)],[f_910_1]) ).

fof(f_910_3,plain,
    ! [U_2949] :
      ( ( ! [U_2947,U_2946] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2949,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2949),U_2947),U_2946)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2949,U_2947)),c_RealVector_Onorm__class_Onorm(U_2949,U_2946))),sK22(U_2949)))
        & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK22(U_2949)) )
      | ~ class_RealVector_Oreal__normed__algebra(U_2949) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_2948,sK22(U_2949))],[f_910_2]) ).

fof(f_910_4,plain,
    ( ! [U_2947,U_2946,U_2949] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2949,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2949),U_2947),U_2946)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2949,U_2947)),c_RealVector_Onorm__class_Onorm(U_2949,U_2946))),sK22(U_2949)))
        | ~ sP261(U_2947,U_2946,U_2949) )
    & ! [U_2947,U_2946,U_2949] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK22(U_2949))
        | ~ sP261(U_2947,U_2946,U_2949) )
    & ! [U_2947,U_2946,U_2949] :
        ( sP261(U_2947,U_2946,U_2949)
        | ~ class_RealVector_Oreal__normed__algebra(U_2949) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP261])],[f_910_3]) ).

cnf(f_910_5,plain,
    ( sP261(U_2947,U_2946,U_2949)
    | ~ class_RealVector_Oreal__normed__algebra(U_2949) ),
    inference(clausify,[status(thm)],[f_910_4]) ).

cnf(f_910_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK22(U_2949))
    | ~ sP261(U_2947,U_2946,U_2949) ),
    inference(clausify,[status(thm)],[f_910_4]) ).

cnf(f_910_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2949,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2949),U_2947),U_2946)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2949,U_2947)),c_RealVector_Onorm__class_Onorm(U_2949,U_2946))),sK22(U_2949)))
    | ~ sP261(U_2947,U_2946,U_2949) ),
    inference(clausify,[status(thm)],[f_910_4]) ).

fof(f_911_1,plain,
    ! [V_x,T_a] :
      ( ? [B_K] :
          ( ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__right_Opos__bounded]) ).

fof(f_911_2,plain,
    ! [U_2953,U_2952] :
      ( ? [U_2951] :
          ( ! [U_2950] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2952,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2952),U_2953),U_2950)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2952,U_2950)),U_2951))
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2951) )
      | ~ class_RealVector_Oreal__normed__algebra(U_2952) ),
    inference(variable_rename,[status(thm)],[f_911_1]) ).

fof(f_911_3,plain,
    ! [U_2953,U_2952] :
      ( ( ! [U_2950] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2952,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2952),U_2953),U_2950)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2952,U_2950)),sK23(U_2953,U_2952)))
        & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK23(U_2953,U_2952)) )
      | ~ class_RealVector_Oreal__normed__algebra(U_2952) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_2951,sK23(U_2953,U_2952))],[f_911_2]) ).

fof(f_911_4,plain,
    ( ! [U_2950,U_2952,U_2953] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2952,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2952),U_2953),U_2950)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2952,U_2950)),sK23(U_2953,U_2952)))
        | ~ sP262(U_2950,U_2952,U_2953) )
    & ! [U_2950,U_2952,U_2953] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK23(U_2953,U_2952))
        | ~ sP262(U_2950,U_2952,U_2953) )
    & ! [U_2950,U_2952,U_2953] :
        ( sP262(U_2950,U_2952,U_2953)
        | ~ class_RealVector_Oreal__normed__algebra(U_2952) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP262])],[f_911_3]) ).

cnf(f_911_5,plain,
    ( sP262(U_2950,U_2952,U_2953)
    | ~ class_RealVector_Oreal__normed__algebra(U_2952) ),
    inference(clausify,[status(thm)],[f_911_4]) ).

cnf(f_911_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK23(U_2953,U_2952))
    | ~ sP262(U_2950,U_2952,U_2953) ),
    inference(clausify,[status(thm)],[f_911_4]) ).

cnf(f_911_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2952,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2952),U_2953),U_2950)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2952,U_2950)),sK23(U_2953,U_2952)))
    | ~ sP262(U_2950,U_2952,U_2953) ),
    inference(clausify,[status(thm)],[f_911_4]) ).

fof(f_912_1,plain,
    ! [V_y,T_a] :
      ( ? [B_K] :
          ( ! [B_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
      | ~ class_RealVector_Oreal__normed__algebra(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_mult__left_Opos__bounded]) ).

fof(f_912_2,plain,
    ! [U_2957,U_2956] :
      ( ? [U_2955] :
          ( ! [U_2954] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2956,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2956),U_2954),U_2957)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2956,U_2954)),U_2955))
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2955) )
      | ~ class_RealVector_Oreal__normed__algebra(U_2956) ),
    inference(variable_rename,[status(thm)],[f_912_1]) ).

fof(f_912_3,plain,
    ! [U_2957,U_2956] :
      ( ( ! [U_2954] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2956,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2956),U_2954),U_2957)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2956,U_2954)),sK24(U_2957,U_2956)))
        & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK24(U_2957,U_2956)) )
      | ~ class_RealVector_Oreal__normed__algebra(U_2956) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_2955,sK24(U_2957,U_2956))],[f_912_2]) ).

fof(f_912_4,plain,
    ( ! [U_2954,U_2956,U_2957] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2956,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2956),U_2954),U_2957)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2956,U_2954)),sK24(U_2957,U_2956)))
        | ~ sP263(U_2954,U_2956,U_2957) )
    & ! [U_2954,U_2956,U_2957] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK24(U_2957,U_2956))
        | ~ sP263(U_2954,U_2956,U_2957) )
    & ! [U_2954,U_2956,U_2957] :
        ( sP263(U_2954,U_2956,U_2957)
        | ~ class_RealVector_Oreal__normed__algebra(U_2956) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP263])],[f_912_3]) ).

cnf(f_912_5,plain,
    ( sP263(U_2954,U_2956,U_2957)
    | ~ class_RealVector_Oreal__normed__algebra(U_2956) ),
    inference(clausify,[status(thm)],[f_912_4]) ).

cnf(f_912_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK24(U_2957,U_2956))
    | ~ sP263(U_2954,U_2956,U_2957) ),
    inference(clausify,[status(thm)],[f_912_4]) ).

cnf(f_912_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2956,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2956),U_2954),U_2957)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2956,U_2954)),sK24(U_2957,U_2956)))
    | ~ sP263(U_2954,U_2956,U_2957) ),
    inference(clausify,[status(thm)],[f_912_4]) ).

fof(f_913_1,plain,
    ! [V_p,V_z,V_e] :
      ( ? [B_d] :
          ( ! [B_w] :
              ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),B_w),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),V_z))),V_e)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B_w,V_z)),B_d)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,B_w,V_z))) )
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_d) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_e) ),
    inference(fof_nnf,[status(thm)],[fact_poly__cont]) ).

fof(f_913_2,plain,
    ! [U_2962,U_2961,U_2960] :
      ( ? [U_2959] :
          ( ! [U_2958] :
              ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_2962),U_2958),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_2962),U_2961))),U_2960)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2958,U_2961)),U_2959)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2958,U_2961))) )
          & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2959) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2960) ),
    inference(variable_rename,[status(thm)],[f_913_1]) ).

fof(f_913_3,plain,
    ! [U_2962,U_2961,U_2960] :
      ( ( ! [U_2958] :
            ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_2962),U_2958),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_2962),U_2961))),U_2960)
            | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2958,U_2961)),sK25(U_2962,U_2961,U_2960))
            | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2958,U_2961))) )
        & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK25(U_2962,U_2961,U_2960)) )
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2960) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_2959,sK25(U_2962,U_2961,U_2960))],[f_913_2]) ).

fof(f_913_4,plain,
    ( ! [U_2958,U_2960,U_2961,U_2962] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_2962),U_2958),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_2962),U_2961))),U_2960)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2958,U_2961)),sK25(U_2962,U_2961,U_2960))
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2958,U_2961)))
        | ~ sP264(U_2958,U_2960,U_2961,U_2962) )
    & ! [U_2958,U_2960,U_2961,U_2962] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK25(U_2962,U_2961,U_2960))
        | ~ sP264(U_2958,U_2960,U_2961,U_2962) )
    & ! [U_2958,U_2960,U_2961,U_2962] :
        ( sP264(U_2958,U_2960,U_2961,U_2962)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2960) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP264])],[f_913_3]) ).

cnf(f_913_5,plain,
    ( sP264(U_2958,U_2960,U_2961,U_2962)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2960) ),
    inference(clausify,[status(thm)],[f_913_4]) ).

cnf(f_913_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK25(U_2962,U_2961,U_2960))
    | ~ sP264(U_2958,U_2960,U_2961,U_2962) ),
    inference(clausify,[status(thm)],[f_913_4]) ).

cnf(f_913_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_2962),U_2958),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_2962),U_2961))),U_2960)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2958,U_2961)),sK25(U_2962,U_2961,U_2960))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2958,U_2961)))
    | ~ sP264(U_2958,U_2960,U_2961,U_2962) ),
    inference(clausify,[status(thm)],[f_913_4]) ).

fof(f_914_1,plain,
    ! [V_x,V_y] :
      ( ( c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x) )
      & ( c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x) ) ),
    inference(fof_nnf,[status(thm)],[fact_tsub__def]) ).

fof(f_914_2,plain,
    ! [U_2964,U_2963] :
      ( ( c_Nat__Transfer_Otsub(U_2964,U_2963) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2963,U_2964) )
      & ( c_Nat__Transfer_Otsub(U_2964,U_2963) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2964,U_2963)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2963,U_2964) ) ),
    inference(variable_rename,[status(thm)],[f_914_1]) ).

fof(f_914_3,plain,
    ( ! [U_2968,U_2966] :
        ( c_Nat__Transfer_Otsub(U_2968,U_2966) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2966,U_2968) )
    & ! [U_2967,U_2965] :
        ( c_Nat__Transfer_Otsub(U_2967,U_2965) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2967,U_2965)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2965,U_2967) ) ),
    inference(miniscope,[status(thm)],[f_914_2]) ).

fof(f_914_4,plain,
    ( ! [U_2966,U_2968] :
        ( c_Nat__Transfer_Otsub(U_2968,U_2966) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2966,U_2968) )
    & ! [U_2967,U_2965] :
        ( c_Nat__Transfer_Otsub(U_2967,U_2965) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2967,U_2965)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2965,U_2967) ) ),
    inference(definitional_conversion,[status(esa)],[f_914_3]) ).

cnf(f_914_5,plain,
    ( c_Nat__Transfer_Otsub(U_2967,U_2965) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2967,U_2965)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2965,U_2967) ),
    inference(clausify,[status(thm)],[f_914_4]) ).

cnf(f_914_6,plain,
    ( c_Nat__Transfer_Otsub(U_2968,U_2966) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2966,U_2968) ),
    inference(clausify,[status(thm)],[f_914_4]) ).

fof(f_915_1,plain,
    ! [V_x,V_n] :
      ( c_RComplete_Onatceiling(V_x) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x) ),
    inference(fof_nnf,[status(thm)],[fact_natceiling__eq]) ).

fof(f_915_2,plain,
    ! [U_2970,U_2969] :
      ( c_RComplete_Onatceiling(U_2970) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2969,c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2970,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2969),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2969),U_2970) ),
    inference(variable_rename,[status(thm)],[f_915_1]) ).

fof(f_915_3,plain,
    ! [U_2970,U_2969] :
      ( c_RComplete_Onatceiling(U_2970) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2969,c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2970,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2969),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2969),U_2970) ),
    inference(definitional_conversion,[status(esa)],[f_915_2]) ).

cnf(f_915_4,plain,
    ( c_RComplete_Onatceiling(U_2970) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2969,c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2970,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2969),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2969),U_2970) ),
    inference(clausify,[status(thm)],[f_915_3]) ).

fof(f_916_1,plain,
    ! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__ge__zero]) ).

fof(f_916_2,plain,
    ! [U_2971] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2971)),
    inference(variable_rename,[status(thm)],[f_916_1]) ).

fof(f_916_3,plain,
    ! [U_2971] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2971)),
    inference(definitional_conversion,[status(esa)],[f_916_2]) ).

cnf(f_916_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2971)),
    inference(clausify,[status(thm)],[f_916_3]) ).

fof(f_917_1,plain,
    ! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__power]) ).

fof(f_917_2,plain,
    ! [U_2973,U_2972] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2972),U_2973)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2972)),U_2973),
    inference(variable_rename,[status(thm)],[f_917_1]) ).

fof(f_917_3,plain,
    ! [U_2972,U_2973] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2972),U_2973)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2972)),U_2973),
    inference(definitional_conversion,[status(esa)],[f_917_2]) ).

cnf(f_917_4,plain,
    c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2972),U_2973)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2972)),U_2973),
    inference(clausify,[status(thm)],[f_917_3]) ).

fof(f_918_1,plain,
    ! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)),
    inference(fof_nnf,[status(thm)],[fact_power__real__of__nat]) ).

fof(f_918_2,plain,
    ! [U_2975,U_2974] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2974)),U_2975) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2974),U_2975)),
    inference(variable_rename,[status(thm)],[f_918_1]) ).

fof(f_918_3,plain,
    ! [U_2974,U_2975] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2974)),U_2975) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2974),U_2975)),
    inference(definitional_conversion,[status(esa)],[f_918_2]) ).

cnf(f_918_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2974)),U_2975) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2974),U_2975)),
    inference(clausify,[status(thm)],[f_918_3]) ).

fof(f_919_1,plain,
    ! [V_n_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__le__zero__cancel__iff]) ).

fof(f_919_2,plain,
    ! [U_2976] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2976),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | U_2976 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_2976 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2976),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
    inference(variable_rename,[status(thm)],[f_919_1]) ).

fof(f_919_3,plain,
    ( ! [U_2978] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2978),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | U_2978 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2977] :
        ( U_2977 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2977),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
    inference(miniscope,[status(thm)],[f_919_2]) ).

fof(f_919_4,plain,
    ( ! [U_2978] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2978),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
        | U_2978 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_2977] :
        ( U_2977 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2977),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
    inference(definitional_conversion,[status(esa)],[f_919_3]) ).

cnf(f_919_5,plain,
    ( U_2977 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2977),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
    inference(clausify,[status(thm)],[f_919_4]) ).

cnf(f_919_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2978),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
    | U_2978 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_919_4]) ).

fof(f_920_1,plain,
    ! [V_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__Suc__gt__zero]) ).

fof(f_920_2,plain,
    ! [U_2979] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2979))),
    inference(variable_rename,[status(thm)],[f_920_1]) ).

fof(f_920_3,plain,
    ! [U_2979] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2979))),
    inference(definitional_conversion,[status(esa)],[f_920_2]) ).

cnf(f_920_4,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2979))),
    inference(clausify,[status(thm)],[f_920_3]) ).

fof(f_921_1,plain,
    c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__one]) ).

fof(f_921_2,plain,
    c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_921_1]) ).

cnf(f_921_3,plain,
    c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_921_2]) ).

fof(f_922_1,plain,
    c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__1]) ).

fof(f_922_2,plain,
    c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_922_1]) ).

cnf(f_922_3,plain,
    c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_922_2]) ).

fof(f_923_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__less__iff]) ).

fof(f_923_2,plain,
    ! [U_2981,U_2980] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2980),c_RealDef_Oreal(tc_Nat_Onat,U_2981))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2980,U_2981) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2980,U_2981)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2980),c_RealDef_Oreal(tc_Nat_Onat,U_2981)) ) ),
    inference(variable_rename,[status(thm)],[f_923_1]) ).

fof(f_923_3,plain,
    ( ! [U_2985,U_2983] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2983),c_RealDef_Oreal(tc_Nat_Onat,U_2985))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2983,U_2985) )
    & ! [U_2984,U_2982] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2982,U_2984)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2982),c_RealDef_Oreal(tc_Nat_Onat,U_2984)) ) ),
    inference(miniscope,[status(thm)],[f_923_2]) ).

fof(f_923_4,plain,
    ( ! [U_2983,U_2985] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2983),c_RealDef_Oreal(tc_Nat_Onat,U_2985))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2983,U_2985) )
    & ! [U_2984,U_2982] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2982,U_2984)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2982),c_RealDef_Oreal(tc_Nat_Onat,U_2984)) ) ),
    inference(definitional_conversion,[status(esa)],[f_923_3]) ).

cnf(f_923_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2982,U_2984)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2982),c_RealDef_Oreal(tc_Nat_Onat,U_2984)) ),
    inference(clausify,[status(thm)],[f_923_4]) ).

cnf(f_923_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2983),c_RealDef_Oreal(tc_Nat_Onat,U_2985))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2983,U_2985) ),
    inference(clausify,[status(thm)],[f_923_4]) ).

fof(f_924_1,plain,
    ! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__add]) ).

fof(f_924_2,plain,
    ! [U_2987,U_2986] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2986,U_2987)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2986),c_RealDef_Oreal(tc_Nat_Onat,U_2987)),
    inference(variable_rename,[status(thm)],[f_924_1]) ).

fof(f_924_3,plain,
    ! [U_2987,U_2986] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2986,U_2987)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2986),c_RealDef_Oreal(tc_Nat_Onat,U_2987)),
    inference(definitional_conversion,[status(esa)],[f_924_2]) ).

cnf(f_924_4,plain,
    c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2986,U_2987)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2986),c_RealDef_Oreal(tc_Nat_Onat,U_2987)),
    inference(clausify,[status(thm)],[f_924_3]) ).

fof(f_925_1,plain,
    ! [V_n] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n,
    inference(fof_nnf,[status(thm)],[fact_natfloor__real__of__nat]) ).

fof(f_925_2,plain,
    ! [U_2988] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,U_2988)) = U_2988,
    inference(variable_rename,[status(thm)],[f_925_1]) ).

fof(f_925_3,plain,
    ! [U_2988] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,U_2988)) = U_2988,
    inference(definitional_conversion,[status(esa)],[f_925_2]) ).

cnf(f_925_4,plain,
    c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,U_2988)) = U_2988,
    inference(clausify,[status(thm)],[f_925_3]) ).

fof(f_926_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_RealDef_Oreal(tc_Nat_Onat,V_m_2)
        | V_n_2 != V_m_2 )
      & ( V_n_2 = V_m_2
        | c_RealDef_Oreal(tc_Nat_Onat,V_n_2) != c_RealDef_Oreal(tc_Nat_Onat,V_m_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__inject]) ).

fof(f_926_2,plain,
    ! [U_2990,U_2989] :
      ( ( c_RealDef_Oreal(tc_Nat_Onat,U_2989) = c_RealDef_Oreal(tc_Nat_Onat,U_2990)
        | U_2989 != U_2990 )
      & ( U_2989 = U_2990
        | c_RealDef_Oreal(tc_Nat_Onat,U_2989) != c_RealDef_Oreal(tc_Nat_Onat,U_2990) ) ),
    inference(variable_rename,[status(thm)],[f_926_1]) ).

fof(f_926_3,plain,
    ( ! [U_2994,U_2992] :
        ( c_RealDef_Oreal(tc_Nat_Onat,U_2992) = c_RealDef_Oreal(tc_Nat_Onat,U_2994)
        | U_2992 != U_2994 )
    & ! [U_2993,U_2991] :
        ( U_2991 = U_2993
        | c_RealDef_Oreal(tc_Nat_Onat,U_2991) != c_RealDef_Oreal(tc_Nat_Onat,U_2993) ) ),
    inference(miniscope,[status(thm)],[f_926_2]) ).

fof(f_926_4,plain,
    ( ! [U_2992,U_2994] :
        ( c_RealDef_Oreal(tc_Nat_Onat,U_2992) = c_RealDef_Oreal(tc_Nat_Onat,U_2994)
        | U_2992 != U_2994 )
    & ! [U_2993,U_2991] :
        ( U_2991 = U_2993
        | c_RealDef_Oreal(tc_Nat_Onat,U_2991) != c_RealDef_Oreal(tc_Nat_Onat,U_2993) ) ),
    inference(definitional_conversion,[status(esa)],[f_926_3]) ).

cnf(f_926_5,plain,
    ( U_2991 = U_2993
    | c_RealDef_Oreal(tc_Nat_Onat,U_2991) != c_RealDef_Oreal(tc_Nat_Onat,U_2993) ),
    inference(clausify,[status(thm)],[f_926_4]) ).

cnf(f_926_6,plain,
    ( c_RealDef_Oreal(tc_Nat_Onat,U_2992) = c_RealDef_Oreal(tc_Nat_Onat,U_2994)
    | U_2992 != U_2994 ),
    inference(clausify,[status(thm)],[f_926_4]) ).

fof(f_927_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__le__iff]) ).

fof(f_927_2,plain,
    ! [U_2996,U_2995] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2995),c_RealDef_Oreal(tc_Nat_Onat,U_2996))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2995,U_2996) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2995,U_2996)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2995),c_RealDef_Oreal(tc_Nat_Onat,U_2996)) ) ),
    inference(variable_rename,[status(thm)],[f_927_1]) ).

fof(f_927_3,plain,
    ( ! [U_3000,U_2998] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2998),c_RealDef_Oreal(tc_Nat_Onat,U_3000))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2998,U_3000) )
    & ! [U_2999,U_2997] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2997,U_2999)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2997),c_RealDef_Oreal(tc_Nat_Onat,U_2999)) ) ),
    inference(miniscope,[status(thm)],[f_927_2]) ).

fof(f_927_4,plain,
    ( ! [U_2998,U_3000] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2998),c_RealDef_Oreal(tc_Nat_Onat,U_3000))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2998,U_3000) )
    & ! [U_2999,U_2997] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2997,U_2999)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2997),c_RealDef_Oreal(tc_Nat_Onat,U_2999)) ) ),
    inference(definitional_conversion,[status(esa)],[f_927_3]) ).

cnf(f_927_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2997,U_2999)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2997),c_RealDef_Oreal(tc_Nat_Onat,U_2999)) ),
    inference(clausify,[status(thm)],[f_927_4]) ).

cnf(f_927_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2998),c_RealDef_Oreal(tc_Nat_Onat,U_3000))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2998,U_3000) ),
    inference(clausify,[status(thm)],[f_927_4]) ).

fof(f_928_1,plain,
    ! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x))),
    inference(fof_nnf,[status(thm)],[fact_real__natceiling__ge]) ).

fof(f_928_2,plain,
    ! [U_3001] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_3001,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(U_3001))),
    inference(variable_rename,[status(thm)],[f_928_1]) ).

fof(f_928_3,plain,
    ! [U_3001] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_3001,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(U_3001))),
    inference(definitional_conversion,[status(esa)],[f_928_2]) ).

cnf(f_928_4,plain,
    c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_3001,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(U_3001))),
    inference(clausify,[status(thm)],[f_928_3]) ).

fof(f_929_1,plain,
    ! [V_n] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n,
    inference(fof_nnf,[status(thm)],[fact_natceiling__real__of__nat]) ).

fof(f_929_2,plain,
    ! [U_3002] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,U_3002)) = U_3002,
    inference(variable_rename,[status(thm)],[f_929_1]) ).

fof(f_929_3,plain,
    ! [U_3002] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,U_3002)) = U_3002,
    inference(definitional_conversion,[status(esa)],[f_929_2]) ).

cnf(f_929_4,plain,
    c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,U_3002)) = U_3002,
    inference(clausify,[status(thm)],[f_929_3]) ).

fof(f_930_1,plain,
    ! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n)),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__mult]) ).

fof(f_930_2,plain,
    ! [U_3004,U_3003] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3003),U_3004)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_3003)),c_RealDef_Oreal(tc_Nat_Onat,U_3004)),
    inference(variable_rename,[status(thm)],[f_930_1]) ).

fof(f_930_3,plain,
    ! [U_3003,U_3004] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3003),U_3004)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_3003)),c_RealDef_Oreal(tc_Nat_Onat,U_3004)),
    inference(definitional_conversion,[status(esa)],[f_930_2]) ).

cnf(f_930_4,plain,
    c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3003),U_3004)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_3003)),c_RealDef_Oreal(tc_Nat_Onat,U_3004)),
    inference(clausify,[status(thm)],[f_930_3]) ).

fof(f_931_1,plain,
    c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__zero]) ).

fof(f_931_2,plain,
    c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_931_1]) ).

cnf(f_931_3,plain,
    c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_931_2]) ).

fof(f_932_1,plain,
    ! [V_n_2] :
      ( ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_RealDef_Oreal(tc_Nat_Onat,V_n_2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__zero__iff]) ).

fof(f_932_2,plain,
    ! [U_3005] :
      ( ( c_RealDef_Oreal(tc_Nat_Onat,U_3005) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_3005 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_3005 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_RealDef_Oreal(tc_Nat_Onat,U_3005) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(variable_rename,[status(thm)],[f_932_1]) ).

fof(f_932_3,plain,
    ( ! [U_3007] :
        ( c_RealDef_Oreal(tc_Nat_Onat,U_3007) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_3007 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_3006] :
        ( U_3006 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_RealDef_Oreal(tc_Nat_Onat,U_3006) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(miniscope,[status(thm)],[f_932_2]) ).

fof(f_932_4,plain,
    ( ! [U_3007] :
        ( c_RealDef_Oreal(tc_Nat_Onat,U_3007) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
        | U_3007 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_3006] :
        ( U_3006 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_RealDef_Oreal(tc_Nat_Onat,U_3006) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
    inference(definitional_conversion,[status(esa)],[f_932_3]) ).

cnf(f_932_5,plain,
    ( U_3006 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_RealDef_Oreal(tc_Nat_Onat,U_3006) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
    inference(clausify,[status(thm)],[f_932_4]) ).

cnf(f_932_6,plain,
    ( c_RealDef_Oreal(tc_Nat_Onat,U_3007) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
    | U_3007 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_932_4]) ).

fof(f_933_1,plain,
    ! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(fof_nnf,[status(thm)],[fact_not__real__of__nat__less__zero]) ).

fof(f_933_2,plain,
    ! [U_3008] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3008),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(variable_rename,[status(thm)],[f_933_1]) ).

fof(f_933_3,plain,
    ! [U_3008] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3008),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(definitional_conversion,[status(esa)],[f_933_2]) ).

cnf(f_933_4,plain,
    ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3008),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
    inference(clausify,[status(thm)],[f_933_3]) ).

fof(f_934_1,plain,
    ! [V_a,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)) ),
    inference(fof_nnf,[status(thm)],[fact_natceiling__le]) ).

fof(f_934_2,plain,
    ! [U_3010,U_3009] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_3009),U_3010)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_3009,c_RealDef_Oreal(tc_Nat_Onat,U_3010)) ),
    inference(variable_rename,[status(thm)],[f_934_1]) ).

fof(f_934_3,plain,
    ! [U_3009,U_3010] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_3009),U_3010)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_3009,c_RealDef_Oreal(tc_Nat_Onat,U_3010)) ),
    inference(definitional_conversion,[status(esa)],[f_934_2]) ).

cnf(f_934_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_3009),U_3010)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_3009,c_RealDef_Oreal(tc_Nat_Onat,U_3010)) ),
    inference(clausify,[status(thm)],[f_934_3]) ).

fof(f_935_1,plain,
    ! [V_a,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a) ),
    inference(fof_nnf,[status(thm)],[fact_le__natfloor]) ).

fof(f_935_2,plain,
    ! [U_3012,U_3011] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3011,c_RComplete_Onatfloor(U_3012))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3011),U_3012) ),
    inference(variable_rename,[status(thm)],[f_935_1]) ).

fof(f_935_3,plain,
    ! [U_3011,U_3012] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3011,c_RComplete_Onatfloor(U_3012))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3011),U_3012) ),
    inference(definitional_conversion,[status(esa)],[f_935_2]) ).

cnf(f_935_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3011,c_RComplete_Onatfloor(U_3012))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3011),U_3012) ),
    inference(clausify,[status(thm)],[f_935_3]) ).

fof(f_936_1,plain,
    ! [V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_x)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
    inference(fof_nnf,[status(thm)],[fact_real__natfloor__le]) ).

fof(f_936_2,plain,
    ! [U_3013] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_3013)),U_3013)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3013) ),
    inference(variable_rename,[status(thm)],[f_936_1]) ).

fof(f_936_3,plain,
    ! [U_3013] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_3013)),U_3013)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3013) ),
    inference(definitional_conversion,[status(esa)],[f_936_2]) ).

cnf(f_936_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_3013)),U_3013)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3013) ),
    inference(clausify,[status(thm)],[f_936_3]) ).

fof(f_937_1,plain,
    ! [V_m,V_n] :
      ( c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__diff]) ).

fof(f_937_2,plain,
    ! [U_3015,U_3014] :
      ( c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3015,U_3014)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3015),c_RealDef_Oreal(tc_Nat_Onat,U_3014))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3014,U_3015) ),
    inference(variable_rename,[status(thm)],[f_937_1]) ).

fof(f_937_3,plain,
    ! [U_3014,U_3015] :
      ( c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3015,U_3014)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3015),c_RealDef_Oreal(tc_Nat_Onat,U_3014))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3014,U_3015) ),
    inference(definitional_conversion,[status(esa)],[f_937_2]) ).

cnf(f_937_4,plain,
    ( c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3015,U_3014)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3015),c_RealDef_Oreal(tc_Nat_Onat,U_3014))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3014,U_3015) ),
    inference(clausify,[status(thm)],[f_937_3]) ).

fof(f_938_1,plain,
    ! [V_n] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__Suc]) ).

fof(f_938_2,plain,
    ! [U_3016] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_3016)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3016),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(variable_rename,[status(thm)],[f_938_1]) ).

fof(f_938_3,plain,
    ! [U_3016] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_3016)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3016),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(definitional_conversion,[status(esa)],[f_938_2]) ).

cnf(f_938_4,plain,
    c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_3016)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3016),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
    inference(clausify,[status(thm)],[f_938_3]) ).

fof(f_939_1,plain,
    ! [V_n,V_x] :
      ( c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_n)
      | V_x != c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)) ),
    inference(fof_nnf,[status(thm)],[fact_natfloor__power]) ).

fof(f_939_2,plain,
    ! [U_3018,U_3017] :
      ( c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_3017),U_3018)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(U_3017)),U_3018)
      | U_3017 != c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_3017)) ),
    inference(variable_rename,[status(thm)],[f_939_1]) ).

fof(f_939_3,plain,
    ! [U_3017,U_3018] :
      ( c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_3017),U_3018)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(U_3017)),U_3018)
      | U_3017 != c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_3017)) ),
    inference(definitional_conversion,[status(esa)],[f_939_2]) ).

cnf(f_939_4,plain,
    ( c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_3017),U_3018)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(U_3017)),U_3018)
    | U_3017 != c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_3017)) ),
    inference(clausify,[status(thm)],[f_939_3]) ).

fof(f_940_1,plain,
    ! [V_n_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_real__of__nat__gt__zero__cancel__iff]) ).

fof(f_940_2,plain,
    ! [U_3019] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_3019))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3019) )
      & ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3019)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_3019)) ) ),
    inference(variable_rename,[status(thm)],[f_940_1]) ).

fof(f_940_3,plain,
    ( ! [U_3021] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_3021))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3021) )
    & ! [U_3020] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3020)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_3020)) ) ),
    inference(miniscope,[status(thm)],[f_940_2]) ).

fof(f_940_4,plain,
    ( ! [U_3021] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_3021))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3021) )
    & ! [U_3020] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3020)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_3020)) ) ),
    inference(definitional_conversion,[status(esa)],[f_940_3]) ).

cnf(f_940_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3020)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_3020)) ),
    inference(clausify,[status(thm)],[f_940_4]) ).

cnf(f_940_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_3021))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3021) ),
    inference(clausify,[status(thm)],[f_940_4]) ).

fof(f_941_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2)) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_m_2))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__less__real__le]) ).

fof(f_941_2,plain,
    ! [U_3023,U_3022] :
      ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3022,U_3023)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3022),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_3023)) )
      & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3022),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_3023))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3022,U_3023) ) ),
    inference(variable_rename,[status(thm)],[f_941_1]) ).

fof(f_941_3,plain,
    ( ! [U_3027,U_3025] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3025,U_3027)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3025),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_3027)) )
    & ! [U_3026,U_3024] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3024),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_3026))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3024,U_3026) ) ),
    inference(miniscope,[status(thm)],[f_941_2]) ).

fof(f_941_4,plain,
    ( ! [U_3025,U_3027] :
        ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3025,U_3027)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3025),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_3027)) )
    & ! [U_3024,U_3026] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3024),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_3026))
        | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3024,U_3026) ) ),
    inference(definitional_conversion,[status(esa)],[f_941_3]) ).

cnf(f_941_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3024),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_3026))
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3024,U_3026) ),
    inference(clausify,[status(thm)],[f_941_4]) ).

cnf(f_941_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3025,U_3027)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3025),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_3027)) ),
    inference(clausify,[status(thm)],[f_941_4]) ).

fof(f_942_1,plain,
    ! [V_m_2,V_n_2] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_m_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_nat__le__real__less]) ).

fof(f_942_2,plain,
    ! [U_3029,U_3028] :
      ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3028,U_3029)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3028),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3029),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
      & ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3028),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3029),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3028,U_3029) ) ),
    inference(variable_rename,[status(thm)],[f_942_1]) ).

fof(f_942_3,plain,
    ( ! [U_3033,U_3031] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3031,U_3033)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3031),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3033),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
    & ! [U_3032,U_3030] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3030),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3032),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3030,U_3032) ) ),
    inference(miniscope,[status(thm)],[f_942_2]) ).

fof(f_942_4,plain,
    ( ! [U_3031,U_3033] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3031,U_3033)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3031),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3033),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
    & ! [U_3032,U_3030] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3030),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3032),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3030,U_3032) ) ),
    inference(definitional_conversion,[status(esa)],[f_942_3]) ).

cnf(f_942_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3030),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3032),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3030,U_3032) ),
    inference(clausify,[status(thm)],[f_942_4]) ).

cnf(f_942_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3031,U_3033)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3031),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3033),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
    inference(clausify,[status(thm)],[f_942_4]) ).

fof(f_943_1,plain,
    ! [V_ab_2,V_x_2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ab_2,c_RComplete_Onatfloor(V_x_2))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_ab_2),V_x_2) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_ab_2),V_x_2)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ab_2,c_RComplete_Onatfloor(V_x_2)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
    inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq]) ).

fof(f_943_2,plain,
    ! [U_3035,U_3034] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3035,c_RComplete_Onatfloor(U_3034))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3035),U_3034) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3035),U_3034)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3035,c_RComplete_Onatfloor(U_3034)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3034) ),
    inference(variable_rename,[status(thm)],[f_943_1]) ).

fof(f_943_3,plain,
    ( ! [U_3034,U_3035] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3035,c_RComplete_Onatfloor(U_3034))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3035),U_3034)
        | ~ sP265(U_3034,U_3035) )
    & ! [U_3034,U_3035] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3035),U_3034)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3035,c_RComplete_Onatfloor(U_3034))
        | ~ sP265(U_3034,U_3035) )
    & ! [U_3034,U_3035] :
        ( sP265(U_3034,U_3035)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3034) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP265])],[f_943_2]) ).

cnf(f_943_4,plain,
    ( sP265(U_3034,U_3035)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3034) ),
    inference(clausify,[status(thm)],[f_943_3]) ).

cnf(f_943_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3035),U_3034)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3035,c_RComplete_Onatfloor(U_3034))
    | ~ sP265(U_3034,U_3035) ),
    inference(clausify,[status(thm)],[f_943_3]) ).

cnf(f_943_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3035,c_RComplete_Onatfloor(U_3034))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3035),U_3034)
    | ~ sP265(U_3034,U_3035) ),
    inference(clausify,[status(thm)],[f_943_3]) ).

fof(f_944_1,plain,
    ! [V_ab_2,V_x_2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_ab_2)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_ab_2)) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_ab_2))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_ab_2) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
    inference(fof_nnf,[status(thm)],[fact_natceiling__le__eq]) ).

fof(f_944_2,plain,
    ! [U_3037,U_3036] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_3036),U_3037)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_3036,c_RealDef_Oreal(tc_Nat_Onat,U_3037)) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_3036,c_RealDef_Oreal(tc_Nat_Onat,U_3037))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_3036),U_3037) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3036) ),
    inference(variable_rename,[status(thm)],[f_944_1]) ).

fof(f_944_3,plain,
    ( ! [U_3037,U_3036] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_3036),U_3037)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_3036,c_RealDef_Oreal(tc_Nat_Onat,U_3037))
        | ~ sP266(U_3037,U_3036) )
    & ! [U_3037,U_3036] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_3036,c_RealDef_Oreal(tc_Nat_Onat,U_3037))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_3036),U_3037)
        | ~ sP266(U_3037,U_3036) )
    & ! [U_3037,U_3036] :
        ( sP266(U_3037,U_3036)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3036) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP266])],[f_944_2]) ).

cnf(f_944_4,plain,
    ( sP266(U_3037,U_3036)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3036) ),
    inference(clausify,[status(thm)],[f_944_3]) ).

cnf(f_944_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_3036,c_RealDef_Oreal(tc_Nat_Onat,U_3037))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_3036),U_3037)
    | ~ sP266(U_3037,U_3036) ),
    inference(clausify,[status(thm)],[f_944_3]) ).

cnf(f_944_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_3036),U_3037)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_3036,c_RealDef_Oreal(tc_Nat_Onat,U_3037))
    | ~ sP266(U_3037,U_3036) ),
    inference(clausify,[status(thm)],[f_944_3]) ).

fof(f_945_1,plain,
    ! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
    inference(fof_nnf,[status(thm)],[fact_real__natfloor__add__one__gt]) ).

fof(f_945_2,plain,
    ! [U_3038] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_3038,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_3038)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
    inference(variable_rename,[status(thm)],[f_945_1]) ).

fof(f_945_3,plain,
    ! [U_3038] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_3038,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_3038)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
    inference(definitional_conversion,[status(esa)],[f_945_2]) ).

cnf(f_945_4,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_3038,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_3038)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
    inference(clausify,[status(thm)],[f_945_3]) ).

fof(f_946_1,plain,
    ! [V_x,V_a] :
      ( c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x) ),
    inference(fof_nnf,[status(thm)],[fact_natfloor__subtract]) ).

fof(f_946_2,plain,
    ! [U_3040,U_3039] :
      ( c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3040,c_RealDef_Oreal(tc_Nat_Onat,U_3039))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(U_3040),U_3039)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3039),U_3040) ),
    inference(variable_rename,[status(thm)],[f_946_1]) ).

fof(f_946_3,plain,
    ! [U_3040,U_3039] :
      ( c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3040,c_RealDef_Oreal(tc_Nat_Onat,U_3039))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(U_3040),U_3039)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3039),U_3040) ),
    inference(definitional_conversion,[status(esa)],[f_946_2]) ).

cnf(f_946_4,plain,
    ( c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3040,c_RealDef_Oreal(tc_Nat_Onat,U_3039))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(U_3040),U_3039)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3039),U_3040) ),
    inference(clausify,[status(thm)],[f_946_3]) ).

fof(f_947_1,plain,
    ! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))),
    inference(fof_nnf,[status(thm)],[fact_real__natfloor__gt__diff__one]) ).

fof(f_947_2,plain,
    ! [U_3041] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3041,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_3041))),
    inference(variable_rename,[status(thm)],[f_947_1]) ).

fof(f_947_3,plain,
    ! [U_3041] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3041,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_3041))),
    inference(definitional_conversion,[status(esa)],[f_947_2]) ).

cnf(f_947_4,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3041,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_3041))),
    inference(clausify,[status(thm)],[f_947_3]) ).

fof(f_948_1,plain,
    ! [V_x,V_a] :
      ( c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x) ),
    inference(fof_nnf,[status(thm)],[fact_natceiling__subtract]) ).

fof(f_948_2,plain,
    ! [U_3043,U_3042] :
      ( c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3043,c_RealDef_Oreal(tc_Nat_Onat,U_3042))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(U_3043),U_3042)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3042),U_3043) ),
    inference(variable_rename,[status(thm)],[f_948_1]) ).

fof(f_948_3,plain,
    ! [U_3042,U_3043] :
      ( c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3043,c_RealDef_Oreal(tc_Nat_Onat,U_3042))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(U_3043),U_3042)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3042),U_3043) ),
    inference(definitional_conversion,[status(esa)],[f_948_2]) ).

cnf(f_948_4,plain,
    ( c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3043,c_RealDef_Oreal(tc_Nat_Onat,U_3042))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(U_3043),U_3042)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3042),U_3043) ),
    inference(clausify,[status(thm)],[f_948_3]) ).

fof(f_949_1,plain,
    ! [V_y,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(V_x,V_y))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_y)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) ),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J]) ).

fof(f_949_2,plain,
    ! [U_3045,U_3044] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(U_3044,U_3045))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3045)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3044) ),
    inference(variable_rename,[status(thm)],[f_949_1]) ).

fof(f_949_3,plain,
    ! [U_3044,U_3045] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(U_3044,U_3045))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3045)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3044) ),
    inference(definitional_conversion,[status(esa)],[f_949_2]) ).

cnf(f_949_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(U_3044,U_3045))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3045)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3044) ),
    inference(clausify,[status(thm)],[f_949_3]) ).

fof(f_950_1,plain,
    ! [V_n,V_x] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
    inference(fof_nnf,[status(thm)],[fact_less__natfloor]) ).

fof(f_950_2,plain,
    ! [U_3047,U_3046] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(U_3046),U_3047)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_3046,c_RealDef_Oreal(tc_Nat_Onat,U_3047))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3046) ),
    inference(variable_rename,[status(thm)],[f_950_1]) ).

fof(f_950_3,plain,
    ! [U_3047,U_3046] :
      ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(U_3046),U_3047)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_3046,c_RealDef_Oreal(tc_Nat_Onat,U_3047))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3046) ),
    inference(definitional_conversion,[status(esa)],[f_950_2]) ).

cnf(f_950_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(U_3046),U_3047)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_3046,c_RealDef_Oreal(tc_Nat_Onat,U_3047))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3046) ),
    inference(clausify,[status(thm)],[f_950_3]) ).

fof(f_951_1,plain,
    ! [V_x,V_y] :
      ( c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x) ),
    inference(fof_nnf,[status(thm)],[fact_tsub__eq]) ).

fof(f_951_2,plain,
    ! [U_3049,U_3048] :
      ( c_Nat__Transfer_Otsub(U_3049,U_3048) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_3049,U_3048)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3048,U_3049) ),
    inference(variable_rename,[status(thm)],[f_951_1]) ).

fof(f_951_3,plain,
    ! [U_3049,U_3048] :
      ( c_Nat__Transfer_Otsub(U_3049,U_3048) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_3049,U_3048)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3048,U_3049) ),
    inference(definitional_conversion,[status(esa)],[f_951_2]) ).

cnf(f_951_4,plain,
    ( c_Nat__Transfer_Otsub(U_3049,U_3048) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_3049,U_3048)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3048,U_3049) ),
    inference(clausify,[status(thm)],[f_951_3]) ).

fof(f_952_1,plain,
    ! [V_a,V_x] :
      ( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
    inference(fof_nnf,[status(thm)],[fact_natfloor__add]) ).

fof(f_952_2,plain,
    ! [U_3051,U_3050] :
      ( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_3050,c_RealDef_Oreal(tc_Nat_Onat,U_3051))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_3050),U_3051)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3050) ),
    inference(variable_rename,[status(thm)],[f_952_1]) ).

fof(f_952_3,plain,
    ! [U_3050,U_3051] :
      ( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_3050,c_RealDef_Oreal(tc_Nat_Onat,U_3051))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_3050),U_3051)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3050) ),
    inference(definitional_conversion,[status(esa)],[f_952_2]) ).

cnf(f_952_4,plain,
    ( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_3050,c_RealDef_Oreal(tc_Nat_Onat,U_3051))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_3050),U_3051)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3050) ),
    inference(clausify,[status(thm)],[f_952_3]) ).

fof(f_953_1,plain,
    ! [V_n,V_z] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,c_RealDef_Oreal(tc_Nat_Onat,V_n))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_z),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ),
    inference(fof_nnf,[status(thm)],[fact_ge__natfloor__plus__one__imp__gt]) ).

fof(f_953_2,plain,
    ! [U_3053,U_3052] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_3052,c_RealDef_Oreal(tc_Nat_Onat,U_3053))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_3052),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3053) ),
    inference(variable_rename,[status(thm)],[f_953_1]) ).

fof(f_953_3,plain,
    ! [U_3053,U_3052] :
      ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_3052,c_RealDef_Oreal(tc_Nat_Onat,U_3053))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_3052),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3053) ),
    inference(definitional_conversion,[status(esa)],[f_953_2]) ).

cnf(f_953_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_3052,c_RealDef_Oreal(tc_Nat_Onat,U_3053))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_3052),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3053) ),
    inference(clausify,[status(thm)],[f_953_3]) ).

fof(f_954_1,plain,
    ! [V_x,V_n] :
      ( c_RComplete_Onatfloor(V_x) = V_n
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x) ),
    inference(fof_nnf,[status(thm)],[fact_natfloor__eq]) ).

fof(f_954_2,plain,
    ! [U_3055,U_3054] :
      ( c_RComplete_Onatfloor(U_3055) = U_3054
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_3055,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3054),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3054),U_3055) ),
    inference(variable_rename,[status(thm)],[f_954_1]) ).

fof(f_954_3,plain,
    ! [U_3054,U_3055] :
      ( c_RComplete_Onatfloor(U_3055) = U_3054
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_3055,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3054),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3054),U_3055) ),
    inference(definitional_conversion,[status(esa)],[f_954_2]) ).

cnf(f_954_4,plain,
    ( c_RComplete_Onatfloor(U_3055) = U_3054
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_3055,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3054),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3054),U_3055) ),
    inference(clausify,[status(thm)],[f_954_3]) ).

fof(f_955_1,plain,
    ! [V_a,V_x] :
      ( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
    inference(fof_nnf,[status(thm)],[fact_natceiling__add]) ).

fof(f_955_2,plain,
    ! [U_3057,U_3056] :
      ( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_3056,c_RealDef_Oreal(tc_Nat_Onat,U_3057))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_3056),U_3057)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3056) ),
    inference(variable_rename,[status(thm)],[f_955_1]) ).

fof(f_955_3,plain,
    ! [U_3057,U_3056] :
      ( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_3056,c_RealDef_Oreal(tc_Nat_Onat,U_3057))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_3056),U_3057)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3056) ),
    inference(definitional_conversion,[status(esa)],[f_955_2]) ).

cnf(f_955_4,plain,
    ( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_3056,c_RealDef_Oreal(tc_Nat_Onat,U_3057))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_3056),U_3057)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3056) ),
    inference(clausify,[status(thm)],[f_955_3]) ).

fof(f_956_1,plain,
    ! [V_n,V_x] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ),
    inference(fof_nnf,[status(thm)],[fact_LIMSEQ__inverse__realpow__zero__lemma]) ).

fof(f_956_2,plain,
    ! [U_3059,U_3058] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_3059)),U_3058),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_3058,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),U_3059))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3058) ),
    inference(variable_rename,[status(thm)],[f_956_1]) ).

fof(f_956_3,plain,
    ! [U_3059,U_3058] :
      ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_3059)),U_3058),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_3058,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),U_3059))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3058) ),
    inference(definitional_conversion,[status(esa)],[f_956_2]) ).

cnf(f_956_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_3059)),U_3058),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_3058,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),U_3059))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3058) ),
    inference(clausify,[status(thm)],[f_956_3]) ).

fof(f_957_1,plain,
    ! [V_X_2,T_b] :
      ( ( ( ? [B_K] :
              ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K)
              & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
          | ! [B_N] :
            ? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) )
        & ( ? [B_N] :
            ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))
          | ! [B_K] :
              ( ? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ) )
      | ~ class_RealVector_Oreal__normed__vector(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_lemma__NBseq__def]) ).

fof(f_957_2,plain,
    ! [U_3069,U_3068] :
      ( ( ( ? [U_3067] :
              ( ! [U_3066] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,U_3066)),U_3067)
              & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3067) )
          | ! [U_3065] :
            ? [U_3064] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,U_3064)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_3065))) )
        & ( ? [U_3063] :
            ! [U_3062] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,U_3062)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_3063)))
          | ! [U_3061] :
              ( ? [U_3060] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,U_3060)),U_3061)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3061) ) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_3068) ),
    inference(variable_rename,[status(thm)],[f_957_1]) ).

fof(f_957_3,plain,
    ! [U_3069,U_3068] :
      ( ( ( ? [U_3067] :
              ( ! [U_3066] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,U_3066)),U_3067)
              & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3067) )
          | ! [U_3065] :
            ? [U_3064] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,U_3064)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_3065))) )
        & ( ? [U_3063] :
            ! [U_3062] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,U_3062)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_3063)))
          | ! [U_3061] :
              ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,sK26(U_3069,U_3068,U_3061))),U_3061)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3061) ) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_3068) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_3060,sK26(U_3069,U_3068,U_3061))],[f_957_2]) ).

fof(f_957_4,plain,
    ! [U_3069,U_3068] :
      ( ( ( ? [U_3067] :
              ( ! [U_3066] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,U_3066)),U_3067)
              & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3067) )
          | ! [U_3065] :
            ? [U_3064] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,U_3064)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_3065))) )
        & ( ! [U_3062] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,U_3062)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK27(U_3069,U_3068))))
          | ! [U_3061] :
              ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,sK26(U_3069,U_3068,U_3061))),U_3061)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3061) ) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_3068) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_3063,sK27(U_3069,U_3068))],[f_957_3]) ).

fof(f_957_5,plain,
    ! [U_3069,U_3068] :
      ( ( ( ? [U_3067] :
              ( ! [U_3066] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,U_3066)),U_3067)
              & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3067) )
          | ! [U_3065] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,sK28(U_3069,U_3068,U_3065))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_3065))) )
        & ( ! [U_3062] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,U_3062)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK27(U_3069,U_3068))))
          | ! [U_3061] :
              ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,sK26(U_3069,U_3068,U_3061))),U_3061)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3061) ) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_3068) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_3064,sK28(U_3069,U_3068,U_3065))],[f_957_4]) ).

fof(f_957_6,plain,
    ! [U_3069,U_3068] :
      ( ( ( ( ! [U_3066] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,U_3066)),sK29(U_3069,U_3068))
            & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK29(U_3069,U_3068)) )
          | ! [U_3065] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,sK28(U_3069,U_3068,U_3065))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_3065))) )
        & ( ! [U_3062] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,U_3062)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK27(U_3069,U_3068))))
          | ! [U_3061] :
              ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,sK26(U_3069,U_3068,U_3061))),U_3061)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3061) ) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_3068) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_3067,sK29(U_3069,U_3068))],[f_957_5]) ).

fof(f_957_7,plain,
    ( ! [U_3066,U_3068,U_3069] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,U_3066)),sK29(U_3069,U_3068))
        | ~ sP267(U_3066,U_3068,U_3069) )
    & ! [U_3066,U_3068,U_3069] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK29(U_3069,U_3068))
        | ~ sP267(U_3066,U_3068,U_3069) )
    & ! [U_3061,U_3062,U_3065,U_3066,U_3068,U_3069] :
        ( sP267(U_3066,U_3068,U_3069)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,sK28(U_3069,U_3068,U_3065))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_3065)))
        | ~ sP268(U_3061,U_3062,U_3065,U_3066,U_3068,U_3069) )
    & ! [U_3061,U_3062,U_3065,U_3066,U_3068,U_3069] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,U_3062)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK27(U_3069,U_3068))))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,sK26(U_3069,U_3068,U_3061))),U_3061)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3061)
        | ~ sP268(U_3061,U_3062,U_3065,U_3066,U_3068,U_3069) )
    & ! [U_3061,U_3062,U_3065,U_3066,U_3068,U_3069] :
        ( sP268(U_3061,U_3062,U_3065,U_3066,U_3068,U_3069)
        | ~ class_RealVector_Oreal__normed__vector(U_3068) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP267,sP268])],[f_957_6]) ).

cnf(f_957_8,plain,
    ( sP268(U_3061,U_3062,U_3065,U_3066,U_3068,U_3069)
    | ~ class_RealVector_Oreal__normed__vector(U_3068) ),
    inference(clausify,[status(thm)],[f_957_7]) ).

cnf(f_957_9,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,U_3062)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK27(U_3069,U_3068))))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,sK26(U_3069,U_3068,U_3061))),U_3061)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3061)
    | ~ sP268(U_3061,U_3062,U_3065,U_3066,U_3068,U_3069) ),
    inference(clausify,[status(thm)],[f_957_7]) ).

cnf(f_957_10,plain,
    ( sP267(U_3066,U_3068,U_3069)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,sK28(U_3069,U_3068,U_3065))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_3065)))
    | ~ sP268(U_3061,U_3062,U_3065,U_3066,U_3068,U_3069) ),
    inference(clausify,[status(thm)],[f_957_7]) ).

cnf(f_957_11,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK29(U_3069,U_3068))
    | ~ sP267(U_3066,U_3068,U_3069) ),
    inference(clausify,[status(thm)],[f_957_7]) ).

cnf(f_957_12,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3068,hAPP(U_3069,U_3066)),sK29(U_3069,U_3068))
    | ~ sP267(U_3066,U_3068,U_3069) ),
    inference(clausify,[status(thm)],[f_957_7]) ).

fof(f_958_1,plain,
    ! [V_X_2,T_b] :
      ( ( ( ? [B_K] :
              ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K)
              & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
          | ! [B_N] :
            ? [B_n] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) )
        & ( ? [B_N] :
            ! [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))
          | ! [B_K] :
              ( ? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ) )
      | ~ class_RealVector_Oreal__normed__vector(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_lemma__NBseq__def2]) ).

fof(f_958_2,plain,
    ! [U_3079,U_3078] :
      ( ( ( ? [U_3077] :
              ( ! [U_3076] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,U_3076)),U_3077)
              & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3077) )
          | ! [U_3075] :
            ? [U_3074] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,U_3074)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_3075))) )
        & ( ? [U_3073] :
            ! [U_3072] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,U_3072)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_3073)))
          | ! [U_3071] :
              ( ? [U_3070] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,U_3070)),U_3071)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3071) ) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_3078) ),
    inference(variable_rename,[status(thm)],[f_958_1]) ).

fof(f_958_3,plain,
    ! [U_3079,U_3078] :
      ( ( ( ? [U_3077] :
              ( ! [U_3076] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,U_3076)),U_3077)
              & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3077) )
          | ! [U_3075] :
            ? [U_3074] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,U_3074)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_3075))) )
        & ( ? [U_3073] :
            ! [U_3072] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,U_3072)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_3073)))
          | ! [U_3071] :
              ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,sK30(U_3079,U_3078,U_3071))),U_3071)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3071) ) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_3078) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_3070,sK30(U_3079,U_3078,U_3071))],[f_958_2]) ).

fof(f_958_4,plain,
    ! [U_3079,U_3078] :
      ( ( ( ? [U_3077] :
              ( ! [U_3076] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,U_3076)),U_3077)
              & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3077) )
          | ! [U_3075] :
            ? [U_3074] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,U_3074)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_3075))) )
        & ( ! [U_3072] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,U_3072)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK31(U_3079,U_3078))))
          | ! [U_3071] :
              ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,sK30(U_3079,U_3078,U_3071))),U_3071)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3071) ) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_3078) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_3073,sK31(U_3079,U_3078))],[f_958_3]) ).

fof(f_958_5,plain,
    ! [U_3079,U_3078] :
      ( ( ( ? [U_3077] :
              ( ! [U_3076] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,U_3076)),U_3077)
              & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3077) )
          | ! [U_3075] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,sK32(U_3079,U_3078,U_3075))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_3075))) )
        & ( ! [U_3072] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,U_3072)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK31(U_3079,U_3078))))
          | ! [U_3071] :
              ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,sK30(U_3079,U_3078,U_3071))),U_3071)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3071) ) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_3078) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_3074,sK32(U_3079,U_3078,U_3075))],[f_958_4]) ).

fof(f_958_6,plain,
    ! [U_3079,U_3078] :
      ( ( ( ( ! [U_3076] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,U_3076)),sK33(U_3079,U_3078))
            & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK33(U_3079,U_3078)) )
          | ! [U_3075] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,sK32(U_3079,U_3078,U_3075))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_3075))) )
        & ( ! [U_3072] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,U_3072)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK31(U_3079,U_3078))))
          | ! [U_3071] :
              ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,sK30(U_3079,U_3078,U_3071))),U_3071)
              | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3071) ) ) )
      | ~ class_RealVector_Oreal__normed__vector(U_3078) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_3077,sK33(U_3079,U_3078))],[f_958_5]) ).

fof(f_958_7,plain,
    ( ! [U_3076,U_3079,U_3078] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,U_3076)),sK33(U_3079,U_3078))
        | ~ sP269(U_3076,U_3079,U_3078) )
    & ! [U_3076,U_3079,U_3078] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK33(U_3079,U_3078))
        | ~ sP269(U_3076,U_3079,U_3078) )
    & ! [U_3072,U_3076,U_3079,U_3078,U_3071,U_3075] :
        ( sP269(U_3076,U_3079,U_3078)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,sK32(U_3079,U_3078,U_3075))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_3075)))
        | ~ sP270(U_3072,U_3076,U_3079,U_3078,U_3071,U_3075) )
    & ! [U_3072,U_3076,U_3079,U_3078,U_3071,U_3075] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,U_3072)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK31(U_3079,U_3078))))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,sK30(U_3079,U_3078,U_3071))),U_3071)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3071)
        | ~ sP270(U_3072,U_3076,U_3079,U_3078,U_3071,U_3075) )
    & ! [U_3072,U_3076,U_3079,U_3078,U_3071,U_3075] :
        ( sP270(U_3072,U_3076,U_3079,U_3078,U_3071,U_3075)
        | ~ class_RealVector_Oreal__normed__vector(U_3078) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP269,sP270])],[f_958_6]) ).

cnf(f_958_8,plain,
    ( sP270(U_3072,U_3076,U_3079,U_3078,U_3071,U_3075)
    | ~ class_RealVector_Oreal__normed__vector(U_3078) ),
    inference(clausify,[status(thm)],[f_958_7]) ).

cnf(f_958_9,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,U_3072)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK31(U_3079,U_3078))))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,sK30(U_3079,U_3078,U_3071))),U_3071)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3071)
    | ~ sP270(U_3072,U_3076,U_3079,U_3078,U_3071,U_3075) ),
    inference(clausify,[status(thm)],[f_958_7]) ).

cnf(f_958_10,plain,
    ( sP269(U_3076,U_3079,U_3078)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,sK32(U_3079,U_3078,U_3075))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_3075)))
    | ~ sP270(U_3072,U_3076,U_3079,U_3078,U_3071,U_3075) ),
    inference(clausify,[status(thm)],[f_958_7]) ).

cnf(f_958_11,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK33(U_3079,U_3078))
    | ~ sP269(U_3076,U_3079,U_3078) ),
    inference(clausify,[status(thm)],[f_958_7]) ).

cnf(f_958_12,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3078,hAPP(U_3079,U_3076)),sK33(U_3079,U_3078))
    | ~ sP269(U_3076,U_3079,U_3078) ),
    inference(clausify,[status(thm)],[f_958_7]) ).

fof(f_959_1,plain,
    ! [V_r] :
      ( ? [B_n] :
          ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,B_n))
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_r) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r) ),
    inference(fof_nnf,[status(thm)],[fact_reals__Archimedean6]) ).

fof(f_959_2,plain,
    ! [U_3081] :
      ( ? [U_3080] :
          ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_3081,c_RealDef_Oreal(tc_Nat_Onat,U_3080))
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3080,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3081) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3081) ),
    inference(variable_rename,[status(thm)],[f_959_1]) ).

fof(f_959_3,plain,
    ! [U_3081] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_3081,c_RealDef_Oreal(tc_Nat_Onat,sK34(U_3081)))
        & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,sK34(U_3081),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3081) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3081) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_3080,sK34(U_3081))],[f_959_2]) ).

fof(f_959_4,plain,
    ( ! [U_3081] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_3081,c_RealDef_Oreal(tc_Nat_Onat,sK34(U_3081)))
        | ~ sP271(U_3081) )
    & ! [U_3081] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,sK34(U_3081),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3081)
        | ~ sP271(U_3081) )
    & ! [U_3081] :
        ( sP271(U_3081)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3081) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP271])],[f_959_3]) ).

cnf(f_959_5,plain,
    ( sP271(U_3081)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3081) ),
    inference(clausify,[status(thm)],[f_959_4]) ).

cnf(f_959_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,sK34(U_3081),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3081)
    | ~ sP271(U_3081) ),
    inference(clausify,[status(thm)],[f_959_4]) ).

cnf(f_959_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_3081,c_RealDef_Oreal(tc_Nat_Onat,sK34(U_3081)))
    | ~ sP271(U_3081) ),
    inference(clausify,[status(thm)],[f_959_4]) ).

fof(f_960_1,plain,
    ! [V_x,V_y] :
      ( ? [B_n] :
          ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n))),V_y))
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,B_n)),V_y),V_x) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y) ),
    inference(fof_nnf,[status(thm)],[fact_reals__Archimedean4]) ).

fof(f_960_2,plain,
    ! [U_3084,U_3083] :
      ( ? [U_3082] :
          ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_3084,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_3082))),U_3083))
          & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_3082)),U_3083),U_3084) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3084)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3083) ),
    inference(variable_rename,[status(thm)],[f_960_1]) ).

fof(f_960_3,plain,
    ! [U_3084,U_3083] :
      ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_3084,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK35(U_3084,U_3083)))),U_3083))
        & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,sK35(U_3084,U_3083))),U_3083),U_3084) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3084)
      | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3083) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_3082,sK35(U_3084,U_3083))],[f_960_2]) ).

fof(f_960_4,plain,
    ( ! [U_3083,U_3084] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_3084,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK35(U_3084,U_3083)))),U_3083))
        | ~ sP272(U_3083,U_3084) )
    & ! [U_3083,U_3084] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,sK35(U_3084,U_3083))),U_3083),U_3084)
        | ~ sP272(U_3083,U_3084) )
    & ! [U_3083,U_3084] :
        ( sP272(U_3083,U_3084)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3084)
        | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3083) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP272])],[f_960_3]) ).

cnf(f_960_5,plain,
    ( sP272(U_3083,U_3084)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3084)
    | ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3083) ),
    inference(clausify,[status(thm)],[f_960_4]) ).

cnf(f_960_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,sK35(U_3084,U_3083))),U_3083),U_3084)
    | ~ sP272(U_3083,U_3084) ),
    inference(clausify,[status(thm)],[f_960_4]) ).

cnf(f_960_7,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_3084,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK35(U_3084,U_3083)))),U_3083))
    | ~ sP272(U_3083,U_3084) ),
    inference(clausify,[status(thm)],[f_960_4]) ).

fof(f_961_1,plain,
    ! [V_X_2,V_M_2,T_a,T_b] :
      ( ! [B_n] :
          ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2))))
          | ~ c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n) )
      | ? [B_n] :
          ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,c_Groups_Ominus__class_Ominus(T_b,hAPP(V_X_2,V_M_2),hAPP(V_X_2,B_n))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
          & c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n) )
      | ~ class_Orderings_Oord(T_a)
      | ~ class_RealVector_Oreal__normed__vector(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_lemmaCauchy]) ).

fof(f_961_2,plain,
    ! [U_3090,U_3089,U_3088,U_3087] :
      ( ! [U_3086] :
          ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3087,hAPP(U_3090,U_3086)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_3087,hAPP(U_3090,U_3089))))
          | ~ c_Orderings_Oord__class_Oless__eq(U_3088,U_3089,U_3086) )
      | ? [U_3085] :
          ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3087,c_Groups_Ominus__class_Ominus(U_3087,hAPP(U_3090,U_3089),hAPP(U_3090,U_3085))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
          & c_Orderings_Oord__class_Oless__eq(U_3088,U_3089,U_3085) )
      | ~ class_Orderings_Oord(U_3088)
      | ~ class_RealVector_Oreal__normed__vector(U_3087) ),
    inference(variable_rename,[status(thm)],[f_961_1]) ).

fof(f_961_3,plain,
    ! [U_3090,U_3089,U_3088,U_3087] :
      ( ! [U_3086] :
          ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3087,hAPP(U_3090,U_3086)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_3087,hAPP(U_3090,U_3089))))
          | ~ c_Orderings_Oord__class_Oless__eq(U_3088,U_3089,U_3086) )
      | ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3087,c_Groups_Ominus__class_Ominus(U_3087,hAPP(U_3090,U_3089),hAPP(U_3090,sK36(U_3090,U_3089,U_3088,U_3087)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        & c_Orderings_Oord__class_Oless__eq(U_3088,U_3089,sK36(U_3090,U_3089,U_3088,U_3087)) )
      | ~ class_Orderings_Oord(U_3088)
      | ~ class_RealVector_Oreal__normed__vector(U_3087) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_3085,sK36(U_3090,U_3089,U_3088,U_3087))],[f_961_2]) ).

fof(f_961_4,plain,
    ( ! [U_3087,U_3088,U_3089,U_3090] :
        ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3087,c_Groups_Ominus__class_Ominus(U_3087,hAPP(U_3090,U_3089),hAPP(U_3090,sK36(U_3090,U_3089,U_3088,U_3087)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
        | ~ sP273(U_3087,U_3088,U_3089,U_3090) )
    & ! [U_3087,U_3088,U_3089,U_3090] :
        ( c_Orderings_Oord__class_Oless__eq(U_3088,U_3089,sK36(U_3090,U_3089,U_3088,U_3087))
        | ~ sP273(U_3087,U_3088,U_3089,U_3090) )
    & ! [U_3086,U_3087,U_3088,U_3089,U_3090] :
        ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3087,hAPP(U_3090,U_3086)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_3087,hAPP(U_3090,U_3089))))
        | ~ c_Orderings_Oord__class_Oless__eq(U_3088,U_3089,U_3086)
        | sP273(U_3087,U_3088,U_3089,U_3090)
        | ~ class_Orderings_Oord(U_3088)
        | ~ class_RealVector_Oreal__normed__vector(U_3087) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP273])],[f_961_3]) ).

cnf(f_961_5,plain,
    ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3087,hAPP(U_3090,U_3086)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_3087,hAPP(U_3090,U_3089))))
    | ~ c_Orderings_Oord__class_Oless__eq(U_3088,U_3089,U_3086)
    | sP273(U_3087,U_3088,U_3089,U_3090)
    | ~ class_Orderings_Oord(U_3088)
    | ~ class_RealVector_Oreal__normed__vector(U_3087) ),
    inference(clausify,[status(thm)],[f_961_4]) ).

cnf(f_961_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(U_3088,U_3089,sK36(U_3090,U_3089,U_3088,U_3087))
    | ~ sP273(U_3087,U_3088,U_3089,U_3090) ),
    inference(clausify,[status(thm)],[f_961_4]) ).

cnf(f_961_7,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3087,c_Groups_Ominus__class_Ominus(U_3087,hAPP(U_3090,U_3089),hAPP(U_3090,sK36(U_3090,U_3089,U_3088,U_3087)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
    | ~ sP273(U_3087,U_3088,U_3089,U_3090) ),
    inference(clausify,[status(thm)],[f_961_4]) ).

fof(f_962_1,plain,
    ! [V_p,V_r] :
    ? [B_m] :
      ( ! [B_z] :
          ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,V_p),B_z)),B_m)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),V_r) )
      & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_m) ),
    inference(fof_nnf,[status(thm)],[fact_poly__bound__exists]) ).

fof(f_962_2,plain,
    ! [U_3094,U_3093] :
    ? [U_3092] :
      ( ! [U_3091] :
          ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_3094),U_3091)),U_3092)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_3091),U_3093) )
      & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3092) ),
    inference(variable_rename,[status(thm)],[f_962_1]) ).

fof(f_962_3,plain,
    ! [U_3094,U_3093] :
      ( ! [U_3091] :
          ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_3094),U_3091)),sK37(U_3094,U_3093))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_3091),U_3093) )
      & c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK37(U_3094,U_3093)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_3092,sK37(U_3094,U_3093))],[f_962_2]) ).

fof(f_962_4,plain,
    ( ! [U_3091,U_3094,U_3093] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_3094),U_3091)),sK37(U_3094,U_3093))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_3091),U_3093) )
    & ! [U_3094,U_3093] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK37(U_3094,U_3093)) ),
    inference(definitional_conversion,[status(esa)],[f_962_3]) ).

cnf(f_962_5,plain,
    c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK37(U_3094,U_3093)),
    inference(clausify,[status(thm)],[f_962_4]) ).

cnf(f_962_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,U_3094),U_3091)),sK37(U_3094,U_3093))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_3091),U_3093) ),
    inference(clausify,[status(thm)],[f_962_4]) ).

fof(f_963_1,plain,
    ! [V_b,V_a,T_a] :
      ( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))
      | ~ class_Groups_Oab__group__add(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_Limits_Ominus__diff__minus]) ).

fof(f_963_2,plain,
    ! [U_3097,U_3096,U_3095] :
      ( c_Groups_Ominus__class_Ominus(U_3095,c_Groups_Ouminus__class_Ouminus(U_3095,U_3096),c_Groups_Ouminus__class_Ouminus(U_3095,U_3097)) = c_Groups_Ouminus__class_Ouminus(U_3095,c_Groups_Ominus__class_Ominus(U_3095,U_3096,U_3097))
      | ~ class_Groups_Oab__group__add(U_3095) ),
    inference(variable_rename,[status(thm)],[f_963_1]) ).

fof(f_963_3,plain,
    ! [U_3095,U_3096,U_3097] :
      ( c_Groups_Ominus__class_Ominus(U_3095,c_Groups_Ouminus__class_Ouminus(U_3095,U_3096),c_Groups_Ouminus__class_Ouminus(U_3095,U_3097)) = c_Groups_Ouminus__class_Ouminus(U_3095,c_Groups_Ominus__class_Ominus(U_3095,U_3096,U_3097))
      | ~ class_Groups_Oab__group__add(U_3095) ),
    inference(definitional_conversion,[status(esa)],[f_963_2]) ).

cnf(f_963_4,plain,
    ( c_Groups_Ominus__class_Ominus(U_3095,c_Groups_Ouminus__class_Ouminus(U_3095,U_3096),c_Groups_Ouminus__class_Ouminus(U_3095,U_3097)) = c_Groups_Ouminus__class_Ouminus(U_3095,c_Groups_Ominus__class_Ominus(U_3095,U_3096,U_3097))
    | ~ class_Groups_Oab__group__add(U_3095) ),
    inference(clausify,[status(thm)],[f_963_3]) ).

fof(f_964_1,plain,
    ! [V_k,V_m] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),V_m),V_k) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) ),
    inference(fof_nnf,[status(thm)],[fact_int__power__div__base]) ).

fof(f_964_2,plain,
    ! [U_3099,U_3098] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3099),U_3098),U_3099) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3099),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3098,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3099)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3098) ),
    inference(variable_rename,[status(thm)],[f_964_1]) ).

fof(f_964_3,plain,
    ! [U_3098,U_3099] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3099),U_3098),U_3099) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3099),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3098,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3099)
      | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3098) ),
    inference(definitional_conversion,[status(esa)],[f_964_2]) ).

cnf(f_964_4,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3099),U_3098),U_3099) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3099),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3098,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3099)
    | ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3098) ),
    inference(clausify,[status(thm)],[f_964_3]) ).

fof(f_965_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)),V_b) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__self1]) ).

fof(f_965_2,plain,
    ! [U_3103,U_3102,U_3101,U_3100] :
      ( c_Divides_Odiv__class_Odiv(U_3100,c_Groups_Oplus__class_Oplus(U_3100,U_3102,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3100),U_3103),U_3101)),U_3101) = c_Groups_Oplus__class_Oplus(U_3100,U_3103,c_Divides_Odiv__class_Odiv(U_3100,U_3102,U_3101))
      | U_3101 = c_Groups_Ozero__class_Ozero(U_3100)
      | ~ class_Divides_Osemiring__div(U_3100) ),
    inference(variable_rename,[status(thm)],[f_965_1]) ).

fof(f_965_3,plain,
    ! [U_3101,U_3100,U_3102,U_3103] :
      ( c_Divides_Odiv__class_Odiv(U_3100,c_Groups_Oplus__class_Oplus(U_3100,U_3102,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3100),U_3103),U_3101)),U_3101) = c_Groups_Oplus__class_Oplus(U_3100,U_3103,c_Divides_Odiv__class_Odiv(U_3100,U_3102,U_3101))
      | U_3101 = c_Groups_Ozero__class_Ozero(U_3100)
      | ~ class_Divides_Osemiring__div(U_3100) ),
    inference(definitional_conversion,[status(esa)],[f_965_2]) ).

cnf(f_965_4,plain,
    ( c_Divides_Odiv__class_Odiv(U_3100,c_Groups_Oplus__class_Oplus(U_3100,U_3102,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3100),U_3103),U_3101)),U_3101) = c_Groups_Oplus__class_Oplus(U_3100,U_3103,c_Divides_Odiv__class_Odiv(U_3100,U_3102,U_3101))
    | U_3101 = c_Groups_Ozero__class_Ozero(U_3100)
    | ~ class_Divides_Osemiring__div(U_3100) ),
    inference(clausify,[status(thm)],[f_965_3]) ).

fof(f_966_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_b) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b))
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__self2]) ).

fof(f_966_2,plain,
    ! [U_3107,U_3106,U_3105,U_3104] :
      ( c_Divides_Odiv__class_Odiv(U_3104,c_Groups_Oplus__class_Oplus(U_3104,U_3106,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3104),U_3105),U_3107)),U_3105) = c_Groups_Oplus__class_Oplus(U_3104,U_3107,c_Divides_Odiv__class_Odiv(U_3104,U_3106,U_3105))
      | U_3105 = c_Groups_Ozero__class_Ozero(U_3104)
      | ~ class_Divides_Osemiring__div(U_3104) ),
    inference(variable_rename,[status(thm)],[f_966_1]) ).

fof(f_966_3,plain,
    ! [U_3105,U_3104,U_3106,U_3107] :
      ( c_Divides_Odiv__class_Odiv(U_3104,c_Groups_Oplus__class_Oplus(U_3104,U_3106,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3104),U_3105),U_3107)),U_3105) = c_Groups_Oplus__class_Oplus(U_3104,U_3107,c_Divides_Odiv__class_Odiv(U_3104,U_3106,U_3105))
      | U_3105 = c_Groups_Ozero__class_Ozero(U_3104)
      | ~ class_Divides_Osemiring__div(U_3104) ),
    inference(definitional_conversion,[status(esa)],[f_966_2]) ).

cnf(f_966_4,plain,
    ( c_Divides_Odiv__class_Odiv(U_3104,c_Groups_Oplus__class_Oplus(U_3104,U_3106,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3104),U_3105),U_3107)),U_3105) = c_Groups_Oplus__class_Oplus(U_3104,U_3107,c_Divides_Odiv__class_Odiv(U_3104,U_3106,U_3105))
    | U_3105 = c_Groups_Ozero__class_Ozero(U_3104)
    | ~ class_Divides_Osemiring__div(U_3104) ),
    inference(clausify,[status(thm)],[f_966_3]) ).

fof(f_967_1,plain,
    ! [V_a,V_b,T_a] :
      ( c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b) = c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b),c_Groups_Oone__class_Oone(T_a))
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__add__self2]) ).

fof(f_967_2,plain,
    ! [U_3110,U_3109,U_3108] :
      ( c_Divides_Odiv__class_Odiv(U_3108,c_Groups_Oplus__class_Oplus(U_3108,U_3110,U_3109),U_3109) = c_Groups_Oplus__class_Oplus(U_3108,c_Divides_Odiv__class_Odiv(U_3108,U_3110,U_3109),c_Groups_Oone__class_Oone(U_3108))
      | U_3109 = c_Groups_Ozero__class_Ozero(U_3108)
      | ~ class_Divides_Osemiring__div(U_3108) ),
    inference(variable_rename,[status(thm)],[f_967_1]) ).

fof(f_967_3,plain,
    ! [U_3109,U_3108,U_3110] :
      ( c_Divides_Odiv__class_Odiv(U_3108,c_Groups_Oplus__class_Oplus(U_3108,U_3110,U_3109),U_3109) = c_Groups_Oplus__class_Oplus(U_3108,c_Divides_Odiv__class_Odiv(U_3108,U_3110,U_3109),c_Groups_Oone__class_Oone(U_3108))
      | U_3109 = c_Groups_Ozero__class_Ozero(U_3108)
      | ~ class_Divides_Osemiring__div(U_3108) ),
    inference(definitional_conversion,[status(esa)],[f_967_2]) ).

cnf(f_967_4,plain,
    ( c_Divides_Odiv__class_Odiv(U_3108,c_Groups_Oplus__class_Oplus(U_3108,U_3110,U_3109),U_3109) = c_Groups_Oplus__class_Oplus(U_3108,c_Divides_Odiv__class_Odiv(U_3108,U_3110,U_3109),c_Groups_Oone__class_Oone(U_3108))
    | U_3109 = c_Groups_Ozero__class_Ozero(U_3108)
    | ~ class_Divides_Osemiring__div(U_3108) ),
    inference(clausify,[status(thm)],[f_967_3]) ).

fof(f_968_1,plain,
    ! [V_a,V_b,T_a] :
      ( c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_a),V_b) = c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_a,V_b),c_Groups_Oone__class_Oone(T_a))
      | V_b = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__add__self1]) ).

fof(f_968_2,plain,
    ! [U_3113,U_3112,U_3111] :
      ( c_Divides_Odiv__class_Odiv(U_3111,c_Groups_Oplus__class_Oplus(U_3111,U_3112,U_3113),U_3112) = c_Groups_Oplus__class_Oplus(U_3111,c_Divides_Odiv__class_Odiv(U_3111,U_3113,U_3112),c_Groups_Oone__class_Oone(U_3111))
      | U_3112 = c_Groups_Ozero__class_Ozero(U_3111)
      | ~ class_Divides_Osemiring__div(U_3111) ),
    inference(variable_rename,[status(thm)],[f_968_1]) ).

fof(f_968_3,plain,
    ! [U_3111,U_3112,U_3113] :
      ( c_Divides_Odiv__class_Odiv(U_3111,c_Groups_Oplus__class_Oplus(U_3111,U_3112,U_3113),U_3112) = c_Groups_Oplus__class_Oplus(U_3111,c_Divides_Odiv__class_Odiv(U_3111,U_3113,U_3112),c_Groups_Oone__class_Oone(U_3111))
      | U_3112 = c_Groups_Ozero__class_Ozero(U_3111)
      | ~ class_Divides_Osemiring__div(U_3111) ),
    inference(definitional_conversion,[status(esa)],[f_968_2]) ).

cnf(f_968_4,plain,
    ( c_Divides_Odiv__class_Odiv(U_3111,c_Groups_Oplus__class_Oplus(U_3111,U_3112,U_3113),U_3112) = c_Groups_Oplus__class_Oplus(U_3111,c_Divides_Odiv__class_Odiv(U_3111,U_3113,U_3112),c_Groups_Oone__class_Oone(U_3111))
    | U_3112 = c_Groups_Ozero__class_Ozero(U_3111)
    | ~ class_Divides_Osemiring__div(U_3111) ),
    inference(clausify,[status(thm)],[f_968_3]) ).

fof(f_969_1,plain,
    ! [V_ca_2,V_b_2,V_ab_2,T_a] :
      ( ( ( c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_ab_2) = V_ca_2
          | V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2) )
        & ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_ab_2)
          | c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_ab_2) != V_ca_2 ) )
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_b_2)
      | V_ab_2 = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__div__eq__mult]) ).

fof(f_969_2,plain,
    ! [U_3117,U_3116,U_3115,U_3114] :
      ( ( ( c_Divides_Odiv__class_Odiv(U_3114,U_3116,U_3115) = U_3117
          | U_3116 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3114),U_3117),U_3115) )
        & ( U_3116 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3114),U_3117),U_3115)
          | c_Divides_Odiv__class_Odiv(U_3114,U_3116,U_3115) != U_3117 ) )
      | ~ c_Rings_Odvd__class_Odvd(U_3114,U_3115,U_3116)
      | U_3115 = c_Groups_Ozero__class_Ozero(U_3114)
      | ~ class_Divides_Osemiring__div(U_3114) ),
    inference(variable_rename,[status(thm)],[f_969_1]) ).

fof(f_969_3,plain,
    ( ! [U_3114,U_3115,U_3116,U_3117] :
        ( c_Divides_Odiv__class_Odiv(U_3114,U_3116,U_3115) = U_3117
        | U_3116 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3114),U_3117),U_3115)
        | ~ sP274(U_3114,U_3115,U_3116,U_3117) )
    & ! [U_3114,U_3115,U_3116,U_3117] :
        ( U_3116 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3114),U_3117),U_3115)
        | c_Divides_Odiv__class_Odiv(U_3114,U_3116,U_3115) != U_3117
        | ~ sP274(U_3114,U_3115,U_3116,U_3117) )
    & ! [U_3114,U_3115,U_3116,U_3117] :
        ( sP274(U_3114,U_3115,U_3116,U_3117)
        | ~ c_Rings_Odvd__class_Odvd(U_3114,U_3115,U_3116)
        | U_3115 = c_Groups_Ozero__class_Ozero(U_3114)
        | ~ class_Divides_Osemiring__div(U_3114) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP274])],[f_969_2]) ).

cnf(f_969_4,plain,
    ( sP274(U_3114,U_3115,U_3116,U_3117)
    | ~ c_Rings_Odvd__class_Odvd(U_3114,U_3115,U_3116)
    | U_3115 = c_Groups_Ozero__class_Ozero(U_3114)
    | ~ class_Divides_Osemiring__div(U_3114) ),
    inference(clausify,[status(thm)],[f_969_3]) ).

cnf(f_969_5,plain,
    ( U_3116 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3114),U_3117),U_3115)
    | c_Divides_Odiv__class_Odiv(U_3114,U_3116,U_3115) != U_3117
    | ~ sP274(U_3114,U_3115,U_3116,U_3117) ),
    inference(clausify,[status(thm)],[f_969_3]) ).

cnf(f_969_6,plain,
    ( c_Divides_Odiv__class_Odiv(U_3114,U_3116,U_3115) = U_3117
    | U_3116 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3114),U_3117),U_3115)
    | ~ sP274(U_3114,U_3115,U_3116,U_3117) ),
    inference(clausify,[status(thm)],[f_969_3]) ).

fof(f_970_1,plain,
    ! [V_db_2,V_b_2,V_ca_2,V_ab_2,T_a] :
      ( ( ( c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_ab_2) = c_Divides_Odiv__class_Odiv(T_a,V_db_2,V_ca_2)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_db_2) )
        & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ab_2),V_db_2)
          | c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_ab_2) != c_Divides_Odiv__class_Odiv(T_a,V_db_2,V_ca_2) ) )
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_ca_2,V_db_2)
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_b_2)
      | V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
      | V_ab_2 = c_Groups_Ozero__class_Ozero(T_a)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__div__div__eq__mult]) ).

fof(f_970_2,plain,
    ! [U_3122,U_3121,U_3120,U_3119,U_3118] :
      ( ( ( c_Divides_Odiv__class_Odiv(U_3118,U_3121,U_3119) = c_Divides_Odiv__class_Odiv(U_3118,U_3122,U_3120)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3118),U_3121),U_3120) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3118),U_3119),U_3122) )
        & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3118),U_3121),U_3120) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3118),U_3119),U_3122)
          | c_Divides_Odiv__class_Odiv(U_3118,U_3121,U_3119) != c_Divides_Odiv__class_Odiv(U_3118,U_3122,U_3120) ) )
      | ~ c_Rings_Odvd__class_Odvd(U_3118,U_3120,U_3122)
      | ~ c_Rings_Odvd__class_Odvd(U_3118,U_3119,U_3121)
      | U_3120 = c_Groups_Ozero__class_Ozero(U_3118)
      | U_3119 = c_Groups_Ozero__class_Ozero(U_3118)
      | ~ class_Divides_Osemiring__div(U_3118) ),
    inference(variable_rename,[status(thm)],[f_970_1]) ).

fof(f_970_3,plain,
    ( ! [U_3119,U_3122,U_3121,U_3120,U_3118] :
        ( c_Divides_Odiv__class_Odiv(U_3118,U_3121,U_3119) = c_Divides_Odiv__class_Odiv(U_3118,U_3122,U_3120)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3118),U_3121),U_3120) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3118),U_3119),U_3122)
        | ~ sP275(U_3119,U_3122,U_3121,U_3120,U_3118) )
    & ! [U_3119,U_3122,U_3121,U_3120,U_3118] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3118),U_3121),U_3120) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3118),U_3119),U_3122)
        | c_Divides_Odiv__class_Odiv(U_3118,U_3121,U_3119) != c_Divides_Odiv__class_Odiv(U_3118,U_3122,U_3120)
        | ~ sP275(U_3119,U_3122,U_3121,U_3120,U_3118) )
    & ! [U_3119,U_3122,U_3121,U_3120,U_3118] :
        ( sP275(U_3119,U_3122,U_3121,U_3120,U_3118)
        | ~ c_Rings_Odvd__class_Odvd(U_3118,U_3120,U_3122)
        | ~ c_Rings_Odvd__class_Odvd(U_3118,U_3119,U_3121)
        | U_3120 = c_Groups_Ozero__class_Ozero(U_3118)
        | U_3119 = c_Groups_Ozero__class_Ozero(U_3118)
        | ~ class_Divides_Osemiring__div(U_3118) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP275])],[f_970_2]) ).

cnf(f_970_4,plain,
    ( sP275(U_3119,U_3122,U_3121,U_3120,U_3118)
    | ~ c_Rings_Odvd__class_Odvd(U_3118,U_3120,U_3122)
    | ~ c_Rings_Odvd__class_Odvd(U_3118,U_3119,U_3121)
    | U_3120 = c_Groups_Ozero__class_Ozero(U_3118)
    | U_3119 = c_Groups_Ozero__class_Ozero(U_3118)
    | ~ class_Divides_Osemiring__div(U_3118) ),
    inference(clausify,[status(thm)],[f_970_3]) ).

cnf(f_970_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3118),U_3121),U_3120) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3118),U_3119),U_3122)
    | c_Divides_Odiv__class_Odiv(U_3118,U_3121,U_3119) != c_Divides_Odiv__class_Odiv(U_3118,U_3122,U_3120)
    | ~ sP275(U_3119,U_3122,U_3121,U_3120,U_3118) ),
    inference(clausify,[status(thm)],[f_970_3]) ).

cnf(f_970_6,plain,
    ( c_Divides_Odiv__class_Odiv(U_3118,U_3121,U_3119) = c_Divides_Odiv__class_Odiv(U_3118,U_3122,U_3120)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3118),U_3121),U_3120) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3118),U_3119),U_3122)
    | ~ sP275(U_3119,U_3122,U_3121,U_3120,U_3118) ),
    inference(clausify,[status(thm)],[f_970_3]) ).

fof(f_971_1,plain,
    ! [V_x,V_y,T_a] :
      ( c_Divides_Odiv__class_Odiv(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_y))
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_y,V_x)
      | ~ class_Divides_Oring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__neg__div]) ).

fof(f_971_2,plain,
    ! [U_3125,U_3124,U_3123] :
      ( c_Divides_Odiv__class_Odiv(U_3123,c_Groups_Ouminus__class_Ouminus(U_3123,U_3125),U_3124) = c_Groups_Ouminus__class_Ouminus(U_3123,c_Divides_Odiv__class_Odiv(U_3123,U_3125,U_3124))
      | ~ c_Rings_Odvd__class_Odvd(U_3123,U_3124,U_3125)
      | ~ class_Divides_Oring__div(U_3123) ),
    inference(variable_rename,[status(thm)],[f_971_1]) ).

fof(f_971_3,plain,
    ! [U_3123,U_3125,U_3124] :
      ( c_Divides_Odiv__class_Odiv(U_3123,c_Groups_Ouminus__class_Ouminus(U_3123,U_3125),U_3124) = c_Groups_Ouminus__class_Ouminus(U_3123,c_Divides_Odiv__class_Odiv(U_3123,U_3125,U_3124))
      | ~ c_Rings_Odvd__class_Odvd(U_3123,U_3124,U_3125)
      | ~ class_Divides_Oring__div(U_3123) ),
    inference(definitional_conversion,[status(esa)],[f_971_2]) ).

cnf(f_971_4,plain,
    ( c_Divides_Odiv__class_Odiv(U_3123,c_Groups_Ouminus__class_Ouminus(U_3123,U_3125),U_3124) = c_Groups_Ouminus__class_Ouminus(U_3123,c_Divides_Odiv__class_Odiv(U_3123,U_3125,U_3124))
    | ~ c_Rings_Odvd__class_Odvd(U_3123,U_3124,U_3125)
    | ~ class_Divides_Oring__div(U_3123) ),
    inference(clausify,[status(thm)],[f_971_3]) ).

fof(f_972_1,plain,
    ! [V_x,V_y,T_a] :
      ( c_Divides_Odiv__class_Odiv(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_y))
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_y,V_x)
      | ~ class_Divides_Oring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__div__neg]) ).

fof(f_972_2,plain,
    ! [U_3128,U_3127,U_3126] :
      ( c_Divides_Odiv__class_Odiv(U_3126,U_3128,c_Groups_Ouminus__class_Ouminus(U_3126,U_3127)) = c_Groups_Ouminus__class_Ouminus(U_3126,c_Divides_Odiv__class_Odiv(U_3126,U_3128,U_3127))
      | ~ c_Rings_Odvd__class_Odvd(U_3126,U_3127,U_3128)
      | ~ class_Divides_Oring__div(U_3126) ),
    inference(variable_rename,[status(thm)],[f_972_1]) ).

fof(f_972_3,plain,
    ! [U_3126,U_3127,U_3128] :
      ( c_Divides_Odiv__class_Odiv(U_3126,U_3128,c_Groups_Ouminus__class_Ouminus(U_3126,U_3127)) = c_Groups_Ouminus__class_Ouminus(U_3126,c_Divides_Odiv__class_Odiv(U_3126,U_3128,U_3127))
      | ~ c_Rings_Odvd__class_Odvd(U_3126,U_3127,U_3128)
      | ~ class_Divides_Oring__div(U_3126) ),
    inference(definitional_conversion,[status(esa)],[f_972_2]) ).

cnf(f_972_4,plain,
    ( c_Divides_Odiv__class_Odiv(U_3126,U_3128,c_Groups_Ouminus__class_Ouminus(U_3126,U_3127)) = c_Groups_Ouminus__class_Ouminus(U_3126,c_Divides_Odiv__class_Odiv(U_3126,U_3128,U_3127))
    | ~ c_Rings_Odvd__class_Odvd(U_3126,U_3127,U_3128)
    | ~ class_Divides_Oring__div(U_3126) ),
    inference(clausify,[status(thm)],[f_972_3]) ).

fof(f_973_1,plain,
    ! [V_y,V_x,V_z,T_a] :
      ( c_Divides_Odiv__class_Odiv(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_z) = c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Odiv(T_a,V_x,V_z),c_Divides_Odiv__class_Odiv(T_a,V_y,V_z))
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_z,V_y)
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_z,V_x)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__add]) ).

fof(f_973_2,plain,
    ! [U_3132,U_3131,U_3130,U_3129] :
      ( c_Divides_Odiv__class_Odiv(U_3129,c_Groups_Oplus__class_Oplus(U_3129,U_3131,U_3132),U_3130) = c_Groups_Oplus__class_Oplus(U_3129,c_Divides_Odiv__class_Odiv(U_3129,U_3131,U_3130),c_Divides_Odiv__class_Odiv(U_3129,U_3132,U_3130))
      | ~ c_Rings_Odvd__class_Odvd(U_3129,U_3130,U_3132)
      | ~ c_Rings_Odvd__class_Odvd(U_3129,U_3130,U_3131)
      | ~ class_Divides_Osemiring__div(U_3129) ),
    inference(variable_rename,[status(thm)],[f_973_1]) ).

fof(f_973_3,plain,
    ! [U_3132,U_3129,U_3131,U_3130] :
      ( c_Divides_Odiv__class_Odiv(U_3129,c_Groups_Oplus__class_Oplus(U_3129,U_3131,U_3132),U_3130) = c_Groups_Oplus__class_Oplus(U_3129,c_Divides_Odiv__class_Odiv(U_3129,U_3131,U_3130),c_Divides_Odiv__class_Odiv(U_3129,U_3132,U_3130))
      | ~ c_Rings_Odvd__class_Odvd(U_3129,U_3130,U_3132)
      | ~ c_Rings_Odvd__class_Odvd(U_3129,U_3130,U_3131)
      | ~ class_Divides_Osemiring__div(U_3129) ),
    inference(definitional_conversion,[status(esa)],[f_973_2]) ).

cnf(f_973_4,plain,
    ( c_Divides_Odiv__class_Odiv(U_3129,c_Groups_Oplus__class_Oplus(U_3129,U_3131,U_3132),U_3130) = c_Groups_Oplus__class_Oplus(U_3129,c_Divides_Odiv__class_Odiv(U_3129,U_3131,U_3130),c_Divides_Odiv__class_Odiv(U_3129,U_3132,U_3130))
    | ~ c_Rings_Odvd__class_Odvd(U_3129,U_3130,U_3132)
    | ~ c_Rings_Odvd__class_Odvd(U_3129,U_3130,U_3131)
    | ~ class_Divides_Osemiring__div(U_3129) ),
    inference(clausify,[status(thm)],[f_973_3]) ).

fof(f_974_1,plain,
    ! [V_ca_2,V_b_2,V_ab_2,T_a] :
      ( ( ( c_Rings_Odvd__class_Odvd(T_a,c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_ab_2),c_Divides_Odiv__class_Odiv(T_a,V_ca_2,V_ab_2))
          | ~ c_Rings_Odvd__class_Odvd(T_a,V_b_2,V_ca_2) )
        & ( c_Rings_Odvd__class_Odvd(T_a,V_b_2,V_ca_2)
          | ~ c_Rings_Odvd__class_Odvd(T_a,c_Divides_Odiv__class_Odiv(T_a,V_b_2,V_ab_2),c_Divides_Odiv__class_Odiv(T_a,V_ca_2,V_ab_2)) ) )
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_ca_2)
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_ab_2,V_b_2)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__dvd__div]) ).

fof(f_974_2,plain,
    ! [U_3136,U_3135,U_3134,U_3133] :
      ( ( ( c_Rings_Odvd__class_Odvd(U_3133,c_Divides_Odiv__class_Odiv(U_3133,U_3135,U_3134),c_Divides_Odiv__class_Odiv(U_3133,U_3136,U_3134))
          | ~ c_Rings_Odvd__class_Odvd(U_3133,U_3135,U_3136) )
        & ( c_Rings_Odvd__class_Odvd(U_3133,U_3135,U_3136)
          | ~ c_Rings_Odvd__class_Odvd(U_3133,c_Divides_Odiv__class_Odiv(U_3133,U_3135,U_3134),c_Divides_Odiv__class_Odiv(U_3133,U_3136,U_3134)) ) )
      | ~ c_Rings_Odvd__class_Odvd(U_3133,U_3134,U_3136)
      | ~ c_Rings_Odvd__class_Odvd(U_3133,U_3134,U_3135)
      | ~ class_Divides_Osemiring__div(U_3133) ),
    inference(variable_rename,[status(thm)],[f_974_1]) ).

fof(f_974_3,plain,
    ( ! [U_3136,U_3133,U_3135,U_3134] :
        ( c_Rings_Odvd__class_Odvd(U_3133,c_Divides_Odiv__class_Odiv(U_3133,U_3135,U_3134),c_Divides_Odiv__class_Odiv(U_3133,U_3136,U_3134))
        | ~ c_Rings_Odvd__class_Odvd(U_3133,U_3135,U_3136)
        | ~ sP276(U_3136,U_3133,U_3135,U_3134) )
    & ! [U_3136,U_3133,U_3135,U_3134] :
        ( c_Rings_Odvd__class_Odvd(U_3133,U_3135,U_3136)
        | ~ c_Rings_Odvd__class_Odvd(U_3133,c_Divides_Odiv__class_Odiv(U_3133,U_3135,U_3134),c_Divides_Odiv__class_Odiv(U_3133,U_3136,U_3134))
        | ~ sP276(U_3136,U_3133,U_3135,U_3134) )
    & ! [U_3136,U_3133,U_3135,U_3134] :
        ( sP276(U_3136,U_3133,U_3135,U_3134)
        | ~ c_Rings_Odvd__class_Odvd(U_3133,U_3134,U_3136)
        | ~ c_Rings_Odvd__class_Odvd(U_3133,U_3134,U_3135)
        | ~ class_Divides_Osemiring__div(U_3133) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP276])],[f_974_2]) ).

cnf(f_974_4,plain,
    ( sP276(U_3136,U_3133,U_3135,U_3134)
    | ~ c_Rings_Odvd__class_Odvd(U_3133,U_3134,U_3136)
    | ~ c_Rings_Odvd__class_Odvd(U_3133,U_3134,U_3135)
    | ~ class_Divides_Osemiring__div(U_3133) ),
    inference(clausify,[status(thm)],[f_974_3]) ).

cnf(f_974_5,plain,
    ( c_Rings_Odvd__class_Odvd(U_3133,U_3135,U_3136)
    | ~ c_Rings_Odvd__class_Odvd(U_3133,c_Divides_Odiv__class_Odiv(U_3133,U_3135,U_3134),c_Divides_Odiv__class_Odiv(U_3133,U_3136,U_3134))
    | ~ sP276(U_3136,U_3133,U_3135,U_3134) ),
    inference(clausify,[status(thm)],[f_974_3]) ).

cnf(f_974_6,plain,
    ( c_Rings_Odvd__class_Odvd(U_3133,c_Divides_Odiv__class_Odiv(U_3133,U_3135,U_3134),c_Divides_Odiv__class_Odiv(U_3133,U_3136,U_3134))
    | ~ c_Rings_Odvd__class_Odvd(U_3133,U_3135,U_3136)
    | ~ sP276(U_3136,U_3133,U_3135,U_3134) ),
    inference(clausify,[status(thm)],[f_974_3]) ).

fof(f_975_1,plain,
    ! [V_w,V_z,V_x,V_y,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)),c_Divides_Odiv__class_Odiv(T_a,V_w,V_z)) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z))
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_z,V_w)
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_y,V_x)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__div__if__dvd]) ).

fof(f_975_2,plain,
    ! [U_3141,U_3140,U_3139,U_3138,U_3137] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3137),c_Divides_Odiv__class_Odiv(U_3137,U_3139,U_3138)),c_Divides_Odiv__class_Odiv(U_3137,U_3141,U_3140)) = c_Divides_Odiv__class_Odiv(U_3137,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3137),U_3139),U_3141),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3137),U_3138),U_3140))
      | ~ c_Rings_Odvd__class_Odvd(U_3137,U_3140,U_3141)
      | ~ c_Rings_Odvd__class_Odvd(U_3137,U_3138,U_3139)
      | ~ class_Divides_Osemiring__div(U_3137) ),
    inference(variable_rename,[status(thm)],[f_975_1]) ).

fof(f_975_3,plain,
    ! [U_3140,U_3141,U_3138,U_3139,U_3137] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3137),c_Divides_Odiv__class_Odiv(U_3137,U_3139,U_3138)),c_Divides_Odiv__class_Odiv(U_3137,U_3141,U_3140)) = c_Divides_Odiv__class_Odiv(U_3137,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3137),U_3139),U_3141),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3137),U_3138),U_3140))
      | ~ c_Rings_Odvd__class_Odvd(U_3137,U_3140,U_3141)
      | ~ c_Rings_Odvd__class_Odvd(U_3137,U_3138,U_3139)
      | ~ class_Divides_Osemiring__div(U_3137) ),
    inference(definitional_conversion,[status(esa)],[f_975_2]) ).

cnf(f_975_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3137),c_Divides_Odiv__class_Odiv(U_3137,U_3139,U_3138)),c_Divides_Odiv__class_Odiv(U_3137,U_3141,U_3140)) = c_Divides_Odiv__class_Odiv(U_3137,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3137),U_3139),U_3141),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3137),U_3138),U_3140))
    | ~ c_Rings_Odvd__class_Odvd(U_3137,U_3140,U_3141)
    | ~ c_Rings_Odvd__class_Odvd(U_3137,U_3138,U_3139)
    | ~ class_Divides_Osemiring__div(U_3137) ),
    inference(clausify,[status(thm)],[f_975_3]) ).

fof(f_976_1,plain,
    ! [V_c,V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)),V_c) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c),V_a)
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__div__mult]) ).

fof(f_976_2,plain,
    ! [U_3145,U_3144,U_3143,U_3142] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3142),c_Divides_Odiv__class_Odiv(U_3142,U_3144,U_3143)),U_3145) = c_Divides_Odiv__class_Odiv(U_3142,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3142),U_3144),U_3145),U_3143)
      | ~ c_Rings_Odvd__class_Odvd(U_3142,U_3143,U_3144)
      | ~ class_Divides_Osemiring__div(U_3142) ),
    inference(variable_rename,[status(thm)],[f_976_1]) ).

fof(f_976_3,plain,
    ! [U_3143,U_3144,U_3145,U_3142] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3142),c_Divides_Odiv__class_Odiv(U_3142,U_3144,U_3143)),U_3145) = c_Divides_Odiv__class_Odiv(U_3142,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3142),U_3144),U_3145),U_3143)
      | ~ c_Rings_Odvd__class_Odvd(U_3142,U_3143,U_3144)
      | ~ class_Divides_Osemiring__div(U_3142) ),
    inference(definitional_conversion,[status(esa)],[f_976_2]) ).

cnf(f_976_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3142),c_Divides_Odiv__class_Odiv(U_3142,U_3144,U_3143)),U_3145) = c_Divides_Odiv__class_Odiv(U_3142,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3142),U_3144),U_3145),U_3143)
    | ~ c_Rings_Odvd__class_Odvd(U_3142,U_3143,U_3144)
    | ~ class_Divides_Osemiring__div(U_3142) ),
    inference(clausify,[status(thm)],[f_976_3]) ).

fof(f_977_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)),V_a) = V_b
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__div__mult__self]) ).

fof(f_977_2,plain,
    ! [U_3148,U_3147,U_3146] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3146),c_Divides_Odiv__class_Odiv(U_3146,U_3148,U_3147)),U_3147) = U_3148
      | ~ c_Rings_Odvd__class_Odvd(U_3146,U_3147,U_3148)
      | ~ class_Divides_Osemiring__div(U_3146) ),
    inference(variable_rename,[status(thm)],[f_977_1]) ).

fof(f_977_3,plain,
    ! [U_3147,U_3146,U_3148] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3146),c_Divides_Odiv__class_Odiv(U_3146,U_3148,U_3147)),U_3147) = U_3148
      | ~ c_Rings_Odvd__class_Odvd(U_3146,U_3147,U_3148)
      | ~ class_Divides_Osemiring__div(U_3146) ),
    inference(definitional_conversion,[status(esa)],[f_977_2]) ).

cnf(f_977_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3146),c_Divides_Odiv__class_Odiv(U_3146,U_3148,U_3147)),U_3147) = U_3148
    | ~ c_Rings_Odvd__class_Odvd(U_3146,U_3147,U_3148)
    | ~ class_Divides_Osemiring__div(U_3146) ),
    inference(clausify,[status(thm)],[f_977_3]) ).

fof(f_978_1,plain,
    ! [V_a,V_b,V_c,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_c)) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_c,V_b)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__mult__swap]) ).

fof(f_978_2,plain,
    ! [U_3152,U_3151,U_3150,U_3149] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3149),U_3152),c_Divides_Odiv__class_Odiv(U_3149,U_3151,U_3150)) = c_Divides_Odiv__class_Odiv(U_3149,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3149),U_3152),U_3151),U_3150)
      | ~ c_Rings_Odvd__class_Odvd(U_3149,U_3150,U_3151)
      | ~ class_Divides_Osemiring__div(U_3149) ),
    inference(variable_rename,[status(thm)],[f_978_1]) ).

fof(f_978_3,plain,
    ! [U_3149,U_3150,U_3151,U_3152] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3149),U_3152),c_Divides_Odiv__class_Odiv(U_3149,U_3151,U_3150)) = c_Divides_Odiv__class_Odiv(U_3149,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3149),U_3152),U_3151),U_3150)
      | ~ c_Rings_Odvd__class_Odvd(U_3149,U_3150,U_3151)
      | ~ class_Divides_Osemiring__div(U_3149) ),
    inference(definitional_conversion,[status(esa)],[f_978_2]) ).

cnf(f_978_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3149),U_3152),c_Divides_Odiv__class_Odiv(U_3149,U_3151,U_3150)) = c_Divides_Odiv__class_Odiv(U_3149,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3149),U_3152),U_3151),U_3150)
    | ~ c_Rings_Odvd__class_Odvd(U_3149,U_3150,U_3151)
    | ~ class_Divides_Osemiring__div(U_3149) ),
    inference(clausify,[status(thm)],[f_978_3]) ).

fof(f_979_1,plain,
    ! [V_m,V_n] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_n),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_m,V_n)) = V_m
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m) ),
    inference(fof_nnf,[status(thm)],[fact_zdvd__mult__div__cancel]) ).

fof(f_979_2,plain,
    ! [U_3154,U_3153] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3153),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3154,U_3153)) = U_3154
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_3153,U_3154) ),
    inference(variable_rename,[status(thm)],[f_979_1]) ).

fof(f_979_3,plain,
    ! [U_3154,U_3153] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3153),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3154,U_3153)) = U_3154
      | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_3153,U_3154) ),
    inference(definitional_conversion,[status(esa)],[f_979_2]) ).

cnf(f_979_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3153),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3154,U_3153)) = U_3154
    | ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_3153,U_3154) ),
    inference(clausify,[status(thm)],[f_979_3]) ).

fof(f_980_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Divides_Odiv__class_Odiv(T_a,V_b,V_a)) = V_b
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_dvd__mult__div__cancel]) ).

fof(f_980_2,plain,
    ! [U_3157,U_3156,U_3155] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3155),U_3156),c_Divides_Odiv__class_Odiv(U_3155,U_3157,U_3156)) = U_3157
      | ~ c_Rings_Odvd__class_Odvd(U_3155,U_3156,U_3157)
      | ~ class_Divides_Osemiring__div(U_3155) ),
    inference(variable_rename,[status(thm)],[f_980_1]) ).

fof(f_980_3,plain,
    ! [U_3155,U_3156,U_3157] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3155),U_3156),c_Divides_Odiv__class_Odiv(U_3155,U_3157,U_3156)) = U_3157
      | ~ c_Rings_Odvd__class_Odvd(U_3155,U_3156,U_3157)
      | ~ class_Divides_Osemiring__div(U_3155) ),
    inference(definitional_conversion,[status(esa)],[f_980_2]) ).

cnf(f_980_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3155),U_3156),c_Divides_Odiv__class_Odiv(U_3155,U_3157,U_3156)) = U_3157
    | ~ c_Rings_Odvd__class_Odvd(U_3155,U_3156,U_3157)
    | ~ class_Divides_Osemiring__div(U_3155) ),
    inference(clausify,[status(thm)],[f_980_3]) ).

fof(f_981_1,plain,
    ! [V_n,V_x,V_y,T_a] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Divides_Odiv__class_Odiv(T_a,V_x,V_y)),V_n) = c_Divides_Odiv__class_Odiv(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n))
      | ~ c_Rings_Odvd__class_Odvd(T_a,V_y,V_x)
      | ~ class_Divides_Osemiring__div(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__power]) ).

fof(f_981_2,plain,
    ! [U_3161,U_3160,U_3159,U_3158] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_3158),c_Divides_Odiv__class_Odiv(U_3158,U_3160,U_3159)),U_3161) = c_Divides_Odiv__class_Odiv(U_3158,hAPP(hAPP(c_Power_Opower__class_Opower(U_3158),U_3160),U_3161),hAPP(hAPP(c_Power_Opower__class_Opower(U_3158),U_3159),U_3161))
      | ~ c_Rings_Odvd__class_Odvd(U_3158,U_3159,U_3160)
      | ~ class_Divides_Osemiring__div(U_3158) ),
    inference(variable_rename,[status(thm)],[f_981_1]) ).

fof(f_981_3,plain,
    ! [U_3158,U_3159,U_3160,U_3161] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_3158),c_Divides_Odiv__class_Odiv(U_3158,U_3160,U_3159)),U_3161) = c_Divides_Odiv__class_Odiv(U_3158,hAPP(hAPP(c_Power_Opower__class_Opower(U_3158),U_3160),U_3161),hAPP(hAPP(c_Power_Opower__class_Opower(U_3158),U_3159),U_3161))
      | ~ c_Rings_Odvd__class_Odvd(U_3158,U_3159,U_3160)
      | ~ class_Divides_Osemiring__div(U_3158) ),
    inference(definitional_conversion,[status(esa)],[f_981_2]) ).

cnf(f_981_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_3158),c_Divides_Odiv__class_Odiv(U_3158,U_3160,U_3159)),U_3161) = c_Divides_Odiv__class_Odiv(U_3158,hAPP(hAPP(c_Power_Opower__class_Opower(U_3158),U_3160),U_3161),hAPP(hAPP(c_Power_Opower__class_Opower(U_3158),U_3159),U_3161))
    | ~ c_Rings_Odvd__class_Odvd(U_3158,U_3159,U_3160)
    | ~ class_Divides_Osemiring__div(U_3158) ),
    inference(clausify,[status(thm)],[f_981_3]) ).

fof(f_982_1,plain,
    ! [V_k_2,V_i_2] :
      ( ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2)
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,V_k_2)
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i_2) )
          & V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_i_2)
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_i_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        | ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i_2,V_k_2)
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i_2) )
        | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__eq__0__iff]) ).

fof(f_982_2,plain,
    ! [U_3163,U_3162] :
      ( ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3162,U_3163) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3163,U_3162)
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3162,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3162,U_3163)
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3162) )
          & U_3163 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3163,U_3162)
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3162,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        | ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3162,U_3163)
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3162) )
        | U_3163 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3162,U_3163) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_982_1]) ).

fof(f_982_3,plain,
    ( ! [U_3167,U_3165] :
        ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3165,U_3167) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3167,U_3165)
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3165,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
          & ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3165,U_3167)
            | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3165) )
          & U_3167 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3166,U_3164] :
        ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3166,U_3164)
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3164,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        | ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3164,U_3166)
          & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3164) )
        | U_3166 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3164,U_3166) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_982_2]) ).

fof(f_982_4,plain,
    ( ! [U_3165,U_3167] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3167,U_3165)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3165,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ sP279(U_3165,U_3167) )
    & ! [U_3165,U_3167] :
        ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3165,U_3167)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3165)
        | ~ sP279(U_3165,U_3167) )
    & ! [U_3165,U_3167] :
        ( U_3167 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP279(U_3165,U_3167) )
    & ! [U_3164,U_3166] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3166,U_3164)
        | ~ sP278(U_3164,U_3166) )
    & ! [U_3164,U_3166] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3164,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ sP278(U_3164,U_3166) )
    & ! [U_3164,U_3166] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3164,U_3166)
        | ~ sP277(U_3164,U_3166) )
    & ! [U_3164,U_3166] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3164)
        | ~ sP277(U_3164,U_3166) )
    & ! [U_3165,U_3167] :
        ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3165,U_3167) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | sP279(U_3165,U_3167) )
    & ! [U_3164,U_3166] :
        ( sP278(U_3164,U_3166)
        | sP277(U_3164,U_3166)
        | U_3166 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3164,U_3166) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP277,sP278,sP279])],[f_982_3]) ).

cnf(f_982_5,plain,
    ( sP278(U_3164,U_3166)
    | sP277(U_3164,U_3166)
    | U_3166 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3164,U_3166) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_982_4]) ).

cnf(f_982_6,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3165,U_3167) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | sP279(U_3165,U_3167) ),
    inference(clausify,[status(thm)],[f_982_4]) ).

cnf(f_982_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3164)
    | ~ sP277(U_3164,U_3166) ),
    inference(clausify,[status(thm)],[f_982_4]) ).

cnf(f_982_8,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3164,U_3166)
    | ~ sP277(U_3164,U_3166) ),
    inference(clausify,[status(thm)],[f_982_4]) ).

cnf(f_982_9,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3164,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ sP278(U_3164,U_3166) ),
    inference(clausify,[status(thm)],[f_982_4]) ).

cnf(f_982_10,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3166,U_3164)
    | ~ sP278(U_3164,U_3166) ),
    inference(clausify,[status(thm)],[f_982_4]) ).

cnf(f_982_11,plain,
    ( U_3167 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP279(U_3165,U_3167) ),
    inference(clausify,[status(thm)],[f_982_4]) ).

cnf(f_982_12,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3165,U_3167)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3165)
    | ~ sP279(U_3165,U_3167) ),
    inference(clausify,[status(thm)],[f_982_4]) ).

cnf(f_982_13,plain,
    ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3167,U_3165)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3165,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ sP279(U_3165,U_3167) ),
    inference(clausify,[status(thm)],[f_982_4]) ).

fof(f_983_1,plain,
    ! [V_ab_2,V_b_2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_ab_2,V_b_2))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ab_2) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ab_2)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_ab_2,V_b_2)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2) ),
    inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__nonneg__iff]) ).

fof(f_983_2,plain,
    ! [U_3169,U_3168] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3169,U_3168))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3169) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3169)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3169,U_3168)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3168) ),
    inference(variable_rename,[status(thm)],[f_983_1]) ).

fof(f_983_3,plain,
    ( ! [U_3168,U_3169] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3169,U_3168))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3169)
        | ~ sP280(U_3168,U_3169) )
    & ! [U_3168,U_3169] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3169)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3169,U_3168))
        | ~ sP280(U_3168,U_3169) )
    & ! [U_3168,U_3169] :
        ( sP280(U_3168,U_3169)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3168) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP280])],[f_983_2]) ).

cnf(f_983_4,plain,
    ( sP280(U_3168,U_3169)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3168) ),
    inference(clausify,[status(thm)],[f_983_3]) ).

cnf(f_983_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3169)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3169,U_3168))
    | ~ sP280(U_3168,U_3169) ),
    inference(clausify,[status(thm)],[f_983_3]) ).

cnf(f_983_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3169,U_3168))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3169)
    | ~ sP280(U_3168,U_3169) ),
    inference(clausify,[status(thm)],[f_983_3]) ).

fof(f_984_1,plain,
    ! [V_i_2,V_k_2] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_i_2) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,V_i_2)
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_i_2,V_k_2)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2) ),
    inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__pos__iff]) ).

fof(f_984_2,plain,
    ! [U_3171,U_3170] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3171,U_3170))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3170,U_3171) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3170,U_3171)
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3171,U_3170)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3170) ),
    inference(variable_rename,[status(thm)],[f_984_1]) ).

fof(f_984_3,plain,
    ( ! [U_3171,U_3170] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3171,U_3170))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3170,U_3171)
        | ~ sP281(U_3171,U_3170) )
    & ! [U_3171,U_3170] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3170,U_3171)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3171,U_3170))
        | ~ sP281(U_3171,U_3170) )
    & ! [U_3171,U_3170] :
        ( sP281(U_3171,U_3170)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3170) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP281])],[f_984_2]) ).

cnf(f_984_4,plain,
    ( sP281(U_3171,U_3170)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3170) ),
    inference(clausify,[status(thm)],[f_984_3]) ).

cnf(f_984_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3170,U_3171)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3171,U_3170))
    | ~ sP281(U_3171,U_3170) ),
    inference(clausify,[status(thm)],[f_984_3]) ).

cnf(f_984_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3171,U_3170))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3170,U_3171)
    | ~ sP281(U_3171,U_3170) ),
    inference(clausify,[status(thm)],[f_984_3]) ).

fof(f_985_1,plain,
    ! [V_b_2,V_ab_2] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_ab_2,V_b_2))
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_2,V_ab_2) )
        & ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_2)
            & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_2,V_ab_2) )
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_ab_2,V_b_2)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ab_2) ),
    inference(fof_nnf,[status(thm)],[fact_nonneg1__imp__zdiv__pos__iff]) ).

fof(f_985_2,plain,
    ! [U_3173,U_3172] :
      ( ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3172,U_3173))
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3173)
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3173,U_3172) )
        & ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3173)
            & c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3173,U_3172) )
          | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3172,U_3173)) ) )
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3172) ),
    inference(variable_rename,[status(thm)],[f_985_1]) ).

fof(f_985_3,plain,
    ( ! [U_3173,U_3172] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3173)
        | ~ sP282(U_3173,U_3172) )
    & ! [U_3173,U_3172] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3173,U_3172)
        | ~ sP282(U_3173,U_3172) )
    & ! [U_3173,U_3172] :
        ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3172,U_3173))
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3173)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3173,U_3172)
        | ~ sP283(U_3173,U_3172) )
    & ! [U_3173,U_3172] :
        ( sP282(U_3173,U_3172)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3172,U_3173))
        | ~ sP283(U_3173,U_3172) )
    & ! [U_3173,U_3172] :
        ( sP283(U_3173,U_3172)
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3172) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP282,sP283])],[f_985_2]) ).

cnf(f_985_4,plain,
    ( sP283(U_3173,U_3172)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3172) ),
    inference(clausify,[status(thm)],[f_985_3]) ).

cnf(f_985_5,plain,
    ( sP282(U_3173,U_3172)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3172,U_3173))
    | ~ sP283(U_3173,U_3172) ),
    inference(clausify,[status(thm)],[f_985_3]) ).

cnf(f_985_6,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3172,U_3173))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3173)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3173,U_3172)
    | ~ sP283(U_3173,U_3172) ),
    inference(clausify,[status(thm)],[f_985_3]) ).

cnf(f_985_7,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3173,U_3172)
    | ~ sP282(U_3173,U_3172) ),
    inference(clausify,[status(thm)],[f_985_3]) ).

cnf(f_985_8,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3173)
    | ~ sP282(U_3173,U_3172) ),
    inference(clausify,[status(thm)],[f_985_3]) ).

fof(f_986_1,plain,
    ! [V_b,V_b_H,V_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__mono2]) ).

fof(f_986_2,plain,
    ! [U_3176,U_3175,U_3174] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3174,U_3176),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3174,U_3175))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3175,U_3176)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3175)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3174) ),
    inference(variable_rename,[status(thm)],[f_986_1]) ).

fof(f_986_3,plain,
    ! [U_3176,U_3174,U_3175] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3174,U_3176),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3174,U_3175))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3175,U_3176)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3175)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3174) ),
    inference(definitional_conversion,[status(esa)],[f_986_2]) ).

cnf(f_986_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3174,U_3176),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3174,U_3175))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3175,U_3176)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3175)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3174) ),
    inference(clausify,[status(thm)],[f_986_3]) ).

fof(f_987_1,plain,
    ! [V_b,V_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__nonneg__neg__le0]) ).

fof(f_987_2,plain,
    ! [U_3178,U_3177] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3177,U_3178),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3178,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3177) ),
    inference(variable_rename,[status(thm)],[f_987_1]) ).

fof(f_987_3,plain,
    ! [U_3178,U_3177] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3177,U_3178),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3178,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3177) ),
    inference(definitional_conversion,[status(esa)],[f_987_2]) ).

cnf(f_987_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3177,U_3178),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3178,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3177) ),
    inference(clausify,[status(thm)],[f_987_3]) ).

fof(f_988_1,plain,
    ! [V_b,V_a] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,V_b)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a) ),
    inference(fof_nnf,[status(thm)],[fact_div__pos__pos__trivial]) ).

fof(f_988_2,plain,
    ! [U_3180,U_3179] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3179,U_3180) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3179,U_3180)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3179) ),
    inference(variable_rename,[status(thm)],[f_988_1]) ).

fof(f_988_3,plain,
    ! [U_3179,U_3180] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3179,U_3180) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3179,U_3180)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3179) ),
    inference(definitional_conversion,[status(esa)],[f_988_2]) ).

cnf(f_988_4,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3179,U_3180) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3179,U_3180)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3179) ),
    inference(clausify,[status(thm)],[f_988_3]) ).

fof(f_989_1,plain,
    ! [V_ab_2,V_b_2] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_ab_2,V_b_2))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_ab_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_ab_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_ab_2,V_b_2)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(fof_nnf,[status(thm)],[fact_neg__imp__zdiv__nonneg__iff]) ).

fof(f_989_2,plain,
    ! [U_3182,U_3181] :
      ( ( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3182,U_3181))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3182,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
        & ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3182,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
          | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3182,U_3181)) ) )
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3181,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[f_989_1]) ).

fof(f_989_3,plain,
    ( ! [U_3182,U_3181] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3182,U_3181))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3182,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ sP284(U_3182,U_3181) )
    & ! [U_3182,U_3181] :
        ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3182,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3182,U_3181))
        | ~ sP284(U_3182,U_3181) )
    & ! [U_3182,U_3181] :
        ( sP284(U_3182,U_3181)
        | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3181,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP284])],[f_989_2]) ).

cnf(f_989_4,plain,
    ( sP284(U_3182,U_3181)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3181,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(clausify,[status(thm)],[f_989_3]) ).

cnf(f_989_5,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3182,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3182,U_3181))
    | ~ sP284(U_3182,U_3181) ),
    inference(clausify,[status(thm)],[f_989_3]) ).

cnf(f_989_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3182,U_3181))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3182,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ sP284(U_3182,U_3181) ),
    inference(clausify,[status(thm)],[f_989_3]) ).

fof(f_990_1,plain,
    ! [V_b,V_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(fof_nnf,[status(thm)],[fact_div__nonpos__pos__le0]) ).

fof(f_990_2,plain,
    ! [U_3184,U_3183] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3183,U_3184),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3184)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3183,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[f_990_1]) ).

fof(f_990_3,plain,
    ! [U_3184,U_3183] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3183,U_3184),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3184)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3183,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(definitional_conversion,[status(esa)],[f_990_2]) ).

cnf(f_990_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3183,U_3184),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3184)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3183,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(clausify,[status(thm)],[f_990_3]) ).

fof(f_991_1,plain,
    ! [V_b,V_b_H,V_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b_H),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg]) ).

fof(f_991_2,plain,
    ! [U_3187,U_3186,U_3185] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3185,U_3186),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3185,U_3187))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3186,U_3187)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3186)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3185,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[f_991_1]) ).

fof(f_991_3,plain,
    ! [U_3186,U_3185,U_3187] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3185,U_3186),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3185,U_3187))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3186,U_3187)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3186)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3185,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(definitional_conversion,[status(esa)],[f_991_2]) ).

cnf(f_991_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3185,U_3186),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3185,U_3187))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3186,U_3187)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3186)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3185,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(clausify,[status(thm)],[f_991_3]) ).

fof(f_992_1,plain,
    ! [V_b,V_a] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_a)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(fof_nnf,[status(thm)],[fact_div__neg__neg__trivial]) ).

fof(f_992_2,plain,
    ! [U_3189,U_3188] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3188,U_3189) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3189,U_3188)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3188,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[f_992_1]) ).

fof(f_992_3,plain,
    ! [U_3188,U_3189] :
      ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3188,U_3189) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3189,U_3188)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3188,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(definitional_conversion,[status(esa)],[f_992_2]) ).

cnf(f_992_4,plain,
    ( c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3188,U_3189) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3189,U_3188)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3188,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
    inference(clausify,[status(thm)],[f_992_3]) ).

fof(f_993_1,plain,
    ! [V_b,V_a_H,V_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__mono1]) ).

fof(f_993_2,plain,
    ! [U_3192,U_3191,U_3190] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3190,U_3192),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3191,U_3192))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3192)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3190,U_3191) ),
    inference(variable_rename,[status(thm)],[f_993_1]) ).

fof(f_993_3,plain,
    ! [U_3192,U_3191,U_3190] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3190,U_3192),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3191,U_3192))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3192)
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3190,U_3191) ),
    inference(definitional_conversion,[status(esa)],[f_993_2]) ).

cnf(f_993_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3190,U_3192),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3191,U_3192))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3192)
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3190,U_3191) ),
    inference(clausify,[status(thm)],[f_993_3]) ).

fof(f_994_1,plain,
    ! [V_b,V_a_H,V_a] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a_H,V_b),c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_a,V_b))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_a,V_a_H) ),
    inference(fof_nnf,[status(thm)],[fact_zdiv__mono1__neg]) ).

fof(f_994_2,plain,
    ! [U_3195,U_3194,U_3193] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3194,U_3195),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3193,U_3195))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3195,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3193,U_3194) ),
    inference(variable_rename,[status(thm)],[f_994_1]) ).

fof(f_994_3,plain,
    ! [U_3195,U_3193,U_3194] :
      ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3194,U_3195),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3193,U_3195))
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3195,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
      | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3193,U_3194) ),
    inference(definitional_conversion,[status(esa)],[f_994_2]) ).

cnf(f_994_4,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3194,U_3195),c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3193,U_3195))
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_3195,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_3193,U_3194) ),
    inference(clausify,[status(thm)],[f_994_3]) ).

fof(f_995_1,plain,
    ! [V_k,V_x] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,V_x,V_k),V_x)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_x) ),
    inference(fof_nnf,[status(thm)],[fact_int__div__less__self]) ).

fof(f_995_2,plain,
    ! [U_3197,U_3196] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3196,U_3197),U_3196)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_3197)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3196) ),
    inference(variable_rename,[status(thm)],[f_995_1]) ).

fof(f_995_3,plain,
    ! [U_3196,U_3197] :
      ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3196,U_3197),U_3196)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_3197)
      | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3196) ),
    inference(definitional_conversion,[status(esa)],[f_995_2]) ).

cnf(f_995_4,plain,
    ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Divides_Odiv__class_Odiv(tc_Int_Oint,U_3196,U_3197),U_3196)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_3197)
    | ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_3196) ),
    inference(clausify,[status(thm)],[f_995_3]) ).

fof(f_996_1,plain,
    ! [T_1] :
      ( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1))
      | ~ class_Groups_Ocancel__comm__monoid__add(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add]) ).

fof(f_996_2,plain,
    ! [U_3198] :
      ( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(U_3198))
      | ~ class_Groups_Ocancel__comm__monoid__add(U_3198) ),
    inference(variable_rename,[status(thm)],[f_996_1]) ).

fof(f_996_3,plain,
    ! [U_3198] :
      ( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(U_3198))
      | ~ class_Groups_Ocancel__comm__monoid__add(U_3198) ),
    inference(definitional_conversion,[status(esa)],[f_996_2]) ).

cnf(f_996_4,plain,
    ( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(U_3198))
    | ~ class_Groups_Ocancel__comm__monoid__add(U_3198) ),
    inference(clausify,[status(thm)],[f_996_3]) ).

fof(f_997_1,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add]) ).

fof(f_997_2,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_997_1]) ).

cnf(f_997_3,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_997_2]) ).

fof(f_998_1,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add]) ).

fof(f_998_2,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_998_1]) ).

cnf(f_998_3,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_998_2]) ).

fof(f_999_1,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__comm__monoid__add]) ).

fof(f_999_2,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_999_1]) ).

cnf(f_999_3,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_999_2]) ).

fof(f_1000_1,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__comm__monoid__add]) ).

fof(f_1000_2,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1000_1]) ).

cnf(f_1000_3,plain,
    class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1000_2]) ).

fof(f_1001_1,plain,
    ! [T_2,T_1] :
      ( class_Orderings_Opreorder(tc_fun(T_2,T_1))
      | ~ class_Orderings_Opreorder(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder]) ).

fof(f_1001_2,plain,
    ! [U_3200,U_3199] :
      ( class_Orderings_Opreorder(tc_fun(U_3200,U_3199))
      | ~ class_Orderings_Opreorder(U_3199) ),
    inference(variable_rename,[status(thm)],[f_1001_1]) ).

fof(f_1001_3,plain,
    ! [U_3200,U_3199] :
      ( class_Orderings_Opreorder(tc_fun(U_3200,U_3199))
      | ~ class_Orderings_Opreorder(U_3199) ),
    inference(definitional_conversion,[status(esa)],[f_1001_2]) ).

cnf(f_1001_4,plain,
    ( class_Orderings_Opreorder(tc_fun(U_3200,U_3199))
    | ~ class_Orderings_Opreorder(U_3199) ),
    inference(clausify,[status(thm)],[f_1001_3]) ).

fof(f_1002_1,plain,
    ! [T_2,T_1] :
      ( class_Orderings_Oorder(tc_fun(T_2,T_1))
      | ~ class_Orderings_Oorder(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder]) ).

fof(f_1002_2,plain,
    ! [U_3202,U_3201] :
      ( class_Orderings_Oorder(tc_fun(U_3202,U_3201))
      | ~ class_Orderings_Oorder(U_3201) ),
    inference(variable_rename,[status(thm)],[f_1002_1]) ).

fof(f_1002_3,plain,
    ! [U_3202,U_3201] :
      ( class_Orderings_Oorder(tc_fun(U_3202,U_3201))
      | ~ class_Orderings_Oorder(U_3201) ),
    inference(definitional_conversion,[status(esa)],[f_1002_2]) ).

cnf(f_1002_4,plain,
    ( class_Orderings_Oorder(tc_fun(U_3202,U_3201))
    | ~ class_Orderings_Oorder(U_3201) ),
    inference(clausify,[status(thm)],[f_1002_3]) ).

fof(f_1003_1,plain,
    ! [T_2,T_1] :
      ( class_Orderings_Oord(tc_fun(T_2,T_1))
      | ~ class_Orderings_Oord(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord]) ).

fof(f_1003_2,plain,
    ! [U_3204,U_3203] :
      ( class_Orderings_Oord(tc_fun(U_3204,U_3203))
      | ~ class_Orderings_Oord(U_3203) ),
    inference(variable_rename,[status(thm)],[f_1003_1]) ).

fof(f_1003_3,plain,
    ! [U_3203,U_3204] :
      ( class_Orderings_Oord(tc_fun(U_3204,U_3203))
      | ~ class_Orderings_Oord(U_3203) ),
    inference(definitional_conversion,[status(esa)],[f_1003_2]) ).

cnf(f_1003_4,plain,
    ( class_Orderings_Oord(tc_fun(U_3204,U_3203))
    | ~ class_Orderings_Oord(U_3203) ),
    inference(clausify,[status(thm)],[f_1003_3]) ).

fof(f_1004_1,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).

fof(f_1004_2,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1004_1]) ).

cnf(f_1004_3,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1004_2]) ).

fof(f_1005_1,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add]) ).

fof(f_1005_2,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1005_1]) ).

cnf(f_1005_3,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1005_2]) ).

fof(f_1006_1,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le]) ).

fof(f_1006_2,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1006_1]) ).

cnf(f_1006_3,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1006_2]) ).

fof(f_1007_1,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__comm__semiring__strict]) ).

fof(f_1007_2,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1007_1]) ).

cnf(f_1007_3,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1007_2]) ).

fof(f_1008_1,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1__strict]) ).

fof(f_1008_2,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1008_1]) ).

cnf(f_1008_3,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1008_2]) ).

fof(f_1009_1,plain,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__strict]) ).

fof(f_1009_2,plain,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1009_1]) ).

cnf(f_1009_3,plain,
    class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1009_2]) ).

fof(f_1010_1,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add]) ).

fof(f_1010_2,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1010_1]) ).

cnf(f_1010_3,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1010_2]) ).

fof(f_1011_1,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__comm__monoid__add]) ).

fof(f_1011_2,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1011_1]) ).

cnf(f_1011_3,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1011_2]) ).

fof(f_1012_1,plain,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__group__add]) ).

fof(f_1012_2,plain,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1012_1]) ).

cnf(f_1012_3,plain,
    class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1012_2]) ).

fof(f_1013_1,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__ab__semigroup__add]) ).

fof(f_1013_2,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1013_1]) ).

cnf(f_1013_3,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1013_2]) ).

fof(f_1014_1,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__1__no__zero__divisors]) ).

fof(f_1014_2,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1014_1]) ).

cnf(f_1014_3,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1014_2]) ).

fof(f_1015_1,plain,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__cancel__semiring]) ).

fof(f_1015_2,plain,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1015_1]) ).

cnf(f_1015_3,plain,
    class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1015_2]) ).

fof(f_1016_1,plain,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring__strict]) ).

fof(f_1016_2,plain,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1016_1]) ).

cnf(f_1016_3,plain,
    class_Rings_Olinordered__ring__strict(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1016_2]) ).

fof(f_1017_1,plain,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__no__zero__divisors]) ).

fof(f_1017_2,plain,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1017_1]) ).

cnf(f_1017_3,plain,
    class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1017_2]) ).

fof(f_1018_1,plain,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__comm__semiring]) ).

fof(f_1018_2,plain,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1018_1]) ).

cnf(f_1018_3,plain,
    class_Rings_Oordered__comm__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1018_2]) ).

fof(f_1019_1,plain,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1]) ).

fof(f_1019_2,plain,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1019_1]) ).

cnf(f_1019_3,plain,
    class_Rings_Olinordered__semiring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1019_2]) ).

fof(f_1020_1,plain,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add]) ).

fof(f_1020_2,plain,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1020_1]) ).

cnf(f_1020_3,plain,
    class_Groups_Oordered__ab__group__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1020_2]) ).

fof(f_1021_1,plain,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__semigroup__add]) ).

fof(f_1021_2,plain,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1021_1]) ).

cnf(f_1021_3,plain,
    class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1021_2]) ).

fof(f_1022_1,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]) ).

fof(f_1022_2,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1022_1]) ).

cnf(f_1022_3,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1022_2]) ).

fof(f_1023_1,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]) ).

fof(f_1023_2,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1023_1]) ).

cnf(f_1023_3,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1023_2]) ).

fof(f_1024_1,plain,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__mult]) ).

fof(f_1024_2,plain,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1024_1]) ).

cnf(f_1024_3,plain,
    class_Groups_Oab__semigroup__mult(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1024_2]) ).

fof(f_1025_1,plain,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__mult]) ).

fof(f_1025_2,plain,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1025_1]) ).

cnf(f_1025_3,plain,
    class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1025_2]) ).

fof(f_1026_1,plain,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__add]) ).

fof(f_1026_2,plain,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1026_1]) ).

cnf(f_1026_3,plain,
    class_Groups_Oab__semigroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1026_2]) ).

fof(f_1027_1,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]) ).

fof(f_1027_2,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1027_1]) ).

cnf(f_1027_3,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1027_2]) ).

fof(f_1028_1,plain,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ono__zero__divisors]) ).

fof(f_1028_2,plain,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1028_1]) ).

cnf(f_1028_3,plain,
    class_Rings_Ono__zero__divisors(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1028_2]) ).

fof(f_1029_1,plain,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__add]) ).

fof(f_1029_2,plain,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1029_1]) ).

cnf(f_1029_3,plain,
    class_Groups_Ocomm__monoid__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1029_2]) ).

fof(f_1030_1,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]) ).

fof(f_1030_2,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1030_1]) ).

cnf(f_1030_3,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1030_2]) ).

fof(f_1031_1,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]) ).

fof(f_1031_2,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1031_1]) ).

cnf(f_1031_3,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1031_2]) ).

fof(f_1032_1,plain,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__1]) ).

fof(f_1032_2,plain,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1032_1]) ).

cnf(f_1032_3,plain,
    class_Rings_Ocomm__semiring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1032_2]) ).

fof(f_1033_1,plain,
    class_Rings_Ocomm__semiring__0(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__0]) ).

fof(f_1033_2,plain,
    class_Rings_Ocomm__semiring__0(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1033_1]) ).

cnf(f_1033_3,plain,
    class_Rings_Ocomm__semiring__0(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1033_2]) ).

fof(f_1034_1,plain,
    class_Divides_Osemiring__div(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]) ).

fof(f_1034_2,plain,
    class_Divides_Osemiring__div(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1034_1]) ).

cnf(f_1034_3,plain,
    class_Divides_Osemiring__div(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1034_2]) ).

fof(f_1035_1,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]) ).

fof(f_1035_2,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1035_1]) ).

cnf(f_1035_3,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1035_2]) ).

fof(f_1036_1,plain,
    class_Groups_Oab__group__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__group__add]) ).

fof(f_1036_2,plain,
    class_Groups_Oab__group__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1036_1]) ).

cnf(f_1036_3,plain,
    class_Groups_Oab__group__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1036_2]) ).

fof(f_1037_1,plain,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ozero__neq__one]) ).

fof(f_1037_2,plain,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1037_1]) ).

cnf(f_1037_3,plain,
    class_Rings_Ozero__neq__one(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1037_2]) ).

fof(f_1038_1,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]) ).

fof(f_1038_2,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1038_1]) ).

cnf(f_1038_3,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1038_2]) ).

fof(f_1039_1,plain,
    class_Orderings_Opreorder(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]) ).

fof(f_1039_2,plain,
    class_Orderings_Opreorder(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1039_1]) ).

cnf(f_1039_3,plain,
    class_Orderings_Opreorder(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1039_2]) ).

fof(f_1040_1,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]) ).

fof(f_1040_2,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1040_1]) ).

cnf(f_1040_3,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1040_2]) ).

fof(f_1041_1,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]) ).

fof(f_1041_2,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1041_1]) ).

cnf(f_1041_3,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1041_2]) ).

fof(f_1042_1,plain,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring__1]) ).

fof(f_1042_2,plain,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1042_1]) ).

cnf(f_1042_3,plain,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1042_2]) ).

fof(f_1043_1,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]) ).

fof(f_1043_2,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1043_1]) ).

cnf(f_1043_3,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1043_2]) ).

fof(f_1044_1,plain,
    class_Rings_Osemiring__0(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]) ).

fof(f_1044_2,plain,
    class_Rings_Osemiring__0(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1044_1]) ).

cnf(f_1044_3,plain,
    class_Rings_Osemiring__0(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1044_2]) ).

fof(f_1045_1,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]) ).

fof(f_1045_2,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1045_1]) ).

cnf(f_1045_3,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1045_2]) ).

fof(f_1046_1,plain,
    class_Divides_Oring__div(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Divides_Oring__div]) ).

fof(f_1046_2,plain,
    class_Divides_Oring__div(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1046_1]) ).

cnf(f_1046_3,plain,
    class_Divides_Oring__div(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1046_2]) ).

fof(f_1047_1,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]) ).

fof(f_1047_2,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1047_1]) ).

cnf(f_1047_3,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1047_2]) ).

fof(f_1048_1,plain,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring]) ).

fof(f_1048_2,plain,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1048_1]) ).

cnf(f_1048_3,plain,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1048_2]) ).

fof(f_1049_1,plain,
    class_Orderings_Oorder(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oorder]) ).

fof(f_1049_2,plain,
    class_Orderings_Oorder(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1049_1]) ).

cnf(f_1049_3,plain,
    class_Orderings_Oorder(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1049_2]) ).

fof(f_1050_1,plain,
    class_Int_Oring__char__0(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Oring__char__0]) ).

fof(f_1050_2,plain,
    class_Int_Oring__char__0(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1050_1]) ).

cnf(f_1050_3,plain,
    class_Int_Oring__char__0(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1050_2]) ).

fof(f_1051_1,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring]) ).

fof(f_1051_2,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1051_1]) ).

cnf(f_1051_3,plain,
    class_Rings_Osemiring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1051_2]) ).

fof(f_1052_1,plain,
    class_Orderings_Oord(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oord]) ).

fof(f_1052_2,plain,
    class_Orderings_Oord(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1052_1]) ).

cnf(f_1052_3,plain,
    class_Orderings_Oord(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1052_2]) ).

fof(f_1053_1,plain,
    class_Rings_Oring__1(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__1]) ).

fof(f_1053_2,plain,
    class_Rings_Oring__1(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1053_1]) ).

cnf(f_1053_3,plain,
    class_Rings_Oring__1(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1053_2]) ).

fof(f_1054_1,plain,
    class_Power_Opower(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Power_Opower]) ).

fof(f_1054_2,plain,
    class_Power_Opower(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1054_1]) ).

cnf(f_1054_3,plain,
    class_Power_Opower(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1054_2]) ).

fof(f_1055_1,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ozero]) ).

fof(f_1055_2,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1055_1]) ).

cnf(f_1055_3,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1055_2]) ).

fof(f_1056_1,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring]) ).

fof(f_1056_2,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1056_1]) ).

cnf(f_1056_3,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1056_2]) ).

fof(f_1057_1,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oidom]) ).

fof(f_1057_2,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1057_1]) ).

cnf(f_1057_3,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1057_2]) ).

fof(f_1058_1,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oone]) ).

fof(f_1058_2,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1058_1]) ).

cnf(f_1058_3,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1058_2]) ).

fof(f_1059_1,plain,
    class_Rings_Odvd(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Odvd]) ).

fof(f_1059_2,plain,
    class_Rings_Odvd(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1059_1]) ).

cnf(f_1059_3,plain,
    class_Rings_Odvd(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1059_2]) ).

fof(f_1060_1,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).

fof(f_1060_2,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1060_1]) ).

cnf(f_1060_3,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1060_2]) ).

fof(f_1061_1,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add]) ).

fof(f_1061_2,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1061_1]) ).

cnf(f_1061_3,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1061_2]) ).

fof(f_1062_1,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le]) ).

fof(f_1062_2,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1062_1]) ).

cnf(f_1062_3,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1062_2]) ).

fof(f_1063_1,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict]) ).

fof(f_1063_2,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1063_1]) ).

cnf(f_1063_3,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1063_2]) ).

fof(f_1064_1,plain,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring__strict]) ).

fof(f_1064_2,plain,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1064_1]) ).

cnf(f_1064_3,plain,
    class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1064_2]) ).

fof(f_1065_1,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add]) ).

fof(f_1065_2,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1065_1]) ).

cnf(f_1065_3,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1065_2]) ).

fof(f_1066_1,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__comm__monoid__add]) ).

fof(f_1066_2,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1066_1]) ).

cnf(f_1066_3,plain,
    class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1066_2]) ).

fof(f_1067_1,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add]) ).

fof(f_1067_2,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1067_1]) ).

cnf(f_1067_3,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1067_2]) ).

fof(f_1068_1,plain,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__cancel__semiring]) ).

fof(f_1068_2,plain,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1068_1]) ).

cnf(f_1068_3,plain,
    class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1068_2]) ).

fof(f_1069_1,plain,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__comm__semiring]) ).

fof(f_1069_2,plain,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1069_1]) ).

cnf(f_1069_3,plain,
    class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1069_2]) ).

fof(f_1070_1,plain,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__semigroup__add]) ).

fof(f_1070_2,plain,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1070_1]) ).

cnf(f_1070_3,plain,
    class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1070_2]) ).

fof(f_1071_1,plain,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]) ).

fof(f_1071_2,plain,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1071_1]) ).

cnf(f_1071_3,plain,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1071_2]) ).

fof(f_1072_1,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]) ).

fof(f_1072_2,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1072_1]) ).

cnf(f_1072_3,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1072_2]) ).

fof(f_1073_1,plain,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__mult]) ).

fof(f_1073_2,plain,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1073_1]) ).

cnf(f_1073_3,plain,
    class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1073_2]) ).

fof(f_1074_1,plain,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__mult]) ).

fof(f_1074_2,plain,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1074_1]) ).

cnf(f_1074_3,plain,
    class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1074_2]) ).

fof(f_1075_1,plain,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__add]) ).

fof(f_1075_2,plain,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1075_1]) ).

cnf(f_1075_3,plain,
    class_Groups_Oab__semigroup__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1075_2]) ).

fof(f_1076_1,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]) ).

fof(f_1076_2,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1076_1]) ).

cnf(f_1076_3,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1076_2]) ).

fof(f_1077_1,plain,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ono__zero__divisors]) ).

fof(f_1077_2,plain,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1077_1]) ).

cnf(f_1077_3,plain,
    class_Rings_Ono__zero__divisors(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1077_2]) ).

fof(f_1078_1,plain,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__add]) ).

fof(f_1078_2,plain,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1078_1]) ).

cnf(f_1078_3,plain,
    class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1078_2]) ).

fof(f_1079_1,plain,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1]) ).

fof(f_1079_2,plain,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1079_1]) ).

cnf(f_1079_3,plain,
    class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1079_2]) ).

fof(f_1080_1,plain,
    class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__0]) ).

fof(f_1080_2,plain,
    class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1080_1]) ).

cnf(f_1080_3,plain,
    class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1080_2]) ).

fof(f_1081_1,plain,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]) ).

fof(f_1081_2,plain,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1081_1]) ).

cnf(f_1081_3,plain,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1081_2]) ).

fof(f_1082_1,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]) ).

fof(f_1082_2,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1082_1]) ).

cnf(f_1082_3,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1082_2]) ).

fof(f_1083_1,plain,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ozero__neq__one]) ).

fof(f_1083_2,plain,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1083_1]) ).

cnf(f_1083_3,plain,
    class_Rings_Ozero__neq__one(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1083_2]) ).

fof(f_1084_1,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]) ).

fof(f_1084_2,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1084_1]) ).

cnf(f_1084_3,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1084_2]) ).

fof(f_1085_1,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]) ).

fof(f_1085_2,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1085_1]) ).

cnf(f_1085_3,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1085_2]) ).

fof(f_1086_1,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]) ).

fof(f_1086_2,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1086_1]) ).

cnf(f_1086_3,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1086_2]) ).

fof(f_1087_1,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]) ).

fof(f_1087_2,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1087_1]) ).

cnf(f_1087_3,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1087_2]) ).

fof(f_1088_1,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]) ).

fof(f_1088_2,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1088_1]) ).

cnf(f_1088_3,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1088_2]) ).

fof(f_1089_1,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]) ).

fof(f_1089_2,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1089_1]) ).

cnf(f_1089_3,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1089_2]) ).

fof(f_1090_1,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]) ).

fof(f_1090_2,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1090_1]) ).

cnf(f_1090_3,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1090_2]) ).

fof(f_1091_1,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]) ).

fof(f_1091_2,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1091_1]) ).

cnf(f_1091_3,plain,
    class_Rings_Osemiring(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1091_2]) ).

fof(f_1092_1,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oord]) ).

fof(f_1092_2,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1092_1]) ).

cnf(f_1092_3,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1092_2]) ).

fof(f_1093_1,plain,
    class_Power_Opower(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Power_Opower]) ).

fof(f_1093_2,plain,
    class_Power_Opower(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1093_1]) ).

cnf(f_1093_3,plain,
    class_Power_Opower(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1093_2]) ).

fof(f_1094_1,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ozero]) ).

fof(f_1094_2,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1094_1]) ).

cnf(f_1094_3,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1094_2]) ).

fof(f_1095_1,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oone]) ).

fof(f_1095_2,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1095_1]) ).

cnf(f_1095_3,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1095_2]) ).

fof(f_1096_1,plain,
    class_Rings_Odvd(tc_Nat_Onat),
    inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Odvd]) ).

fof(f_1096_2,plain,
    class_Rings_Odvd(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1096_1]) ).

cnf(f_1096_3,plain,
    class_Rings_Odvd(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1096_2]) ).

fof(f_1097_1,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]) ).

fof(f_1097_2,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(definitional_conversion,[status(esa)],[f_1097_1]) ).

cnf(f_1097_3,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_1097_2]) ).

fof(f_1098_1,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]) ).

fof(f_1098_2,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(definitional_conversion,[status(esa)],[f_1098_1]) ).

cnf(f_1098_3,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_1098_2]) ).

fof(f_1099_1,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oord]) ).

fof(f_1099_2,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(definitional_conversion,[status(esa)],[f_1099_1]) ).

cnf(f_1099_3,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(clausify,[status(thm)],[f_1099_2]) ).

fof(f_1100_1,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).

fof(f_1100_2,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1100_1]) ).

cnf(f_1100_3,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1100_2]) ).

fof(f_1101_1,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add]) ).

fof(f_1101_2,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1101_1]) ).

cnf(f_1101_3,plain,
    class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1101_2]) ).

fof(f_1102_1,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le]) ).

fof(f_1102_2,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1102_1]) ).

cnf(f_1102_3,plain,
    class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1102_2]) ).

fof(f_1103_1,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict]) ).

fof(f_1103_2,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1103_1]) ).

cnf(f_1103_3,plain,
    class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1103_2]) ).

fof(f_1104_1,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict]) ).

fof(f_1104_2,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1104_1]) ).

cnf(f_1104_3,plain,
    class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1104_2]) ).

fof(f_1105_1,plain,
    class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra]) ).

fof(f_1105_2,plain,
    class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1105_1]) ).

cnf(f_1105_3,plain,
    class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1105_2]) ).

fof(f_1106_1,plain,
    class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__strict]) ).

fof(f_1106_2,plain,
    class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1106_1]) ).

cnf(f_1106_3,plain,
    class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1106_2]) ).

fof(f_1107_1,plain,
    class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1]) ).

fof(f_1107_2,plain,
    class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1107_1]) ).

cnf(f_1107_3,plain,
    class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1107_2]) ).

fof(f_1108_1,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add]) ).

fof(f_1108_2,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1108_1]) ).

cnf(f_1108_3,plain,
    class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1108_2]) ).

fof(f_1109_1,plain,
    class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra]) ).

fof(f_1109_2,plain,
    class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1109_1]) ).

cnf(f_1109_3,plain,
    class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1109_2]) ).

fof(f_1110_1,plain,
    class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add]) ).

fof(f_1110_2,plain,
    class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1110_1]) ).

cnf(f_1110_3,plain,
    class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1110_2]) ).

fof(f_1111_1,plain,
    class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Olinordered__ab__group__add]) ).

fof(f_1111_2,plain,
    class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1111_1]) ).

cnf(f_1111_3,plain,
    class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1111_2]) ).

fof(f_1112_1,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add]) ).

fof(f_1112_2,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1112_1]) ).

cnf(f_1112_3,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1112_2]) ).

fof(f_1113_1,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors]) ).

fof(f_1113_2,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1113_1]) ).

cnf(f_1113_3,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1113_2]) ).

fof(f_1114_1,plain,
    class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__cancel__semiring]) ).

fof(f_1114_2,plain,
    class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1114_1]) ).

cnf(f_1114_3,plain,
    class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1114_2]) ).

fof(f_1115_1,plain,
    class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__vector]) ).

fof(f_1115_2,plain,
    class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1115_1]) ).

cnf(f_1115_3,plain,
    class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1115_2]) ).

fof(f_1116_1,plain,
    class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring__strict]) ).

fof(f_1116_2,plain,
    class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1116_1]) ).

cnf(f_1116_3,plain,
    class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1116_2]) ).

fof(f_1117_1,plain,
    class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__no__zero__divisors]) ).

fof(f_1117_2,plain,
    class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1117_1]) ).

cnf(f_1117_3,plain,
    class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1117_2]) ).

fof(f_1118_1,plain,
    class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__comm__semiring]) ).

fof(f_1118_2,plain,
    class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1118_1]) ).

cnf(f_1118_3,plain,
    class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1118_2]) ).

fof(f_1119_1,plain,
    class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__1]) ).

fof(f_1119_2,plain,
    class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1119_1]) ).

cnf(f_1119_3,plain,
    class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1119_2]) ).

fof(f_1120_1,plain,
    class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add]) ).

fof(f_1120_2,plain,
    class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1120_1]) ).

cnf(f_1120_3,plain,
    class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1120_2]) ).

fof(f_1121_1,plain,
    class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__semigroup__add]) ).

fof(f_1121_2,plain,
    class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1121_1]) ).

cnf(f_1121_3,plain,
    class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1121_2]) ).

fof(f_1122_1,plain,
    class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring]) ).

fof(f_1122_2,plain,
    class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1122_1]) ).

cnf(f_1122_3,plain,
    class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1122_2]) ).

fof(f_1123_1,plain,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]) ).

fof(f_1123_2,plain,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1123_1]) ).

cnf(f_1123_3,plain,
    class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1123_2]) ).

fof(f_1124_1,plain,
    class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__semigroup__mult]) ).

fof(f_1124_2,plain,
    class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1124_1]) ).

cnf(f_1124_3,plain,
    class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1124_2]) ).

fof(f_1125_1,plain,
    class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__mult]) ).

fof(f_1125_2,plain,
    class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1125_1]) ).

cnf(f_1125_3,plain,
    class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1125_2]) ).

fof(f_1126_1,plain,
    class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__semigroup__add]) ).

fof(f_1126_2,plain,
    class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1126_1]) ).

cnf(f_1126_3,plain,
    class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1126_2]) ).

fof(f_1127_1,plain,
    class_Rings_Oordered__semiring(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__semiring]) ).

fof(f_1127_2,plain,
    class_Rings_Oordered__semiring(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1127_1]) ).

cnf(f_1127_3,plain,
    class_Rings_Oordered__semiring(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1127_2]) ).

fof(f_1128_1,plain,
    class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ono__zero__divisors]) ).

fof(f_1128_2,plain,
    class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1128_1]) ).

cnf(f_1128_3,plain,
    class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1128_2]) ).

fof(f_1129_1,plain,
    class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__add]) ).

fof(f_1129_2,plain,
    class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1129_1]) ).

cnf(f_1129_3,plain,
    class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1129_2]) ).

fof(f_1130_1,plain,
    class_Rings_Olinordered__ring(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring]) ).

fof(f_1130_2,plain,
    class_Rings_Olinordered__ring(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1130_1]) ).

cnf(f_1130_3,plain,
    class_Rings_Olinordered__ring(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1130_2]) ).

fof(f_1131_1,plain,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]) ).

fof(f_1131_2,plain,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1131_1]) ).

cnf(f_1131_3,plain,
    class_Rings_Olinordered__idom(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1131_2]) ).

fof(f_1132_1,plain,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).

fof(f_1132_2,plain,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1132_1]) ).

cnf(f_1132_3,plain,
    class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1132_2]) ).

fof(f_1133_1,plain,
    class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__0]) ).

fof(f_1133_2,plain,
    class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1133_1]) ).

cnf(f_1133_3,plain,
    class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1133_2]) ).

fof(f_1134_1,plain,
    class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring]) ).

fof(f_1134_2,plain,
    class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1134_1]) ).

cnf(f_1134_3,plain,
    class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1134_2]) ).

fof(f_1135_1,plain,
    class_Groups_Oab__group__add(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__group__add]) ).

fof(f_1135_2,plain,
    class_Groups_Oab__group__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1135_1]) ).

cnf(f_1135_3,plain,
    class_Groups_Oab__group__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1135_2]) ).

fof(f_1136_1,plain,
    class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ozero__neq__one]) ).

fof(f_1136_2,plain,
    class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1136_1]) ).

cnf(f_1136_3,plain,
    class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1136_2]) ).

fof(f_1137_1,plain,
    class_Rings_Oordered__ring(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring]) ).

fof(f_1137_2,plain,
    class_Rings_Oordered__ring(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1137_1]) ).

cnf(f_1137_3,plain,
    class_Rings_Oordered__ring(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1137_2]) ).

fof(f_1138_1,plain,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).

fof(f_1138_2,plain,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1138_1]) ).

cnf(f_1138_3,plain,
    class_Orderings_Opreorder(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1138_2]) ).

fof(f_1139_1,plain,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).

fof(f_1139_2,plain,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1139_1]) ).

cnf(f_1139_3,plain,
    class_Orderings_Olinorder(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1139_2]) ).

fof(f_1140_1,plain,
    class_Groups_Omonoid__mult(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__mult]) ).

fof(f_1140_2,plain,
    class_Groups_Omonoid__mult(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1140_1]) ).

cnf(f_1140_3,plain,
    class_Groups_Omonoid__mult(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1140_2]) ).

fof(f_1141_1,plain,
    class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring__1]) ).

fof(f_1141_2,plain,
    class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1141_1]) ).

cnf(f_1141_3,plain,
    class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1141_2]) ).

fof(f_1142_1,plain,
    class_Groups_Omonoid__add(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__add]) ).

fof(f_1142_2,plain,
    class_Groups_Omonoid__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1142_1]) ).

cnf(f_1142_3,plain,
    class_Groups_Omonoid__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1142_2]) ).

fof(f_1143_1,plain,
    class_Rings_Osemiring__0(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__0]) ).

fof(f_1143_2,plain,
    class_Rings_Osemiring__0(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1143_1]) ).

cnf(f_1143_3,plain,
    class_Rings_Osemiring__0(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1143_2]) ).

fof(f_1144_1,plain,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]) ).

fof(f_1144_2,plain,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1144_1]) ).

cnf(f_1144_3,plain,
    class_Groups_Ogroup__add(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1144_2]) ).

fof(f_1145_1,plain,
    class_Rings_Omult__zero(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Omult__zero]) ).

fof(f_1145_2,plain,
    class_Rings_Omult__zero(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1145_1]) ).

cnf(f_1145_3,plain,
    class_Rings_Omult__zero(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1145_2]) ).

fof(f_1146_1,plain,
    class_Rings_Ocomm__ring(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring]) ).

fof(f_1146_2,plain,
    class_Rings_Ocomm__ring(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1146_1]) ).

cnf(f_1146_3,plain,
    class_Rings_Ocomm__ring(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1146_2]) ).

fof(f_1147_1,plain,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).

fof(f_1147_2,plain,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1147_1]) ).

cnf(f_1147_3,plain,
    class_Orderings_Oorder(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1147_2]) ).

fof(f_1148_1,plain,
    class_Int_Oring__char__0(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Int_Oring__char__0]) ).

fof(f_1148_2,plain,
    class_Int_Oring__char__0(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1148_1]) ).

cnf(f_1148_3,plain,
    class_Int_Oring__char__0(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1148_2]) ).

fof(f_1149_1,plain,
    class_Rings_Osemiring(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring]) ).

fof(f_1149_2,plain,
    class_Rings_Osemiring(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1149_1]) ).

cnf(f_1149_3,plain,
    class_Rings_Osemiring(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1149_2]) ).

fof(f_1150_1,plain,
    class_Orderings_Oord(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Oord]) ).

fof(f_1150_2,plain,
    class_Orderings_Oord(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1150_1]) ).

cnf(f_1150_3,plain,
    class_Orderings_Oord(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1150_2]) ).

fof(f_1151_1,plain,
    class_Rings_Oring__1(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1]) ).

fof(f_1151_2,plain,
    class_Rings_Oring__1(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1151_1]) ).

cnf(f_1151_3,plain,
    class_Rings_Oring__1(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1151_2]) ).

fof(f_1152_1,plain,
    class_Fields_Ofield(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield]) ).

fof(f_1152_2,plain,
    class_Fields_Ofield(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1152_1]) ).

cnf(f_1152_3,plain,
    class_Fields_Ofield(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1152_2]) ).

fof(f_1153_1,plain,
    class_Power_Opower(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Power_Opower]) ).

fof(f_1153_2,plain,
    class_Power_Opower(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1153_1]) ).

cnf(f_1153_3,plain,
    class_Power_Opower(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1153_2]) ).

fof(f_1154_1,plain,
    class_Groups_Ozero(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ozero]) ).

fof(f_1154_2,plain,
    class_Groups_Ozero(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1154_1]) ).

cnf(f_1154_3,plain,
    class_Groups_Ozero(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1154_2]) ).

fof(f_1155_1,plain,
    class_Rings_Oring(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oring]) ).

fof(f_1155_2,plain,
    class_Rings_Oring(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1155_1]) ).

cnf(f_1155_3,plain,
    class_Rings_Oring(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1155_2]) ).

fof(f_1156_1,plain,
    class_Rings_Oidom(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oidom]) ).

fof(f_1156_2,plain,
    class_Rings_Oidom(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1156_1]) ).

cnf(f_1156_3,plain,
    class_Rings_Oidom(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1156_2]) ).

fof(f_1157_1,plain,
    class_Groups_Oone(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oone]) ).

fof(f_1157_2,plain,
    class_Groups_Oone(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1157_1]) ).

cnf(f_1157_3,plain,
    class_Groups_Oone(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1157_2]) ).

fof(f_1158_1,plain,
    class_Rings_Odvd(tc_RealDef_Oreal),
    inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Odvd]) ).

fof(f_1158_2,plain,
    class_Rings_Odvd(tc_RealDef_Oreal),
    inference(definitional_conversion,[status(esa)],[f_1158_1]) ).

cnf(f_1158_3,plain,
    class_Rings_Odvd(tc_RealDef_Oreal),
    inference(clausify,[status(thm)],[f_1158_2]) ).

fof(f_1159_1,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).

fof(f_1159_2,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1159_1]) ).

cnf(f_1159_3,plain,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1159_2]) ).

fof(f_1160_1,plain,
    class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra]) ).

fof(f_1160_2,plain,
    class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1160_1]) ).

cnf(f_1160_3,plain,
    class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1160_2]) ).

fof(f_1161_1,plain,
    class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1]) ).

fof(f_1161_2,plain,
    class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1161_1]) ).

cnf(f_1161_3,plain,
    class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1161_2]) ).

fof(f_1162_1,plain,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra]) ).

fof(f_1162_2,plain,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1162_1]) ).

cnf(f_1162_3,plain,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1162_2]) ).

fof(f_1163_1,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add]) ).

fof(f_1163_2,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1163_1]) ).

cnf(f_1163_3,plain,
    class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1163_2]) ).

fof(f_1164_1,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors]) ).

fof(f_1164_2,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1164_1]) ).

cnf(f_1164_3,plain,
    class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1164_2]) ).

fof(f_1165_1,plain,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).

fof(f_1165_2,plain,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1165_1]) ).

cnf(f_1165_3,plain,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1165_2]) ).

fof(f_1166_1,plain,
    class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors]) ).

fof(f_1166_2,plain,
    class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1166_1]) ).

cnf(f_1166_3,plain,
    class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1166_2]) ).

fof(f_1167_1,plain,
    class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add]) ).

fof(f_1167_2,plain,
    class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1167_1]) ).

cnf(f_1167_3,plain,
    class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1167_2]) ).

fof(f_1168_1,plain,
    class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__semigroup__mult]) ).

fof(f_1168_2,plain,
    class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1168_1]) ).

cnf(f_1168_3,plain,
    class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1168_2]) ).

fof(f_1169_1,plain,
    class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult]) ).

fof(f_1169_2,plain,
    class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1169_1]) ).

cnf(f_1169_3,plain,
    class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1169_2]) ).

fof(f_1170_1,plain,
    class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__semigroup__add]) ).

fof(f_1170_2,plain,
    class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1170_1]) ).

cnf(f_1170_3,plain,
    class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1170_2]) ).

fof(f_1171_1,plain,
    class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ono__zero__divisors]) ).

fof(f_1171_2,plain,
    class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1171_1]) ).

cnf(f_1171_3,plain,
    class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1171_2]) ).

fof(f_1172_1,plain,
    class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__add]) ).

fof(f_1172_2,plain,
    class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1172_1]) ).

cnf(f_1172_3,plain,
    class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1172_2]) ).

fof(f_1173_1,plain,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).

fof(f_1173_2,plain,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1173_1]) ).

cnf(f_1173_3,plain,
    class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1173_2]) ).

fof(f_1174_1,plain,
    class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).

fof(f_1174_2,plain,
    class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1174_1]) ).

cnf(f_1174_3,plain,
    class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1174_2]) ).

fof(f_1175_1,plain,
    class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring]) ).

fof(f_1175_2,plain,
    class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1175_1]) ).

cnf(f_1175_3,plain,
    class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1175_2]) ).

fof(f_1176_1,plain,
    class_Groups_Oab__group__add(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__group__add]) ).

fof(f_1176_2,plain,
    class_Groups_Oab__group__add(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1176_1]) ).

cnf(f_1176_3,plain,
    class_Groups_Oab__group__add(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1176_2]) ).

fof(f_1177_1,plain,
    class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ozero__neq__one]) ).

fof(f_1177_2,plain,
    class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1177_1]) ).

cnf(f_1177_3,plain,
    class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1177_2]) ).

fof(f_1178_1,plain,
    class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__mult]) ).

fof(f_1178_2,plain,
    class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1178_1]) ).

cnf(f_1178_3,plain,
    class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1178_2]) ).

fof(f_1179_1,plain,
    class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring__1]) ).

fof(f_1179_2,plain,
    class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1179_1]) ).

cnf(f_1179_3,plain,
    class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1179_2]) ).

fof(f_1180_1,plain,
    class_Groups_Omonoid__add(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__add]) ).

fof(f_1180_2,plain,
    class_Groups_Omonoid__add(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1180_1]) ).

cnf(f_1180_3,plain,
    class_Groups_Omonoid__add(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1180_2]) ).

fof(f_1181_1,plain,
    class_Rings_Osemiring__0(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__0]) ).

fof(f_1181_2,plain,
    class_Rings_Osemiring__0(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1181_1]) ).

cnf(f_1181_3,plain,
    class_Rings_Osemiring__0(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1181_2]) ).

fof(f_1182_1,plain,
    class_Groups_Ogroup__add(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]) ).

fof(f_1182_2,plain,
    class_Groups_Ogroup__add(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1182_1]) ).

cnf(f_1182_3,plain,
    class_Groups_Ogroup__add(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1182_2]) ).

fof(f_1183_1,plain,
    class_Rings_Omult__zero(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Omult__zero]) ).

fof(f_1183_2,plain,
    class_Rings_Omult__zero(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1183_1]) ).

cnf(f_1183_3,plain,
    class_Rings_Omult__zero(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1183_2]) ).

fof(f_1184_1,plain,
    class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring]) ).

fof(f_1184_2,plain,
    class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1184_1]) ).

cnf(f_1184_3,plain,
    class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1184_2]) ).

fof(f_1185_1,plain,
    class_Int_Oring__char__0(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Int_Oring__char__0]) ).

fof(f_1185_2,plain,
    class_Int_Oring__char__0(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1185_1]) ).

cnf(f_1185_3,plain,
    class_Int_Oring__char__0(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1185_2]) ).

fof(f_1186_1,plain,
    class_Rings_Osemiring(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring]) ).

fof(f_1186_2,plain,
    class_Rings_Osemiring(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1186_1]) ).

cnf(f_1186_3,plain,
    class_Rings_Osemiring(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1186_2]) ).

fof(f_1187_1,plain,
    class_Rings_Oring__1(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__1]) ).

fof(f_1187_2,plain,
    class_Rings_Oring__1(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1187_1]) ).

cnf(f_1187_3,plain,
    class_Rings_Oring__1(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1187_2]) ).

fof(f_1188_1,plain,
    class_Fields_Ofield(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield]) ).

fof(f_1188_2,plain,
    class_Fields_Ofield(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1188_1]) ).

cnf(f_1188_3,plain,
    class_Fields_Ofield(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1188_2]) ).

fof(f_1189_1,plain,
    class_Power_Opower(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Power_Opower]) ).

fof(f_1189_2,plain,
    class_Power_Opower(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1189_1]) ).

cnf(f_1189_3,plain,
    class_Power_Opower(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1189_2]) ).

fof(f_1190_1,plain,
    class_Groups_Ozero(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]) ).

fof(f_1190_2,plain,
    class_Groups_Ozero(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1190_1]) ).

cnf(f_1190_3,plain,
    class_Groups_Ozero(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1190_2]) ).

fof(f_1191_1,plain,
    class_Rings_Oring(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring]) ).

fof(f_1191_2,plain,
    class_Rings_Oring(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1191_1]) ).

cnf(f_1191_3,plain,
    class_Rings_Oring(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1191_2]) ).

fof(f_1192_1,plain,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oidom]) ).

fof(f_1192_2,plain,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1192_1]) ).

cnf(f_1192_3,plain,
    class_Rings_Oidom(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1192_2]) ).

fof(f_1193_1,plain,
    class_Groups_Oone(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oone]) ).

fof(f_1193_2,plain,
    class_Groups_Oone(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1193_1]) ).

cnf(f_1193_3,plain,
    class_Groups_Oone(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1193_2]) ).

fof(f_1194_1,plain,
    class_Rings_Odvd(tc_Complex_Ocomplex),
    inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Odvd]) ).

fof(f_1194_2,plain,
    class_Rings_Odvd(tc_Complex_Ocomplex),
    inference(definitional_conversion,[status(esa)],[f_1194_1]) ).

cnf(f_1194_3,plain,
    class_Rings_Odvd(tc_Complex_Ocomplex),
    inference(clausify,[status(thm)],[f_1194_2]) ).

fof(f_1195_1,plain,
    ! [T_1] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Oidom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).

fof(f_1195_2,plain,
    ! [U_3205] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(U_3205))
      | ~ class_Rings_Oidom(U_3205) ),
    inference(variable_rename,[status(thm)],[f_1195_1]) ).

fof(f_1195_3,plain,
    ! [U_3205] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(U_3205))
      | ~ class_Rings_Oidom(U_3205) ),
    inference(definitional_conversion,[status(esa)],[f_1195_2]) ).

cnf(f_1195_4,plain,
    ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(U_3205))
    | ~ class_Rings_Oidom(U_3205) ),
    inference(clausify,[status(thm)],[f_1195_3]) ).

fof(f_1196_1,plain,
    ! [T_1] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add]) ).

fof(f_1196_2,plain,
    ! [U_3206] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3206))
      | ~ class_Rings_Olinordered__idom(U_3206) ),
    inference(variable_rename,[status(thm)],[f_1196_1]) ).

fof(f_1196_3,plain,
    ! [U_3206] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3206))
      | ~ class_Rings_Olinordered__idom(U_3206) ),
    inference(definitional_conversion,[status(esa)],[f_1196_2]) ).

cnf(f_1196_4,plain,
    ( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3206))
    | ~ class_Rings_Olinordered__idom(U_3206) ),
    inference(clausify,[status(thm)],[f_1196_3]) ).

fof(f_1197_1,plain,
    ! [T_1] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le]) ).

fof(f_1197_2,plain,
    ! [U_3207] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(U_3207))
      | ~ class_Rings_Olinordered__idom(U_3207) ),
    inference(variable_rename,[status(thm)],[f_1197_1]) ).

fof(f_1197_3,plain,
    ! [U_3207] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(U_3207))
      | ~ class_Rings_Olinordered__idom(U_3207) ),
    inference(definitional_conversion,[status(esa)],[f_1197_2]) ).

cnf(f_1197_4,plain,
    ( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(U_3207))
    | ~ class_Rings_Olinordered__idom(U_3207) ),
    inference(clausify,[status(thm)],[f_1197_3]) ).

fof(f_1198_1,plain,
    ! [T_1] :
      ( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict]) ).

fof(f_1198_2,plain,
    ! [U_3208] :
      ( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(U_3208))
      | ~ class_Rings_Olinordered__idom(U_3208) ),
    inference(variable_rename,[status(thm)],[f_1198_1]) ).

fof(f_1198_3,plain,
    ! [U_3208] :
      ( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(U_3208))
      | ~ class_Rings_Olinordered__idom(U_3208) ),
    inference(definitional_conversion,[status(esa)],[f_1198_2]) ).

cnf(f_1198_4,plain,
    ( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(U_3208))
    | ~ class_Rings_Olinordered__idom(U_3208) ),
    inference(clausify,[status(thm)],[f_1198_3]) ).

fof(f_1199_1,plain,
    ! [T_1] :
      ( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict]) ).

fof(f_1199_2,plain,
    ! [U_3209] :
      ( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(U_3209))
      | ~ class_Rings_Olinordered__idom(U_3209) ),
    inference(variable_rename,[status(thm)],[f_1199_1]) ).

fof(f_1199_3,plain,
    ! [U_3209] :
      ( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(U_3209))
      | ~ class_Rings_Olinordered__idom(U_3209) ),
    inference(definitional_conversion,[status(esa)],[f_1199_2]) ).

cnf(f_1199_4,plain,
    ( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(U_3209))
    | ~ class_Rings_Olinordered__idom(U_3209) ),
    inference(clausify,[status(thm)],[f_1199_3]) ).

fof(f_1200_1,plain,
    ! [T_1] :
      ( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict]) ).

fof(f_1200_2,plain,
    ! [U_3210] :
      ( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(U_3210))
      | ~ class_Rings_Olinordered__idom(U_3210) ),
    inference(variable_rename,[status(thm)],[f_1200_1]) ).

fof(f_1200_3,plain,
    ! [U_3210] :
      ( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(U_3210))
      | ~ class_Rings_Olinordered__idom(U_3210) ),
    inference(definitional_conversion,[status(esa)],[f_1200_2]) ).

cnf(f_1200_4,plain,
    ( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(U_3210))
    | ~ class_Rings_Olinordered__idom(U_3210) ),
    inference(clausify,[status(thm)],[f_1200_3]) ).

fof(f_1201_1,plain,
    ! [T_1] :
      ( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add]) ).

fof(f_1201_2,plain,
    ! [U_3211] :
      ( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(U_3211))
      | ~ class_Rings_Olinordered__idom(U_3211) ),
    inference(variable_rename,[status(thm)],[f_1201_1]) ).

fof(f_1201_3,plain,
    ! [U_3211] :
      ( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(U_3211))
      | ~ class_Rings_Olinordered__idom(U_3211) ),
    inference(definitional_conversion,[status(esa)],[f_1201_2]) ).

cnf(f_1201_4,plain,
    ( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(U_3211))
    | ~ class_Rings_Olinordered__idom(U_3211) ),
    inference(clausify,[status(thm)],[f_1201_3]) ).

fof(f_1202_1,plain,
    ! [T_1] :
      ( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add]) ).

fof(f_1202_2,plain,
    ! [U_3212] :
      ( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(U_3212))
      | ~ class_Rings_Olinordered__idom(U_3212) ),
    inference(variable_rename,[status(thm)],[f_1202_1]) ).

fof(f_1202_3,plain,
    ! [U_3212] :
      ( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(U_3212))
      | ~ class_Rings_Olinordered__idom(U_3212) ),
    inference(definitional_conversion,[status(esa)],[f_1202_2]) ).

cnf(f_1202_4,plain,
    ( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(U_3212))
    | ~ class_Rings_Olinordered__idom(U_3212) ),
    inference(clausify,[status(thm)],[f_1202_3]) ).

fof(f_1203_1,plain,
    ! [T_1] :
      ( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add]) ).

fof(f_1203_2,plain,
    ! [U_3213] :
      ( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(U_3213))
      | ~ class_Rings_Olinordered__idom(U_3213) ),
    inference(variable_rename,[status(thm)],[f_1203_1]) ).

fof(f_1203_3,plain,
    ! [U_3213] :
      ( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(U_3213))
      | ~ class_Rings_Olinordered__idom(U_3213) ),
    inference(definitional_conversion,[status(esa)],[f_1203_2]) ).

cnf(f_1203_4,plain,
    ( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(U_3213))
    | ~ class_Rings_Olinordered__idom(U_3213) ),
    inference(clausify,[status(thm)],[f_1203_3]) ).

fof(f_1204_1,plain,
    ! [T_1] :
      ( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))
      | ~ class_Groups_Ocancel__comm__monoid__add(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add]) ).

fof(f_1204_2,plain,
    ! [U_3214] :
      ( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3214))
      | ~ class_Groups_Ocancel__comm__monoid__add(U_3214) ),
    inference(variable_rename,[status(thm)],[f_1204_1]) ).

fof(f_1204_3,plain,
    ! [U_3214] :
      ( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3214))
      | ~ class_Groups_Ocancel__comm__monoid__add(U_3214) ),
    inference(definitional_conversion,[status(esa)],[f_1204_2]) ).

cnf(f_1204_4,plain,
    ( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3214))
    | ~ class_Groups_Ocancel__comm__monoid__add(U_3214) ),
    inference(clausify,[status(thm)],[f_1204_3]) ).

fof(f_1205_1,plain,
    ! [T_1] :
      ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Oidom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors]) ).

fof(f_1205_2,plain,
    ! [U_3215] :
      ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(U_3215))
      | ~ class_Rings_Oidom(U_3215) ),
    inference(variable_rename,[status(thm)],[f_1205_1]) ).

fof(f_1205_3,plain,
    ! [U_3215] :
      ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(U_3215))
      | ~ class_Rings_Oidom(U_3215) ),
    inference(definitional_conversion,[status(esa)],[f_1205_2]) ).

cnf(f_1205_4,plain,
    ( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(U_3215))
    | ~ class_Rings_Oidom(U_3215) ),
    inference(clausify,[status(thm)],[f_1205_3]) ).

fof(f_1206_1,plain,
    ! [T_1] :
      ( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring]) ).

fof(f_1206_2,plain,
    ! [U_3216] :
      ( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(U_3216))
      | ~ class_Rings_Olinordered__idom(U_3216) ),
    inference(variable_rename,[status(thm)],[f_1206_1]) ).

fof(f_1206_3,plain,
    ! [U_3216] :
      ( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(U_3216))
      | ~ class_Rings_Olinordered__idom(U_3216) ),
    inference(definitional_conversion,[status(esa)],[f_1206_2]) ).

cnf(f_1206_4,plain,
    ( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(U_3216))
    | ~ class_Rings_Olinordered__idom(U_3216) ),
    inference(clausify,[status(thm)],[f_1206_3]) ).

fof(f_1207_1,plain,
    ! [T_1] :
      ( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring__strict]) ).

fof(f_1207_2,plain,
    ! [U_3217] :
      ( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(U_3217))
      | ~ class_Rings_Olinordered__idom(U_3217) ),
    inference(variable_rename,[status(thm)],[f_1207_1]) ).

fof(f_1207_3,plain,
    ! [U_3217] :
      ( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(U_3217))
      | ~ class_Rings_Olinordered__idom(U_3217) ),
    inference(definitional_conversion,[status(esa)],[f_1207_2]) ).

cnf(f_1207_4,plain,
    ( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(U_3217))
    | ~ class_Rings_Olinordered__idom(U_3217) ),
    inference(clausify,[status(thm)],[f_1207_3]) ).

fof(f_1208_1,plain,
    ! [T_1] :
      ( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Oidom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors]) ).

fof(f_1208_2,plain,
    ! [U_3218] :
      ( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(U_3218))
      | ~ class_Rings_Oidom(U_3218) ),
    inference(variable_rename,[status(thm)],[f_1208_1]) ).

fof(f_1208_3,plain,
    ! [U_3218] :
      ( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(U_3218))
      | ~ class_Rings_Oidom(U_3218) ),
    inference(definitional_conversion,[status(esa)],[f_1208_2]) ).

cnf(f_1208_4,plain,
    ( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(U_3218))
    | ~ class_Rings_Oidom(U_3218) ),
    inference(clausify,[status(thm)],[f_1208_3]) ).

fof(f_1209_1,plain,
    ! [T_1] :
      ( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__comm__semiring]) ).

fof(f_1209_2,plain,
    ! [U_3219] :
      ( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(U_3219))
      | ~ class_Rings_Olinordered__idom(U_3219) ),
    inference(variable_rename,[status(thm)],[f_1209_1]) ).

fof(f_1209_3,plain,
    ! [U_3219] :
      ( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(U_3219))
      | ~ class_Rings_Olinordered__idom(U_3219) ),
    inference(definitional_conversion,[status(esa)],[f_1209_2]) ).

cnf(f_1209_4,plain,
    ( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(U_3219))
    | ~ class_Rings_Olinordered__idom(U_3219) ),
    inference(clausify,[status(thm)],[f_1209_3]) ).

fof(f_1210_1,plain,
    ! [T_1] :
      ( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__1]) ).

fof(f_1210_2,plain,
    ! [U_3220] :
      ( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(U_3220))
      | ~ class_Rings_Olinordered__idom(U_3220) ),
    inference(variable_rename,[status(thm)],[f_1210_1]) ).

fof(f_1210_3,plain,
    ! [U_3220] :
      ( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(U_3220))
      | ~ class_Rings_Olinordered__idom(U_3220) ),
    inference(definitional_conversion,[status(esa)],[f_1210_2]) ).

cnf(f_1210_4,plain,
    ( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(U_3220))
    | ~ class_Rings_Olinordered__idom(U_3220) ),
    inference(clausify,[status(thm)],[f_1210_3]) ).

fof(f_1211_1,plain,
    ! [T_1] :
      ( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__group__add]) ).

fof(f_1211_2,plain,
    ! [U_3221] :
      ( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(U_3221))
      | ~ class_Rings_Olinordered__idom(U_3221) ),
    inference(variable_rename,[status(thm)],[f_1211_1]) ).

fof(f_1211_3,plain,
    ! [U_3221] :
      ( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(U_3221))
      | ~ class_Rings_Olinordered__idom(U_3221) ),
    inference(definitional_conversion,[status(esa)],[f_1211_2]) ).

cnf(f_1211_4,plain,
    ( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(U_3221))
    | ~ class_Rings_Olinordered__idom(U_3221) ),
    inference(clausify,[status(thm)],[f_1211_3]) ).

fof(f_1212_1,plain,
    ! [T_1] :
      ( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1))
      | ~ class_Groups_Ocancel__comm__monoid__add(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add]) ).

fof(f_1212_2,plain,
    ! [U_3222] :
      ( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(U_3222))
      | ~ class_Groups_Ocancel__comm__monoid__add(U_3222) ),
    inference(variable_rename,[status(thm)],[f_1212_1]) ).

fof(f_1212_3,plain,
    ! [U_3222] :
      ( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(U_3222))
      | ~ class_Groups_Ocancel__comm__monoid__add(U_3222) ),
    inference(definitional_conversion,[status(esa)],[f_1212_2]) ).

cnf(f_1212_4,plain,
    ( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(U_3222))
    | ~ class_Groups_Ocancel__comm__monoid__add(U_3222) ),
    inference(clausify,[status(thm)],[f_1212_3]) ).

fof(f_1213_1,plain,
    ! [T_1] :
      ( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring]) ).

fof(f_1213_2,plain,
    ! [U_3223] :
      ( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(U_3223))
      | ~ class_Rings_Olinordered__idom(U_3223) ),
    inference(variable_rename,[status(thm)],[f_1213_1]) ).

fof(f_1213_3,plain,
    ! [U_3223] :
      ( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(U_3223))
      | ~ class_Rings_Olinordered__idom(U_3223) ),
    inference(definitional_conversion,[status(esa)],[f_1213_2]) ).

cnf(f_1213_4,plain,
    ( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(U_3223))
    | ~ class_Rings_Olinordered__idom(U_3223) ),
    inference(clausify,[status(thm)],[f_1213_3]) ).

fof(f_1214_1,plain,
    ! [T_1] :
      ( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semidom]) ).

fof(f_1214_2,plain,
    ! [U_3224] :
      ( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(U_3224))
      | ~ class_Rings_Olinordered__idom(U_3224) ),
    inference(variable_rename,[status(thm)],[f_1214_1]) ).

fof(f_1214_3,plain,
    ! [U_3224] :
      ( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(U_3224))
      | ~ class_Rings_Olinordered__idom(U_3224) ),
    inference(definitional_conversion,[status(esa)],[f_1214_2]) ).

cnf(f_1214_4,plain,
    ( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(U_3224))
    | ~ class_Rings_Olinordered__idom(U_3224) ),
    inference(clausify,[status(thm)],[f_1214_3]) ).

fof(f_1215_1,plain,
    ! [T_1] :
      ( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Ocomm__semiring__0(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__semigroup__mult]) ).

fof(f_1215_2,plain,
    ! [U_3225] :
      ( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(U_3225))
      | ~ class_Rings_Ocomm__semiring__0(U_3225) ),
    inference(variable_rename,[status(thm)],[f_1215_1]) ).

fof(f_1215_3,plain,
    ! [U_3225] :
      ( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(U_3225))
      | ~ class_Rings_Ocomm__semiring__0(U_3225) ),
    inference(definitional_conversion,[status(esa)],[f_1215_2]) ).

cnf(f_1215_4,plain,
    ( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(U_3225))
    | ~ class_Rings_Ocomm__semiring__0(U_3225) ),
    inference(clausify,[status(thm)],[f_1215_3]) ).

fof(f_1216_1,plain,
    ! [T_1] :
      ( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Ocomm__semiring__1(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult]) ).

fof(f_1216_2,plain,
    ! [U_3226] :
      ( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(U_3226))
      | ~ class_Rings_Ocomm__semiring__1(U_3226) ),
    inference(variable_rename,[status(thm)],[f_1216_1]) ).

fof(f_1216_3,plain,
    ! [U_3226] :
      ( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(U_3226))
      | ~ class_Rings_Ocomm__semiring__1(U_3226) ),
    inference(definitional_conversion,[status(esa)],[f_1216_2]) ).

cnf(f_1216_4,plain,
    ( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(U_3226))
    | ~ class_Rings_Ocomm__semiring__1(U_3226) ),
    inference(clausify,[status(thm)],[f_1216_3]) ).

fof(f_1217_1,plain,
    ! [T_1] :
      ( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1))
      | ~ class_Groups_Ocomm__monoid__add(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__semigroup__add]) ).

fof(f_1217_2,plain,
    ! [U_3227] :
      ( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(U_3227))
      | ~ class_Groups_Ocomm__monoid__add(U_3227) ),
    inference(variable_rename,[status(thm)],[f_1217_1]) ).

fof(f_1217_3,plain,
    ! [U_3227] :
      ( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(U_3227))
      | ~ class_Groups_Ocomm__monoid__add(U_3227) ),
    inference(definitional_conversion,[status(esa)],[f_1217_2]) ).

cnf(f_1217_4,plain,
    ( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(U_3227))
    | ~ class_Groups_Ocomm__monoid__add(U_3227) ),
    inference(clausify,[status(thm)],[f_1217_3]) ).

fof(f_1218_1,plain,
    ! [T_1] :
      ( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__semiring]) ).

fof(f_1218_2,plain,
    ! [U_3228] :
      ( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(U_3228))
      | ~ class_Rings_Olinordered__idom(U_3228) ),
    inference(variable_rename,[status(thm)],[f_1218_1]) ).

fof(f_1218_3,plain,
    ! [U_3228] :
      ( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(U_3228))
      | ~ class_Rings_Olinordered__idom(U_3228) ),
    inference(definitional_conversion,[status(esa)],[f_1218_2]) ).

cnf(f_1218_4,plain,
    ( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(U_3228))
    | ~ class_Rings_Olinordered__idom(U_3228) ),
    inference(clausify,[status(thm)],[f_1218_3]) ).

fof(f_1219_1,plain,
    ! [T_1] :
      ( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Oidom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ono__zero__divisors]) ).

fof(f_1219_2,plain,
    ! [U_3229] :
      ( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(U_3229))
      | ~ class_Rings_Oidom(U_3229) ),
    inference(variable_rename,[status(thm)],[f_1219_1]) ).

fof(f_1219_3,plain,
    ! [U_3229] :
      ( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(U_3229))
      | ~ class_Rings_Oidom(U_3229) ),
    inference(definitional_conversion,[status(esa)],[f_1219_2]) ).

cnf(f_1219_4,plain,
    ( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(U_3229))
    | ~ class_Rings_Oidom(U_3229) ),
    inference(clausify,[status(thm)],[f_1219_3]) ).

fof(f_1220_1,plain,
    ! [T_1] :
      ( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1))
      | ~ class_Groups_Ocomm__monoid__add(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__add]) ).

fof(f_1220_2,plain,
    ! [U_3230] :
      ( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(U_3230))
      | ~ class_Groups_Ocomm__monoid__add(U_3230) ),
    inference(variable_rename,[status(thm)],[f_1220_1]) ).

fof(f_1220_3,plain,
    ! [U_3230] :
      ( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(U_3230))
      | ~ class_Groups_Ocomm__monoid__add(U_3230) ),
    inference(definitional_conversion,[status(esa)],[f_1220_2]) ).

cnf(f_1220_4,plain,
    ( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(U_3230))
    | ~ class_Groups_Ocomm__monoid__add(U_3230) ),
    inference(clausify,[status(thm)],[f_1220_3]) ).

fof(f_1221_1,plain,
    ! [T_1] :
      ( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring]) ).

fof(f_1221_2,plain,
    ! [U_3231] :
      ( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(U_3231))
      | ~ class_Rings_Olinordered__idom(U_3231) ),
    inference(variable_rename,[status(thm)],[f_1221_1]) ).

fof(f_1221_3,plain,
    ! [U_3231] :
      ( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(U_3231))
      | ~ class_Rings_Olinordered__idom(U_3231) ),
    inference(definitional_conversion,[status(esa)],[f_1221_2]) ).

cnf(f_1221_4,plain,
    ( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(U_3231))
    | ~ class_Rings_Olinordered__idom(U_3231) ),
    inference(clausify,[status(thm)],[f_1221_3]) ).

fof(f_1222_1,plain,
    ! [T_1] :
      ( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__idom]) ).

fof(f_1222_2,plain,
    ! [U_3232] :
      ( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(U_3232))
      | ~ class_Rings_Olinordered__idom(U_3232) ),
    inference(variable_rename,[status(thm)],[f_1222_1]) ).

fof(f_1222_3,plain,
    ! [U_3232] :
      ( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(U_3232))
      | ~ class_Rings_Olinordered__idom(U_3232) ),
    inference(definitional_conversion,[status(esa)],[f_1222_2]) ).

cnf(f_1222_4,plain,
    ( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(U_3232))
    | ~ class_Rings_Olinordered__idom(U_3232) ),
    inference(clausify,[status(thm)],[f_1222_3]) ).

fof(f_1223_1,plain,
    ! [T_1] :
      ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Ocomm__semiring__1(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__1]) ).

fof(f_1223_2,plain,
    ! [U_3233] :
      ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(U_3233))
      | ~ class_Rings_Ocomm__semiring__1(U_3233) ),
    inference(variable_rename,[status(thm)],[f_1223_1]) ).

fof(f_1223_3,plain,
    ! [U_3233] :
      ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(U_3233))
      | ~ class_Rings_Ocomm__semiring__1(U_3233) ),
    inference(definitional_conversion,[status(esa)],[f_1223_2]) ).

cnf(f_1223_4,plain,
    ( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(U_3233))
    | ~ class_Rings_Ocomm__semiring__1(U_3233) ),
    inference(clausify,[status(thm)],[f_1223_3]) ).

fof(f_1224_1,plain,
    ! [T_1] :
      ( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Ocomm__semiring__0(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__0]) ).

fof(f_1224_2,plain,
    ! [U_3234] :
      ( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(U_3234))
      | ~ class_Rings_Ocomm__semiring__0(U_3234) ),
    inference(variable_rename,[status(thm)],[f_1224_1]) ).

fof(f_1224_3,plain,
    ! [U_3234] :
      ( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(U_3234))
      | ~ class_Rings_Ocomm__semiring__0(U_3234) ),
    inference(definitional_conversion,[status(esa)],[f_1224_2]) ).

cnf(f_1224_4,plain,
    ( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(U_3234))
    | ~ class_Rings_Ocomm__semiring__0(U_3234) ),
    inference(clausify,[status(thm)],[f_1224_3]) ).

fof(f_1225_1,plain,
    ! [T_1] :
      ( class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))
      | ~ class_Fields_Ofield(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Divides_Osemiring__div]) ).

fof(f_1225_2,plain,
    ! [U_3235] :
      ( class_Divides_Osemiring__div(tc_Polynomial_Opoly(U_3235))
      | ~ class_Fields_Ofield(U_3235) ),
    inference(variable_rename,[status(thm)],[f_1225_1]) ).

fof(f_1225_3,plain,
    ! [U_3235] :
      ( class_Divides_Osemiring__div(tc_Polynomial_Opoly(U_3235))
      | ~ class_Fields_Ofield(U_3235) ),
    inference(definitional_conversion,[status(esa)],[f_1225_2]) ).

cnf(f_1225_4,plain,
    ( class_Divides_Osemiring__div(tc_Polynomial_Opoly(U_3235))
    | ~ class_Fields_Ofield(U_3235) ),
    inference(clausify,[status(thm)],[f_1225_3]) ).

fof(f_1226_1,plain,
    ! [T_1] :
      ( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Ocomm__semiring__0(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring]) ).

fof(f_1226_2,plain,
    ! [U_3236] :
      ( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(U_3236))
      | ~ class_Rings_Ocomm__semiring__0(U_3236) ),
    inference(variable_rename,[status(thm)],[f_1226_1]) ).

fof(f_1226_3,plain,
    ! [U_3236] :
      ( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(U_3236))
      | ~ class_Rings_Ocomm__semiring__0(U_3236) ),
    inference(definitional_conversion,[status(esa)],[f_1226_2]) ).

cnf(f_1226_4,plain,
    ( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(U_3236))
    | ~ class_Rings_Ocomm__semiring__0(U_3236) ),
    inference(clausify,[status(thm)],[f_1226_3]) ).

fof(f_1227_1,plain,
    ! [T_1] :
      ( class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1))
      | ~ class_Groups_Oab__group__add(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__group__add]) ).

fof(f_1227_2,plain,
    ! [U_3237] :
      ( class_Groups_Oab__group__add(tc_Polynomial_Opoly(U_3237))
      | ~ class_Groups_Oab__group__add(U_3237) ),
    inference(variable_rename,[status(thm)],[f_1227_1]) ).

fof(f_1227_3,plain,
    ! [U_3237] :
      ( class_Groups_Oab__group__add(tc_Polynomial_Opoly(U_3237))
      | ~ class_Groups_Oab__group__add(U_3237) ),
    inference(definitional_conversion,[status(esa)],[f_1227_2]) ).

cnf(f_1227_4,plain,
    ( class_Groups_Oab__group__add(tc_Polynomial_Opoly(U_3237))
    | ~ class_Groups_Oab__group__add(U_3237) ),
    inference(clausify,[status(thm)],[f_1227_3]) ).

fof(f_1228_1,plain,
    ! [T_1] :
      ( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Ocomm__semiring__1(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ozero__neq__one]) ).

fof(f_1228_2,plain,
    ! [U_3238] :
      ( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(U_3238))
      | ~ class_Rings_Ocomm__semiring__1(U_3238) ),
    inference(variable_rename,[status(thm)],[f_1228_1]) ).

fof(f_1228_3,plain,
    ! [U_3238] :
      ( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(U_3238))
      | ~ class_Rings_Ocomm__semiring__1(U_3238) ),
    inference(definitional_conversion,[status(esa)],[f_1228_2]) ).

cnf(f_1228_4,plain,
    ( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(U_3238))
    | ~ class_Rings_Ocomm__semiring__1(U_3238) ),
    inference(clausify,[status(thm)],[f_1228_3]) ).

fof(f_1229_1,plain,
    ! [T_1] :
      ( class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__ring]) ).

fof(f_1229_2,plain,
    ! [U_3239] :
      ( class_Rings_Oordered__ring(tc_Polynomial_Opoly(U_3239))
      | ~ class_Rings_Olinordered__idom(U_3239) ),
    inference(variable_rename,[status(thm)],[f_1229_1]) ).

fof(f_1229_3,plain,
    ! [U_3239] :
      ( class_Rings_Oordered__ring(tc_Polynomial_Opoly(U_3239))
      | ~ class_Rings_Olinordered__idom(U_3239) ),
    inference(definitional_conversion,[status(esa)],[f_1229_2]) ).

cnf(f_1229_4,plain,
    ( class_Rings_Oordered__ring(tc_Polynomial_Opoly(U_3239))
    | ~ class_Rings_Olinordered__idom(U_3239) ),
    inference(clausify,[status(thm)],[f_1229_3]) ).

fof(f_1230_1,plain,
    ! [T_1] :
      ( class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Opreorder]) ).

fof(f_1230_2,plain,
    ! [U_3240] :
      ( class_Orderings_Opreorder(tc_Polynomial_Opoly(U_3240))
      | ~ class_Rings_Olinordered__idom(U_3240) ),
    inference(variable_rename,[status(thm)],[f_1230_1]) ).

fof(f_1230_3,plain,
    ! [U_3240] :
      ( class_Orderings_Opreorder(tc_Polynomial_Opoly(U_3240))
      | ~ class_Rings_Olinordered__idom(U_3240) ),
    inference(definitional_conversion,[status(esa)],[f_1230_2]) ).

cnf(f_1230_4,plain,
    ( class_Orderings_Opreorder(tc_Polynomial_Opoly(U_3240))
    | ~ class_Rings_Olinordered__idom(U_3240) ),
    inference(clausify,[status(thm)],[f_1230_3]) ).

fof(f_1231_1,plain,
    ! [T_1] :
      ( class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Olinorder]) ).

fof(f_1231_2,plain,
    ! [U_3241] :
      ( class_Orderings_Olinorder(tc_Polynomial_Opoly(U_3241))
      | ~ class_Rings_Olinordered__idom(U_3241) ),
    inference(variable_rename,[status(thm)],[f_1231_1]) ).

fof(f_1231_3,plain,
    ! [U_3241] :
      ( class_Orderings_Olinorder(tc_Polynomial_Opoly(U_3241))
      | ~ class_Rings_Olinordered__idom(U_3241) ),
    inference(definitional_conversion,[status(esa)],[f_1231_2]) ).

cnf(f_1231_4,plain,
    ( class_Orderings_Olinorder(tc_Polynomial_Opoly(U_3241))
    | ~ class_Rings_Olinordered__idom(U_3241) ),
    inference(clausify,[status(thm)],[f_1231_3]) ).

fof(f_1232_1,plain,
    ! [T_1] :
      ( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Ocomm__semiring__1(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__mult]) ).

fof(f_1232_2,plain,
    ! [U_3242] :
      ( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(U_3242))
      | ~ class_Rings_Ocomm__semiring__1(U_3242) ),
    inference(variable_rename,[status(thm)],[f_1232_1]) ).

fof(f_1232_3,plain,
    ! [U_3242] :
      ( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(U_3242))
      | ~ class_Rings_Ocomm__semiring__1(U_3242) ),
    inference(definitional_conversion,[status(esa)],[f_1232_2]) ).

cnf(f_1232_4,plain,
    ( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(U_3242))
    | ~ class_Rings_Ocomm__semiring__1(U_3242) ),
    inference(clausify,[status(thm)],[f_1232_3]) ).

fof(f_1233_1,plain,
    ! [T_1] :
      ( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Ocomm__ring__1(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring__1]) ).

fof(f_1233_2,plain,
    ! [U_3243] :
      ( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(U_3243))
      | ~ class_Rings_Ocomm__ring__1(U_3243) ),
    inference(variable_rename,[status(thm)],[f_1233_1]) ).

fof(f_1233_3,plain,
    ! [U_3243] :
      ( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(U_3243))
      | ~ class_Rings_Ocomm__ring__1(U_3243) ),
    inference(definitional_conversion,[status(esa)],[f_1233_2]) ).

cnf(f_1233_4,plain,
    ( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(U_3243))
    | ~ class_Rings_Ocomm__ring__1(U_3243) ),
    inference(clausify,[status(thm)],[f_1233_3]) ).

fof(f_1234_1,plain,
    ! [T_1] :
      ( class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1))
      | ~ class_Groups_Ocomm__monoid__add(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__add]) ).

fof(f_1234_2,plain,
    ! [U_3244] :
      ( class_Groups_Omonoid__add(tc_Polynomial_Opoly(U_3244))
      | ~ class_Groups_Ocomm__monoid__add(U_3244) ),
    inference(variable_rename,[status(thm)],[f_1234_1]) ).

fof(f_1234_3,plain,
    ! [U_3244] :
      ( class_Groups_Omonoid__add(tc_Polynomial_Opoly(U_3244))
      | ~ class_Groups_Ocomm__monoid__add(U_3244) ),
    inference(definitional_conversion,[status(esa)],[f_1234_2]) ).

cnf(f_1234_4,plain,
    ( class_Groups_Omonoid__add(tc_Polynomial_Opoly(U_3244))
    | ~ class_Groups_Ocomm__monoid__add(U_3244) ),
    inference(clausify,[status(thm)],[f_1234_3]) ).

fof(f_1235_1,plain,
    ! [T_1] :
      ( class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Ocomm__semiring__0(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring__0]) ).

fof(f_1235_2,plain,
    ! [U_3245] :
      ( class_Rings_Osemiring__0(tc_Polynomial_Opoly(U_3245))
      | ~ class_Rings_Ocomm__semiring__0(U_3245) ),
    inference(variable_rename,[status(thm)],[f_1235_1]) ).

fof(f_1235_3,plain,
    ! [U_3245] :
      ( class_Rings_Osemiring__0(tc_Polynomial_Opoly(U_3245))
      | ~ class_Rings_Ocomm__semiring__0(U_3245) ),
    inference(definitional_conversion,[status(esa)],[f_1235_2]) ).

cnf(f_1235_4,plain,
    ( class_Rings_Osemiring__0(tc_Polynomial_Opoly(U_3245))
    | ~ class_Rings_Ocomm__semiring__0(U_3245) ),
    inference(clausify,[status(thm)],[f_1235_3]) ).

fof(f_1236_1,plain,
    ! [T_1] :
      ( class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1))
      | ~ class_Groups_Oab__group__add(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ogroup__add]) ).

fof(f_1236_2,plain,
    ! [U_3246] :
      ( class_Groups_Ogroup__add(tc_Polynomial_Opoly(U_3246))
      | ~ class_Groups_Oab__group__add(U_3246) ),
    inference(variable_rename,[status(thm)],[f_1236_1]) ).

fof(f_1236_3,plain,
    ! [U_3246] :
      ( class_Groups_Ogroup__add(tc_Polynomial_Opoly(U_3246))
      | ~ class_Groups_Oab__group__add(U_3246) ),
    inference(definitional_conversion,[status(esa)],[f_1236_2]) ).

cnf(f_1236_4,plain,
    ( class_Groups_Ogroup__add(tc_Polynomial_Opoly(U_3246))
    | ~ class_Groups_Oab__group__add(U_3246) ),
    inference(clausify,[status(thm)],[f_1236_3]) ).

fof(f_1237_1,plain,
    ! [T_1] :
      ( class_Divides_Oring__div(tc_Polynomial_Opoly(T_1))
      | ~ class_Fields_Ofield(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Divides_Oring__div]) ).

fof(f_1237_2,plain,
    ! [U_3247] :
      ( class_Divides_Oring__div(tc_Polynomial_Opoly(U_3247))
      | ~ class_Fields_Ofield(U_3247) ),
    inference(variable_rename,[status(thm)],[f_1237_1]) ).

fof(f_1237_3,plain,
    ! [U_3247] :
      ( class_Divides_Oring__div(tc_Polynomial_Opoly(U_3247))
      | ~ class_Fields_Ofield(U_3247) ),
    inference(definitional_conversion,[status(esa)],[f_1237_2]) ).

cnf(f_1237_4,plain,
    ( class_Divides_Oring__div(tc_Polynomial_Opoly(U_3247))
    | ~ class_Fields_Ofield(U_3247) ),
    inference(clausify,[status(thm)],[f_1237_3]) ).

fof(f_1238_1,plain,
    ! [T_1] :
      ( class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Ocomm__semiring__0(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Omult__zero]) ).

fof(f_1238_2,plain,
    ! [U_3248] :
      ( class_Rings_Omult__zero(tc_Polynomial_Opoly(U_3248))
      | ~ class_Rings_Ocomm__semiring__0(U_3248) ),
    inference(variable_rename,[status(thm)],[f_1238_1]) ).

fof(f_1238_3,plain,
    ! [U_3248] :
      ( class_Rings_Omult__zero(tc_Polynomial_Opoly(U_3248))
      | ~ class_Rings_Ocomm__semiring__0(U_3248) ),
    inference(definitional_conversion,[status(esa)],[f_1238_2]) ).

cnf(f_1238_4,plain,
    ( class_Rings_Omult__zero(tc_Polynomial_Opoly(U_3248))
    | ~ class_Rings_Ocomm__semiring__0(U_3248) ),
    inference(clausify,[status(thm)],[f_1238_3]) ).

fof(f_1239_1,plain,
    ! [T_1] :
      ( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Ocomm__ring(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring]) ).

fof(f_1239_2,plain,
    ! [U_3249] :
      ( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(U_3249))
      | ~ class_Rings_Ocomm__ring(U_3249) ),
    inference(variable_rename,[status(thm)],[f_1239_1]) ).

fof(f_1239_3,plain,
    ! [U_3249] :
      ( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(U_3249))
      | ~ class_Rings_Ocomm__ring(U_3249) ),
    inference(definitional_conversion,[status(esa)],[f_1239_2]) ).

cnf(f_1239_4,plain,
    ( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(U_3249))
    | ~ class_Rings_Ocomm__ring(U_3249) ),
    inference(clausify,[status(thm)],[f_1239_3]) ).

fof(f_1240_1,plain,
    ! [T_1] :
      ( class_Orderings_Oorder(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oorder]) ).

fof(f_1240_2,plain,
    ! [U_3250] :
      ( class_Orderings_Oorder(tc_Polynomial_Opoly(U_3250))
      | ~ class_Rings_Olinordered__idom(U_3250) ),
    inference(variable_rename,[status(thm)],[f_1240_1]) ).

fof(f_1240_3,plain,
    ! [U_3250] :
      ( class_Orderings_Oorder(tc_Polynomial_Opoly(U_3250))
      | ~ class_Rings_Olinordered__idom(U_3250) ),
    inference(definitional_conversion,[status(esa)],[f_1240_2]) ).

cnf(f_1240_4,plain,
    ( class_Orderings_Oorder(tc_Polynomial_Opoly(U_3250))
    | ~ class_Rings_Olinordered__idom(U_3250) ),
    inference(clausify,[status(thm)],[f_1240_3]) ).

fof(f_1241_1,plain,
    ! [T_1] :
      ( class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Int_Oring__char__0]) ).

fof(f_1241_2,plain,
    ! [U_3251] :
      ( class_Int_Oring__char__0(tc_Polynomial_Opoly(U_3251))
      | ~ class_Rings_Olinordered__idom(U_3251) ),
    inference(variable_rename,[status(thm)],[f_1241_1]) ).

fof(f_1241_3,plain,
    ! [U_3251] :
      ( class_Int_Oring__char__0(tc_Polynomial_Opoly(U_3251))
      | ~ class_Rings_Olinordered__idom(U_3251) ),
    inference(definitional_conversion,[status(esa)],[f_1241_2]) ).

cnf(f_1241_4,plain,
    ( class_Int_Oring__char__0(tc_Polynomial_Opoly(U_3251))
    | ~ class_Rings_Olinordered__idom(U_3251) ),
    inference(clausify,[status(thm)],[f_1241_3]) ).

fof(f_1242_1,plain,
    ! [T_1] :
      ( class_Rings_Osemiring(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Ocomm__semiring__0(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring]) ).

fof(f_1242_2,plain,
    ! [U_3252] :
      ( class_Rings_Osemiring(tc_Polynomial_Opoly(U_3252))
      | ~ class_Rings_Ocomm__semiring__0(U_3252) ),
    inference(variable_rename,[status(thm)],[f_1242_1]) ).

fof(f_1242_3,plain,
    ! [U_3252] :
      ( class_Rings_Osemiring(tc_Polynomial_Opoly(U_3252))
      | ~ class_Rings_Ocomm__semiring__0(U_3252) ),
    inference(definitional_conversion,[status(esa)],[f_1242_2]) ).

cnf(f_1242_4,plain,
    ( class_Rings_Osemiring(tc_Polynomial_Opoly(U_3252))
    | ~ class_Rings_Ocomm__semiring__0(U_3252) ),
    inference(clausify,[status(thm)],[f_1242_3]) ).

fof(f_1243_1,plain,
    ! [T_1] :
      ( class_Orderings_Oord(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Olinordered__idom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oord]) ).

fof(f_1243_2,plain,
    ! [U_3253] :
      ( class_Orderings_Oord(tc_Polynomial_Opoly(U_3253))
      | ~ class_Rings_Olinordered__idom(U_3253) ),
    inference(variable_rename,[status(thm)],[f_1243_1]) ).

fof(f_1243_3,plain,
    ! [U_3253] :
      ( class_Orderings_Oord(tc_Polynomial_Opoly(U_3253))
      | ~ class_Rings_Olinordered__idom(U_3253) ),
    inference(definitional_conversion,[status(esa)],[f_1243_2]) ).

cnf(f_1243_4,plain,
    ( class_Orderings_Oord(tc_Polynomial_Opoly(U_3253))
    | ~ class_Rings_Olinordered__idom(U_3253) ),
    inference(clausify,[status(thm)],[f_1243_3]) ).

fof(f_1244_1,plain,
    ! [T_1] :
      ( class_Rings_Oring__1(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Ocomm__ring__1(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__1]) ).

fof(f_1244_2,plain,
    ! [U_3254] :
      ( class_Rings_Oring__1(tc_Polynomial_Opoly(U_3254))
      | ~ class_Rings_Ocomm__ring__1(U_3254) ),
    inference(variable_rename,[status(thm)],[f_1244_1]) ).

fof(f_1244_3,plain,
    ! [U_3254] :
      ( class_Rings_Oring__1(tc_Polynomial_Opoly(U_3254))
      | ~ class_Rings_Ocomm__ring__1(U_3254) ),
    inference(definitional_conversion,[status(esa)],[f_1244_2]) ).

cnf(f_1244_4,plain,
    ( class_Rings_Oring__1(tc_Polynomial_Opoly(U_3254))
    | ~ class_Rings_Ocomm__ring__1(U_3254) ),
    inference(clausify,[status(thm)],[f_1244_3]) ).

fof(f_1245_1,plain,
    ! [T_1] :
      ( class_Power_Opower(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Ocomm__semiring__1(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Power_Opower]) ).

fof(f_1245_2,plain,
    ! [U_3255] :
      ( class_Power_Opower(tc_Polynomial_Opoly(U_3255))
      | ~ class_Rings_Ocomm__semiring__1(U_3255) ),
    inference(variable_rename,[status(thm)],[f_1245_1]) ).

fof(f_1245_3,plain,
    ! [U_3255] :
      ( class_Power_Opower(tc_Polynomial_Opoly(U_3255))
      | ~ class_Rings_Ocomm__semiring__1(U_3255) ),
    inference(definitional_conversion,[status(esa)],[f_1245_2]) ).

cnf(f_1245_4,plain,
    ( class_Power_Opower(tc_Polynomial_Opoly(U_3255))
    | ~ class_Rings_Ocomm__semiring__1(U_3255) ),
    inference(clausify,[status(thm)],[f_1245_3]) ).

fof(f_1246_1,plain,
    ! [T_1] :
      ( class_Groups_Ozero(tc_Polynomial_Opoly(T_1))
      | ~ class_Groups_Ozero(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ozero]) ).

fof(f_1246_2,plain,
    ! [U_3256] :
      ( class_Groups_Ozero(tc_Polynomial_Opoly(U_3256))
      | ~ class_Groups_Ozero(U_3256) ),
    inference(variable_rename,[status(thm)],[f_1246_1]) ).

fof(f_1246_3,plain,
    ! [U_3256] :
      ( class_Groups_Ozero(tc_Polynomial_Opoly(U_3256))
      | ~ class_Groups_Ozero(U_3256) ),
    inference(definitional_conversion,[status(esa)],[f_1246_2]) ).

cnf(f_1246_4,plain,
    ( class_Groups_Ozero(tc_Polynomial_Opoly(U_3256))
    | ~ class_Groups_Ozero(U_3256) ),
    inference(clausify,[status(thm)],[f_1246_3]) ).

fof(f_1247_1,plain,
    ! [T_1] :
      ( class_Rings_Oring(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Ocomm__ring(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring]) ).

fof(f_1247_2,plain,
    ! [U_3257] :
      ( class_Rings_Oring(tc_Polynomial_Opoly(U_3257))
      | ~ class_Rings_Ocomm__ring(U_3257) ),
    inference(variable_rename,[status(thm)],[f_1247_1]) ).

fof(f_1247_3,plain,
    ! [U_3257] :
      ( class_Rings_Oring(tc_Polynomial_Opoly(U_3257))
      | ~ class_Rings_Ocomm__ring(U_3257) ),
    inference(definitional_conversion,[status(esa)],[f_1247_2]) ).

cnf(f_1247_4,plain,
    ( class_Rings_Oring(tc_Polynomial_Opoly(U_3257))
    | ~ class_Rings_Ocomm__ring(U_3257) ),
    inference(clausify,[status(thm)],[f_1247_3]) ).

fof(f_1248_1,plain,
    ! [T_1] :
      ( class_Rings_Oidom(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Oidom(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oidom]) ).

fof(f_1248_2,plain,
    ! [U_3258] :
      ( class_Rings_Oidom(tc_Polynomial_Opoly(U_3258))
      | ~ class_Rings_Oidom(U_3258) ),
    inference(variable_rename,[status(thm)],[f_1248_1]) ).

fof(f_1248_3,plain,
    ! [U_3258] :
      ( class_Rings_Oidom(tc_Polynomial_Opoly(U_3258))
      | ~ class_Rings_Oidom(U_3258) ),
    inference(definitional_conversion,[status(esa)],[f_1248_2]) ).

cnf(f_1248_4,plain,
    ( class_Rings_Oidom(tc_Polynomial_Opoly(U_3258))
    | ~ class_Rings_Oidom(U_3258) ),
    inference(clausify,[status(thm)],[f_1248_3]) ).

fof(f_1249_1,plain,
    ! [T_1] :
      ( class_Groups_Oone(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Ocomm__semiring__1(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oone]) ).

fof(f_1249_2,plain,
    ! [U_3259] :
      ( class_Groups_Oone(tc_Polynomial_Opoly(U_3259))
      | ~ class_Rings_Ocomm__semiring__1(U_3259) ),
    inference(variable_rename,[status(thm)],[f_1249_1]) ).

fof(f_1249_3,plain,
    ! [U_3259] :
      ( class_Groups_Oone(tc_Polynomial_Opoly(U_3259))
      | ~ class_Rings_Ocomm__semiring__1(U_3259) ),
    inference(definitional_conversion,[status(esa)],[f_1249_2]) ).

cnf(f_1249_4,plain,
    ( class_Groups_Oone(tc_Polynomial_Opoly(U_3259))
    | ~ class_Rings_Ocomm__semiring__1(U_3259) ),
    inference(clausify,[status(thm)],[f_1249_3]) ).

fof(f_1250_1,plain,
    ! [T_1] :
      ( class_Rings_Odvd(tc_Polynomial_Opoly(T_1))
      | ~ class_Rings_Ocomm__semiring__1(T_1) ),
    inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Odvd]) ).

fof(f_1250_2,plain,
    ! [U_3260] :
      ( class_Rings_Odvd(tc_Polynomial_Opoly(U_3260))
      | ~ class_Rings_Ocomm__semiring__1(U_3260) ),
    inference(variable_rename,[status(thm)],[f_1250_1]) ).

fof(f_1250_3,plain,
    ! [U_3260] :
      ( class_Rings_Odvd(tc_Polynomial_Opoly(U_3260))
      | ~ class_Rings_Ocomm__semiring__1(U_3260) ),
    inference(definitional_conversion,[status(esa)],[f_1250_2]) ).

cnf(f_1250_4,plain,
    ( class_Rings_Odvd(tc_Polynomial_Opoly(U_3260))
    | ~ class_Rings_Ocomm__semiring__1(U_3260) ),
    inference(clausify,[status(thm)],[f_1250_3]) ).

fof(f_1251_1,plain,
    ! [V_y_2,V_x_2] :
      ( V_x_2 = V_y_2
      | ~ hBOOL(c_fequal(V_x_2,V_y_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fequal__1]) ).

fof(f_1251_2,plain,
    ! [U_3262,U_3261] :
      ( U_3261 = U_3262
      | ~ hBOOL(c_fequal(U_3261,U_3262)) ),
    inference(variable_rename,[status(thm)],[f_1251_1]) ).

fof(f_1251_3,plain,
    ! [U_3261,U_3262] :
      ( U_3261 = U_3262
      | ~ hBOOL(c_fequal(U_3261,U_3262)) ),
    inference(definitional_conversion,[status(esa)],[f_1251_2]) ).

cnf(f_1251_4,plain,
    ( U_3261 = U_3262
    | ~ hBOOL(c_fequal(U_3261,U_3262)) ),
    inference(clausify,[status(thm)],[f_1251_3]) ).

fof(f_1252_1,plain,
    ! [V_y_2,V_x_2] :
      ( hBOOL(c_fequal(V_x_2,V_y_2))
      | V_x_2 != V_y_2 ),
    inference(fof_nnf,[status(thm)],[help_c__fequal__2]) ).

fof(f_1252_2,plain,
    ! [U_3264,U_3263] :
      ( hBOOL(c_fequal(U_3263,U_3264))
      | U_3263 != U_3264 ),
    inference(variable_rename,[status(thm)],[f_1252_1]) ).

fof(f_1252_3,plain,
    ! [U_3263,U_3264] :
      ( hBOOL(c_fequal(U_3263,U_3264))
      | U_3263 != U_3264 ),
    inference(definitional_conversion,[status(esa)],[f_1252_2]) ).

cnf(f_1252_4,plain,
    ( hBOOL(c_fequal(U_3263,U_3264))
    | U_3263 != U_3264 ),
    inference(clausify,[status(thm)],[f_1252_3]) ).

fof(f_1253_1,plain,
    ( v_thesis____
    | ! [B_r] :
      ? [B_z] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_da____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),B_z)))
        & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,B_r,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z)) ) ),
    inference(fof_nnf,[status(thm)],[conj_0]) ).

fof(f_1253_2,plain,
    ( v_thesis____
    | ! [U_3266] :
      ? [U_3265] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_da____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),U_3265)))
        & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_3266,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_3265)) ) ),
    inference(variable_rename,[status(thm)],[f_1253_1]) ).

fof(f_1253_3,plain,
    ( v_thesis____
    | ! [U_3266] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_da____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),sK38(U_3266))))
        & c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_3266,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK38(U_3266))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_3265,sK38(U_3266))],[f_1253_2]) ).

fof(f_1253_4,plain,
    ( ! [U_3266] :
        ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_da____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),sK38(U_3266))))
        | ~ sP285(U_3266) )
    & ! [U_3266] :
        ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_3266,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK38(U_3266)))
        | ~ sP285(U_3266) )
    & ! [U_3266] :
        ( v_thesis____
        | sP285(U_3266) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP285])],[f_1253_3]) ).

cnf(f_1253_5,plain,
    ( v_thesis____
    | sP285(U_3266) ),
    inference(clausify,[status(thm)],[f_1253_4]) ).

cnf(f_1253_6,plain,
    ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_3266,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK38(U_3266)))
    | ~ sP285(U_3266) ),
    inference(clausify,[status(thm)],[f_1253_4]) ).

cnf(f_1253_7,plain,
    ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_da____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_aa____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),sK38(U_3266))))
    | ~ sP285(U_3266) ),
    inference(clausify,[status(thm)],[f_1253_4]) ).

fof(f_1254_1,negated_conjecture,
    ~ v_thesis____,
    inference(negate,[status(cth)],[conj_1]) ).

fof(f_1254_2,negated_conjecture,
    ~ v_thesis____,
    inference(definitional_conversion,[status(esa)],[f_1254_1]) ).

cnf(f_1254_3,negated_conjecture,
    ~ v_thesis____,
    inference(clausify,[status(thm)],[f_1254_2]) ).

cnf(f_894_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_894_4]) ).

cnf(f_895_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_895_4]) ).

cnf(f_896_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_896_4]) ).

cnf(f_901_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_901_4]) ).

cnf(f_903_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_903_4]) ).

cnf(equality_1,axiom,
    Eq_x_0 = Eq_x_0,
    theory(equality,[reflexivity]) ).

cnf(equality_2,axiom,
    ( Eq_x_1 = Eq_x_0
    | Eq_x_0 != Eq_x_1 ),
    theory(equality,[symmetry]) ).

cnf(equality_3,axiom,
    ( Eq_x_0 = Eq_x_2
    | Eq_x_1 != Eq_x_2
    | Eq_x_0 != Eq_x_1 ),
    theory(equality,[transitivity]) ).

cnf(equality_4,axiom,
    ( hAPP(Eq_x_0,Eq_x_1) = hAPP(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_5,axiom,
    ( tc_Polynomial_Opoly(Eq_x_0) = tc_Polynomial_Opoly(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_6,axiom,
    ( c_Groups_Ozero__class_Ozero(Eq_x_0) = c_Groups_Ozero__class_Ozero(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_7,axiom,
    ( c_Polynomial_OpCons(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_OpCons(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_8,axiom,
    ( c_RealVector_Onorm__class_Onorm(Eq_x_0,Eq_x_1) = c_RealVector_Onorm__class_Onorm(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_9,axiom,
    ( c_Polynomial_Opoly(Eq_x_0,Eq_x_1) = c_Polynomial_Opoly(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_10,axiom,
    ( c_Groups_Oplus__class_Oplus(Eq_x_0,Eq_x_1,Eq_x_2) = c_Groups_Oplus__class_Oplus(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_11,axiom,
    ( tc_fun(Eq_x_0,Eq_x_1) = tc_fun(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_12,axiom,
    ( c_Polynomial_Oorder(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_Oorder(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_13,axiom,
    ( c_Polynomial_Opoly__rec(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Polynomial_Opoly__rec(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_14,axiom,
    ( c_fequal(Eq_x_0,Eq_x_1) = c_fequal(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_15,axiom,
    ( c_If(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_If(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_16,axiom,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(Eq_x_0,Eq_x_1,Eq_x_2) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_17,axiom,
    ( c_Polynomial_Osynthetic__div(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_Osynthetic__div(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_18,axiom,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(Eq_x_0,Eq_x_1) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_19,axiom,
    ( c_Polynomial_Osmult(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_Osmult(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_20,axiom,
    ( c_Polynomial_Omonom(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_Omonom(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_21,axiom,
    ( c_Groups_Ominus__class_Ominus(Eq_x_0,Eq_x_1,Eq_x_2) = c_Groups_Ominus__class_Ominus(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_22,axiom,
    ( c_Groups_Otimes__class_Otimes(Eq_x_0) = c_Groups_Otimes__class_Otimes(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_23,axiom,
    ( c_Polynomial_Opcompose(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_Opcompose(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_24,axiom,
    ( c_Groups_Oone__class_Oone(Eq_x_0) = c_Groups_Oone__class_Oone(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_25,axiom,
    ( c_Groups_Ouminus__class_Ouminus(Eq_x_0,Eq_x_1) = c_Groups_Ouminus__class_Ouminus(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_26,axiom,
    ( c_Power_Opower__class_Opower(Eq_x_0) = c_Power_Opower__class_Opower(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_27,axiom,
    ( c_RComplete_Onatfloor(Eq_x_0) = c_RComplete_Onatfloor(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_28,axiom,
    ( c_Nat_OSuc(Eq_x_0) = c_Nat_OSuc(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_29,axiom,
    ( c_RComplete_Onatceiling(Eq_x_0) = c_RComplete_Onatceiling(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_30,axiom,
    ( c_Power_Opower_Opower(Eq_x_0,Eq_x_1,Eq_x_2) = c_Power_Opower_Opower(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_31,axiom,
    ( c_Nat__Transfer_Otsub(Eq_x_0,Eq_x_1) = c_Nat__Transfer_Otsub(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_32,axiom,
    ( c_RealDef_Oreal(Eq_x_0,Eq_x_1) = c_RealDef_Oreal(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_33,axiom,
    ( c_Divides_Odiv__class_Odiv(Eq_x_0,Eq_x_1,Eq_x_2) = c_Divides_Odiv__class_Odiv(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_34,axiom,
    ( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_35,axiom,
    ( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_36,axiom,
    ( sK3(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK3(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_37,axiom,
    ( sK4(Eq_x_0,Eq_x_1) = sK4(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_38,axiom,
    ( sK5(Eq_x_0,Eq_x_1) = sK5(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_39,axiom,
    ( sK6(Eq_x_0,Eq_x_1) = sK6(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_40,axiom,
    ( sK7(Eq_x_0) = sK7(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_41,axiom,
    ( sK8(Eq_x_0,Eq_x_1) = sK8(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_42,axiom,
    ( sK9(Eq_x_0,Eq_x_1) = sK9(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_43,axiom,
    ( sK10(Eq_x_0) = sK10(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_44,axiom,
    ( sK11(Eq_x_0,Eq_x_1) = sK11(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_45,axiom,
    ( sK12(Eq_x_0,Eq_x_1) = sK12(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_46,axiom,
    ( sK13(Eq_x_0,Eq_x_1,Eq_x_2) = sK13(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_47,axiom,
    ( sK14(Eq_x_0,Eq_x_1,Eq_x_2) = sK14(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_48,axiom,
    ( sK15(Eq_x_0,Eq_x_1) = sK15(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_49,axiom,
    ( sK16(Eq_x_0) = sK16(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_50,axiom,
    ( sK17(Eq_x_0,Eq_x_1) = sK17(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_51,axiom,
    ( sK18(Eq_x_0,Eq_x_1) = sK18(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_52,axiom,
    ( sK19(Eq_x_0,Eq_x_1,Eq_x_2) = sK19(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_53,axiom,
    ( sK20(Eq_x_0,Eq_x_1,Eq_x_2) = sK20(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_54,axiom,
    ( sK21(Eq_x_0,Eq_x_1) = sK21(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_55,axiom,
    ( sK22(Eq_x_0) = sK22(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_56,axiom,
    ( sK23(Eq_x_0,Eq_x_1) = sK23(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_57,axiom,
    ( sK24(Eq_x_0,Eq_x_1) = sK24(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_58,axiom,
    ( sK25(Eq_x_0,Eq_x_1,Eq_x_2) = sK25(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_59,axiom,
    ( sK26(Eq_x_0,Eq_x_1,Eq_x_2) = sK26(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_60,axiom,
    ( sK27(Eq_x_0,Eq_x_1) = sK27(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_61,axiom,
    ( sK28(Eq_x_0,Eq_x_1,Eq_x_2) = sK28(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_62,axiom,
    ( sK29(Eq_x_0,Eq_x_1) = sK29(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_63,axiom,
    ( sK30(Eq_x_0,Eq_x_1,Eq_x_2) = sK30(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_64,axiom,
    ( sK31(Eq_x_0,Eq_x_1) = sK31(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_65,axiom,
    ( sK32(Eq_x_0,Eq_x_1,Eq_x_2) = sK32(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_66,axiom,
    ( sK33(Eq_x_0,Eq_x_1) = sK33(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_67,axiom,
    ( sK34(Eq_x_0) = sK34(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_68,axiom,
    ( sK35(Eq_x_0,Eq_x_1) = sK35(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_69,axiom,
    ( sK36(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK36(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_70,axiom,
    ( sK37(Eq_x_0,Eq_x_1) = sK37(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_71,axiom,
    ( sK38(Eq_x_0) = sK38(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_72,axiom,
    ( c_Orderings_Oord__class_Oless__eq(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Orderings_Oord__class_Oless__eq(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_73,axiom,
    ( class_RealVector_Oreal__normed__vector(Eq_y_0)
    | ~ class_RealVector_Oreal__normed__vector(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_74,axiom,
    ( class_Orderings_Opreorder(Eq_y_0)
    | ~ class_Orderings_Opreorder(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_75,axiom,
    ( class_Rings_Ocomm__semiring__0(Eq_y_0)
    | ~ class_Rings_Ocomm__semiring__0(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_76,axiom,
    ( class_Groups_Ocomm__monoid__add(Eq_y_0)
    | ~ class_Groups_Ocomm__monoid__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_77,axiom,
    ( class_Groups_Oordered__ab__semigroup__add__imp__le(Eq_y_0)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_78,axiom,
    ( class_Groups_Oordered__ab__semigroup__add(Eq_y_0)
    | ~ class_Groups_Oordered__ab__semigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_79,axiom,
    ( class_Groups_Ozero(Eq_y_0)
    | ~ class_Groups_Ozero(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_80,axiom,
    ( class_Groups_Omonoid__add(Eq_y_0)
    | ~ class_Groups_Omonoid__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_81,axiom,
    ( class_Groups_Olinordered__ab__group__add(Eq_y_0)
    | ~ class_Groups_Olinordered__ab__group__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_82,axiom,
    ( class_Int_Oring__char__0(Eq_y_0)
    | ~ class_Int_Oring__char__0(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_83,axiom,
    ( class_Rings_Oidom(Eq_y_0)
    | ~ class_Rings_Oidom(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_84,axiom,
    ( class_Groups_Oordered__comm__monoid__add(Eq_y_0)
    | ~ class_Groups_Oordered__comm__monoid__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_85,axiom,
    ( class_Orderings_Olinorder(Eq_y_0)
    | ~ class_Orderings_Olinorder(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_86,axiom,
    ( class_Orderings_Oord(Eq_y_0)
    | ~ class_Orderings_Oord(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_87,axiom,
    ( class_Orderings_Oorder(Eq_y_0)
    | ~ class_Orderings_Oorder(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_88,axiom,
    ( class_Groups_Ocancel__semigroup__add(Eq_y_0)
    | ~ class_Groups_Ocancel__semigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_89,axiom,
    ( class_Groups_Ocancel__ab__semigroup__add(Eq_y_0)
    | ~ class_Groups_Ocancel__ab__semigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_90,axiom,
    ( class_Groups_Oab__semigroup__add(Eq_y_0)
    | ~ class_Groups_Oab__semigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_91,axiom,
    ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(Eq_y_0)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_92,axiom,
    ( class_Rings_Ocomm__semiring__1(Eq_y_0)
    | ~ class_Rings_Ocomm__semiring__1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_93,axiom,
    ( class_RealVector_Oreal__normed__algebra(Eq_y_0)
    | ~ class_RealVector_Oreal__normed__algebra(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_94,axiom,
    ( class_Rings_Oring(Eq_y_0)
    | ~ class_Rings_Oring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_95,axiom,
    ( class_Groups_Oab__group__add(Eq_y_0)
    | ~ class_Groups_Oab__group__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_96,axiom,
    ( class_Rings_Ocomm__ring(Eq_y_0)
    | ~ class_Rings_Ocomm__ring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_97,axiom,
    ( class_Groups_Oab__semigroup__mult(Eq_y_0)
    | ~ class_Groups_Oab__semigroup__mult(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_98,axiom,
    ( class_RealVector_Oreal__normed__div__algebra(Eq_y_0)
    | ~ class_RealVector_Oreal__normed__div__algebra(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_99,axiom,
    ( class_Groups_Ogroup__add(Eq_y_0)
    | ~ class_Groups_Ogroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_100,axiom,
    ( class_Groups_Oordered__ab__group__add(Eq_y_0)
    | ~ class_Groups_Oordered__ab__group__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_101,axiom,
    ( class_Rings_Oordered__ring(Eq_y_0)
    | ~ class_Rings_Oordered__ring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_102,axiom,
    ( class_Rings_Olinordered__ring__strict(Eq_y_0)
    | ~ class_Rings_Olinordered__ring__strict(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_103,axiom,
    ( class_Rings_Olinordered__ring(Eq_y_0)
    | ~ class_Rings_Olinordered__ring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_104,axiom,
    ( class_Rings_Ono__zero__divisors(Eq_y_0)
    | ~ class_Rings_Ono__zero__divisors(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_105,axiom,
    ( class_Rings_Oring__no__zero__divisors(Eq_y_0)
    | ~ class_Rings_Oring__no__zero__divisors(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_106,axiom,
    ( class_Rings_Omult__zero(Eq_y_0)
    | ~ class_Rings_Omult__zero(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_107,axiom,
    ( class_Rings_Ocomm__semiring(Eq_y_0)
    | ~ class_Rings_Ocomm__semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_108,axiom,
    ( class_Rings_Osemiring(Eq_y_0)
    | ~ class_Rings_Osemiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_109,axiom,
    ( class_Rings_Oordered__cancel__semiring(Eq_y_0)
    | ~ class_Rings_Oordered__cancel__semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_110,axiom,
    ( class_Rings_Oordered__semiring(Eq_y_0)
    | ~ class_Rings_Oordered__semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_111,axiom,
    ( class_Rings_Oordered__comm__semiring(Eq_y_0)
    | ~ class_Rings_Oordered__comm__semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_112,axiom,
    ( c_Orderings_Oord__class_Oless(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Orderings_Oord__class_Oless(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_113,axiom,
    ( class_Rings_Olinordered__semidom(Eq_y_0)
    | ~ class_Rings_Olinordered__semidom(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_114,axiom,
    ( class_Rings_Olinordered__idom(Eq_y_0)
    | ~ class_Rings_Olinordered__idom(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_115,axiom,
    ( class_Groups_Oone(Eq_y_0)
    | ~ class_Groups_Oone(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_116,axiom,
    ( class_RealVector_Oreal__normed__algebra__1(Eq_y_0)
    | ~ class_RealVector_Oreal__normed__algebra__1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_117,axiom,
    ( hBOOL(Eq_y_0)
    | ~ hBOOL(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_118,axiom,
    ( class_Rings_Ozero__neq__one(Eq_y_0)
    | ~ class_Rings_Ozero__neq__one(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_119,axiom,
    ( class_Groups_Oordered__cancel__ab__semigroup__add(Eq_y_0)
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_120,axiom,
    ( class_Groups_Ocomm__monoid__mult(Eq_y_0)
    | ~ class_Groups_Ocomm__monoid__mult(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_121,axiom,
    ( class_Groups_Omonoid__mult(Eq_y_0)
    | ~ class_Groups_Omonoid__mult(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_122,axiom,
    ( class_Rings_Olinordered__semiring__1__strict(Eq_y_0)
    | ~ class_Rings_Olinordered__semiring__1__strict(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_123,axiom,
    ( class_Rings_Olinordered__semiring__strict(Eq_y_0)
    | ~ class_Rings_Olinordered__semiring__strict(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_124,axiom,
    ( class_Rings_Olinordered__comm__semiring__strict(Eq_y_0)
    | ~ class_Rings_Olinordered__comm__semiring__strict(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_125,axiom,
    ( class_Rings_Olinordered__semiring(Eq_y_0)
    | ~ class_Rings_Olinordered__semiring(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_126,axiom,
    ( class_Rings_Oring__1(Eq_y_0)
    | ~ class_Rings_Oring__1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_127,axiom,
    ( class_Rings_Olinordered__semiring__1(Eq_y_0)
    | ~ class_Rings_Olinordered__semiring__1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_128,axiom,
    ( class_Rings_Ocomm__ring__1(Eq_y_0)
    | ~ class_Rings_Ocomm__ring__1(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_129,axiom,
    ( c_Polynomial_Opos__poly(Eq_y_0,Eq_y_1)
    | ~ c_Polynomial_Opos__poly(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_130,axiom,
    ( class_Rings_Oring__1__no__zero__divisors(Eq_y_0)
    | ~ class_Rings_Oring__1__no__zero__divisors(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_131,axiom,
    ( class_Power_Opower(Eq_y_0)
    | ~ class_Power_Opower(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_132,axiom,
    ( class_Rings_Osemiring__0(Eq_y_0)
    | ~ class_Rings_Osemiring__0(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_133,axiom,
    ( c_Rings_Odvd__class_Odvd(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Rings_Odvd__class_Odvd(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_134,axiom,
    ( class_Rings_Odvd(Eq_y_0)
    | ~ class_Rings_Odvd(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_135,axiom,
    ( class_Fields_Ofield(Eq_y_0)
    | ~ class_Fields_Ofield(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_136,axiom,
    ( class_Divides_Osemiring__div(Eq_y_0)
    | ~ class_Divides_Osemiring__div(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_137,axiom,
    ( class_Divides_Oring__div(Eq_y_0)
    | ~ class_Divides_Oring__div(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_138,axiom,
    ( class_Groups_Ocancel__comm__monoid__add(Eq_y_0)
    | ~ class_Groups_Ocancel__comm__monoid__add(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_139,axiom,
    ( sP0(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP0(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_140,axiom,
    ( sP1(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_141,axiom,
    ( sP2(Eq_y_0,Eq_y_1)
    | ~ sP2(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_142,axiom,
    ( sP3(Eq_y_0,Eq_y_1)
    | ~ sP3(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_143,axiom,
    ( sP4(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP4(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_144,axiom,
    ( sP5(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP5(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_145,axiom,
    ( sP6(Eq_y_0,Eq_y_1)
    | ~ sP6(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_146,axiom,
    ( sP7(Eq_y_0,Eq_y_1)
    | ~ sP7(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_147,axiom,
    ( sP8(Eq_y_0,Eq_y_1)
    | ~ sP8(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_148,axiom,
    ( sP9(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP9(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_149,axiom,
    ( sP10(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP10(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_150,axiom,
    ( sP11(Eq_y_0,Eq_y_1)
    | ~ sP11(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_151,axiom,
    ( sP12(Eq_y_0,Eq_y_1)
    | ~ sP12(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_152,axiom,
    ( sP13(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP13(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_153,axiom,
    ( sP14(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP14(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_154,axiom,
    ( sP15(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP15(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_155,axiom,
    ( sP16(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP16(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_156,axiom,
    ( sP17(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP17(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_157,axiom,
    ( sP18(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP18(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_158,axiom,
    ( sP19(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP19(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_159,axiom,
    ( sP20(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP20(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_160,axiom,
    ( sP21(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP21(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_161,axiom,
    ( sP22(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP22(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_162,axiom,
    ( sP23(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP23(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_163,axiom,
    ( sP24(Eq_y_0,Eq_y_1)
    | ~ sP24(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_164,axiom,
    ( sP25(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP25(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_165,axiom,
    ( sP26(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP26(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_166,axiom,
    ( sP27(Eq_y_0,Eq_y_1)
    | ~ sP27(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_167,axiom,
    ( sP28(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP28(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_168,axiom,
    ( sP29(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP29(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_169,axiom,
    ( sP30(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP30(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_170,axiom,
    ( sP31(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP31(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_171,axiom,
    ( sP32(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP32(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_172,axiom,
    ( sP33(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP33(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_173,axiom,
    ( sP34(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP34(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_174,axiom,
    ( sP35(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP35(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_175,axiom,
    ( sP36(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP36(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_176,axiom,
    ( sP37(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP37(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_177,axiom,
    ( sP38(Eq_y_0,Eq_y_1)
    | ~ sP38(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_178,axiom,
    ( sP39(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP39(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_179,axiom,
    ( sP40(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP40(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_180,axiom,
    ( sP41(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP41(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_181,axiom,
    ( sP42(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP42(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_182,axiom,
    ( sP43(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP43(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_183,axiom,
    ( sP44(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP44(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_184,axiom,
    ( sP45(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP45(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_185,axiom,
    ( sP46(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP46(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_186,axiom,
    ( sP47(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP47(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_187,axiom,
    ( sP48(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP48(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_188,axiom,
    ( sP49(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP49(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_189,axiom,
    ( sP50(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP50(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_190,axiom,
    ( sP51(Eq_y_0,Eq_y_1)
    | ~ sP51(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_191,axiom,
    ( sP52(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP52(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_192,axiom,
    ( sP53(Eq_y_0,Eq_y_1)
    | ~ sP53(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_193,axiom,
    ( sP54(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP54(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_194,axiom,
    ( sP55(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP55(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_195,axiom,
    ( sP56(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP56(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_196,axiom,
    ( sP57(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP57(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_197,axiom,
    ( sP58(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP58(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_198,axiom,
    ( sP59(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP59(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_199,axiom,
    ( sP60(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP60(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_200,axiom,
    ( sP61(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP61(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_201,axiom,
    ( sP62(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP62(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_202,axiom,
    ( sP63(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP63(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_203,axiom,
    ( sP64(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP64(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_204,axiom,
    ( sP65(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP65(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_205,axiom,
    ( sP66(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP66(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_206,axiom,
    ( sP67(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP67(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_207,axiom,
    ( sP68(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP68(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_208,axiom,
    ( sP69(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP69(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_209,axiom,
    ( sP70(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP70(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_210,axiom,
    ( sP71(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP71(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_211,axiom,
    ( sP72(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP72(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_212,axiom,
    ( sP73(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP73(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_213,axiom,
    ( sP74(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP74(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_214,axiom,
    ( sP75(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP75(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_215,axiom,
    ( sP76(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP76(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_216,axiom,
    ( sP77(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP77(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_217,axiom,
    ( sP78(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP78(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_218,axiom,
    ( sP79(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP79(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_219,axiom,
    ( sP80(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP80(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_220,axiom,
    ( sP81(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP81(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_221,axiom,
    ( sP82(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP82(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_222,axiom,
    ( sP83(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP83(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_223,axiom,
    ( sP84(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP84(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_224,axiom,
    ( sP85(Eq_y_0,Eq_y_1)
    | ~ sP85(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_225,axiom,
    ( sP86(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP86(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_226,axiom,
    ( sP87(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP87(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_227,axiom,
    ( sP88(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP88(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_228,axiom,
    ( sP89(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP89(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_229,axiom,
    ( sP90(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP90(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_230,axiom,
    ( sP91(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP91(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_231,axiom,
    ( sP92(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP92(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_232,axiom,
    ( sP93(Eq_y_0,Eq_y_1)
    | ~ sP93(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_233,axiom,
    ( sP94(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP94(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_234,axiom,
    ( sP95(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP95(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_235,axiom,
    ( sP96(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP96(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_236,axiom,
    ( sP97(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP97(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_237,axiom,
    ( sP98(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP98(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_238,axiom,
    ( sP99(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP99(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_239,axiom,
    ( sP100(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP100(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_240,axiom,
    ( sP101(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP101(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_241,axiom,
    ( sP102(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP102(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_242,axiom,
    ( sP103(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP103(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_243,axiom,
    ( sP104(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP104(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_244,axiom,
    ( sP105(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP105(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_245,axiom,
    ( sP106(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP106(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_246,axiom,
    ( sP107(Eq_y_0,Eq_y_1)
    | ~ sP107(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_247,axiom,
    ( sP108(Eq_y_0,Eq_y_1)
    | ~ sP108(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_248,axiom,
    ( sP109(Eq_y_0,Eq_y_1)
    | ~ sP109(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_249,axiom,
    ( sP110(Eq_y_0,Eq_y_1)
    | ~ sP110(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_250,axiom,
    ( sP111(Eq_y_0,Eq_y_1)
    | ~ sP111(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_251,axiom,
    ( sP112(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP112(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_252,axiom,
    ( sP113(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP113(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_253,axiom,
    ( sP114(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP114(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_254,axiom,
    ( sP115(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP115(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_255,axiom,
    ( sP116(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP116(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_256,axiom,
    ( sP117(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP117(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_257,axiom,
    ( sP118(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP118(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_258,axiom,
    ( sP119(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP119(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_259,axiom,
    ( sP120(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP120(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_260,axiom,
    ( sP121(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP121(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_261,axiom,
    ( sP122(Eq_y_0,Eq_y_1)
    | ~ sP122(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_262,axiom,
    ( sP123(Eq_y_0,Eq_y_1)
    | ~ sP123(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_263,axiom,
    ( sP124(Eq_y_0,Eq_y_1)
    | ~ sP124(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_264,axiom,
    ( sP125(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP125(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_265,axiom,
    ( sP126(Eq_y_0,Eq_y_1)
    | ~ sP126(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_266,axiom,
    ( sP127(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP127(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_267,axiom,
    ( sP128(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP128(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_268,axiom,
    ( sP129(Eq_y_0,Eq_y_1)
    | ~ sP129(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_269,axiom,
    ( sP130(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP130(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_270,axiom,
    ( sP131(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP131(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_271,axiom,
    ( sP132(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP132(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_272,axiom,
    ( sP133(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP133(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_273,axiom,
    ( sP134(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP134(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_274,axiom,
    ( sP135(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP135(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_275,axiom,
    ( sP136(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP136(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_276,axiom,
    ( sP137(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP137(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_277,axiom,
    ( sP138(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP138(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_278,axiom,
    ( sP139(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP139(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_279,axiom,
    ( sP140(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP140(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_280,axiom,
    ( sP141(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP141(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_281,axiom,
    ( sP142(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP142(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_282,axiom,
    ( sP143(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP143(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_283,axiom,
    ( sP144(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP144(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_284,axiom,
    ( sP145(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP145(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_285,axiom,
    ( sP146(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP146(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_286,axiom,
    ( sP147(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP147(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_287,axiom,
    ( sP148(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP148(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_288,axiom,
    ( sP149(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP149(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_289,axiom,
    ( sP150(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP150(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_290,axiom,
    ( sP151(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP151(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_291,axiom,
    ( sP152(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP152(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_292,axiom,
    ( sP153(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP153(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_293,axiom,
    ( sP154(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP154(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_294,axiom,
    ( sP155(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP155(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_295,axiom,
    ( sP156(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP156(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_296,axiom,
    ( sP157(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP157(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_297,axiom,
    ( sP158(Eq_y_0,Eq_y_1)
    | ~ sP158(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_298,axiom,
    ( sP159(Eq_y_0,Eq_y_1)
    | ~ sP159(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_299,axiom,
    ( sP160(Eq_y_0,Eq_y_1)
    | ~ sP160(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_300,axiom,
    ( sP161(Eq_y_0,Eq_y_1)
    | ~ sP161(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_301,axiom,
    ( sP162(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP162(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_302,axiom,
    ( sP163(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP163(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_303,axiom,
    ( sP164(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP164(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_304,axiom,
    ( sP165(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP165(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_305,axiom,
    ( sP166(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP166(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_306,axiom,
    ( sP167(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP167(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_307,axiom,
    ( sP168(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP168(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_308,axiom,
    ( sP169(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP169(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_309,axiom,
    ( sP170(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP170(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_310,axiom,
    ( sP171(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP171(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_311,axiom,
    ( sP172(Eq_y_0,Eq_y_1)
    | ~ sP172(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_312,axiom,
    ( sP173(Eq_y_0,Eq_y_1)
    | ~ sP173(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_313,axiom,
    ( sP174(Eq_y_0,Eq_y_1)
    | ~ sP174(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_314,axiom,
    ( sP175(Eq_y_0,Eq_y_1)
    | ~ sP175(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_315,axiom,
    ( sP176(Eq_y_0,Eq_y_1)
    | ~ sP176(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_316,axiom,
    ( sP177(Eq_y_0,Eq_y_1)
    | ~ sP177(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_317,axiom,
    ( sP178(Eq_y_0,Eq_y_1)
    | ~ sP178(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_318,axiom,
    ( sP179(Eq_y_0,Eq_y_1)
    | ~ sP179(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_319,axiom,
    ( sP180(Eq_y_0,Eq_y_1)
    | ~ sP180(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_320,axiom,
    ( sP181(Eq_y_0,Eq_y_1)
    | ~ sP181(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_321,axiom,
    ( sP182(Eq_y_0,Eq_y_1)
    | ~ sP182(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_322,axiom,
    ( sP183(Eq_y_0,Eq_y_1)
    | ~ sP183(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_323,axiom,
    ( sP184(Eq_y_0,Eq_y_1)
    | ~ sP184(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_324,axiom,
    ( sP185(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP185(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_325,axiom,
    ( sP186(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP186(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_326,axiom,
    ( sP187(Eq_y_0,Eq_y_1)
    | ~ sP187(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_327,axiom,
    ( sP188(Eq_y_0,Eq_y_1)
    | ~ sP188(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_328,axiom,
    ( sP189(Eq_y_0,Eq_y_1)
    | ~ sP189(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_329,axiom,
    ( sP190(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP190(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_330,axiom,
    ( sP191(Eq_y_0,Eq_y_1)
    | ~ sP191(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_331,axiom,
    ( sP192(Eq_y_0,Eq_y_1)
    | ~ sP192(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_332,axiom,
    ( sP193(Eq_y_0,Eq_y_1)
    | ~ sP193(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_333,axiom,
    ( sP194(Eq_y_0,Eq_y_1)
    | ~ sP194(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_334,axiom,
    ( sP195(Eq_y_0,Eq_y_1)
    | ~ sP195(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_335,axiom,
    ( sP196(Eq_y_0,Eq_y_1)
    | ~ sP196(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_336,axiom,
    ( sP197(Eq_y_0,Eq_y_1)
    | ~ sP197(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_337,axiom,
    ( sP198(Eq_y_0,Eq_y_1)
    | ~ sP198(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_338,axiom,
    ( sP199(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP199(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_339,axiom,
    ( sP200(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP200(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_340,axiom,
    ( sP201(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP201(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_341,axiom,
    ( sP202(Eq_y_0,Eq_y_1)
    | ~ sP202(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_342,axiom,
    ( sP203(Eq_y_0,Eq_y_1)
    | ~ sP203(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_343,axiom,
    ( sP204(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP204(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_344,axiom,
    ( sP205(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP205(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_345,axiom,
    ( sP206(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP206(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_346,axiom,
    ( sP207(Eq_y_0,Eq_y_1)
    | ~ sP207(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_347,axiom,
    ( sP208(Eq_y_0,Eq_y_1)
    | ~ sP208(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_348,axiom,
    ( sP209(Eq_y_0,Eq_y_1)
    | ~ sP209(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_349,axiom,
    ( sP210(Eq_y_0,Eq_y_1)
    | ~ sP210(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_350,axiom,
    ( sP211(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP211(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_351,axiom,
    ( sP212(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP212(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_352,axiom,
    ( sP213(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP213(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_353,axiom,
    ( sP214(Eq_y_0,Eq_y_1)
    | ~ sP214(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_354,axiom,
    ( sP215(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP215(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_355,axiom,
    ( sP216(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP216(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_356,axiom,
    ( sP217(Eq_y_0,Eq_y_1)
    | ~ sP217(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_357,axiom,
    ( sP218(Eq_y_0,Eq_y_1)
    | ~ sP218(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_358,axiom,
    ( sP219(Eq_y_0,Eq_y_1)
    | ~ sP219(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_359,axiom,
    ( sP220(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP220(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_360,axiom,
    ( sP221(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP221(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_361,axiom,
    ( sP222(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP222(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_362,axiom,
    ( sP223(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP223(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_363,axiom,
    ( sP224(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP224(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_364,axiom,
    ( sP225(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP225(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_365,axiom,
    ( sP226(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP226(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_366,axiom,
    ( sP227(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP227(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_367,axiom,
    ( sP228(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP228(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_368,axiom,
    ( sP229(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP229(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_369,axiom,
    ( sP230(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP230(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_370,axiom,
    ( sP231(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP231(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_371,axiom,
    ( sP232(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP232(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_372,axiom,
    ( sP233(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP233(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_373,axiom,
    ( sP234(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP234(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_374,axiom,
    ( sP235(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP235(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_375,axiom,
    ( sP236(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP236(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_376,axiom,
    ( sP237(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP237(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_377,axiom,
    ( sP238(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP238(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_378,axiom,
    ( sP239(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP239(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_379,axiom,
    ( sP240(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP240(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_380,axiom,
    ( sP241(Eq_y_0,Eq_y_1)
    | ~ sP241(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_381,axiom,
    ( sP242(Eq_y_0,Eq_y_1)
    | ~ sP242(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_382,axiom,
    ( sP243(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP243(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_383,axiom,
    ( sP244(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP244(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_384,axiom,
    ( sP245(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP245(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_385,axiom,
    ( sP246(Eq_y_0,Eq_y_1)
    | ~ sP246(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_386,axiom,
    ( sP247(Eq_y_0,Eq_y_1)
    | ~ sP247(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_387,axiom,
    ( sP248(Eq_y_0,Eq_y_1)
    | ~ sP248(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_388,axiom,
    ( sP249(Eq_y_0,Eq_y_1)
    | ~ sP249(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_389,axiom,
    ( sP250(Eq_y_0,Eq_y_1)
    | ~ sP250(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_390,axiom,
    ( sP251(Eq_y_0,Eq_y_1)
    | ~ sP251(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_391,axiom,
    ( sP252(Eq_y_0,Eq_y_1)
    | ~ sP252(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_392,axiom,
    ( sP253(Eq_y_0,Eq_y_1)
    | ~ sP253(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_393,axiom,
    ( sP254(Eq_y_0,Eq_y_1)
    | ~ sP254(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_394,axiom,
    ( sP255(Eq_y_0,Eq_y_1)
    | ~ sP255(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_395,axiom,
    ( sP256(Eq_y_0,Eq_y_1)
    | ~ sP256(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_396,axiom,
    ( sP257(Eq_y_0,Eq_y_1)
    | ~ sP257(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_397,axiom,
    ( sP258(Eq_y_0,Eq_y_1)
    | ~ sP258(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_398,axiom,
    ( sP259(Eq_y_0,Eq_y_1)
    | ~ sP259(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_399,axiom,
    ( sP260(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP260(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_400,axiom,
    ( sP261(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP261(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_401,axiom,
    ( sP262(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP262(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_402,axiom,
    ( sP263(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP263(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_403,axiom,
    ( sP264(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP264(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_404,axiom,
    ( sP265(Eq_y_0,Eq_y_1)
    | ~ sP265(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_405,axiom,
    ( sP266(Eq_y_0,Eq_y_1)
    | ~ sP266(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_406,axiom,
    ( sP267(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP267(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_407,axiom,
    ( sP268(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP268(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_408,axiom,
    ( sP269(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP269(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_409,axiom,
    ( sP270(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP270(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_410,axiom,
    ( sP271(Eq_y_0)
    | ~ sP271(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_411,axiom,
    ( sP272(Eq_y_0,Eq_y_1)
    | ~ sP272(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_412,axiom,
    ( sP273(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP273(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_413,axiom,
    ( sP274(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP274(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_414,axiom,
    ( sP275(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP275(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_415,axiom,
    ( sP276(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP276(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_416,axiom,
    ( sP277(Eq_y_0,Eq_y_1)
    | ~ sP277(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_417,axiom,
    ( sP278(Eq_y_0,Eq_y_1)
    | ~ sP278(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_418,axiom,
    ( sP279(Eq_y_0,Eq_y_1)
    | ~ sP279(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_419,axiom,
    ( sP280(Eq_y_0,Eq_y_1)
    | ~ sP280(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_420,axiom,
    ( sP281(Eq_y_0,Eq_y_1)
    | ~ sP281(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_421,axiom,
    ( sP282(Eq_y_0,Eq_y_1)
    | ~ sP282(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_422,axiom,
    ( sP283(Eq_y_0,Eq_y_1)
    | ~ sP283(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_423,axiom,
    ( sP284(Eq_y_0,Eq_y_1)
    | ~ sP284(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_424,axiom,
    ( sP285(Eq_y_0)
    | ~ sP285(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(sat_proved,plain,
    $false,
    inference(cadical,[status(thm)],[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWW232+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03  This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04  % Command  : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.37  % Computer : n011.cluster.edu
% 0.08/0.37  % Model    : x86_64 x86_64
% 0.08/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37  % Memory   : 8046.5625MB
% 0.08/0.37  % OS       : Linux 6.8.0-71-generic
% 0.08/0.37  % CPULimit : 300
% 0.08/0.37  % WCLimit  : 300
% 0.08/0.37  % DateTime : Sun Sep 20 05:11:40 UTC 2026
% 0.08/0.37  % CPUTime  : 
% 150.25/150.52  % SZS status Theorem for theBenchmark
% 150.25/150.52  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------